1 | /* ecc.c
|
---|
2 | *
|
---|
3 | * Copyright (C) 2006-2015 wolfSSL Inc.
|
---|
4 | *
|
---|
5 | * This file is part of wolfSSL. (formerly known as CyaSSL)
|
---|
6 | *
|
---|
7 | * wolfSSL is free software; you can redistribute it and/or modify
|
---|
8 | * it under the terms of the GNU General Public License as published by
|
---|
9 | * the Free Software Foundation; either version 2 of the License, or
|
---|
10 | * (at your option) any later version.
|
---|
11 | *
|
---|
12 | * wolfSSL is distributed in the hope that it will be useful,
|
---|
13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
|
---|
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
---|
15 | * GNU General Public License for more details.
|
---|
16 | *
|
---|
17 | * You should have received a copy of the GNU General Public License
|
---|
18 | * along with this program; if not, write to the Free Software
|
---|
19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
|
---|
20 | */
|
---|
21 |
|
---|
22 |
|
---|
23 | #ifdef HAVE_CONFIG_H
|
---|
24 | #include <config.h>
|
---|
25 | #endif
|
---|
26 |
|
---|
27 | /* in case user set HAVE_ECC there */
|
---|
28 | #include <wolfssl/wolfcrypt/settings.h>
|
---|
29 |
|
---|
30 | #ifdef HAVE_ECC
|
---|
31 |
|
---|
32 | #include <wolfssl/wolfcrypt/ecc.h>
|
---|
33 | #include <wolfssl/openssl/ec.h>
|
---|
34 | #include <wolfssl/wolfcrypt/asn.h>
|
---|
35 | #include <wolfssl/wolfcrypt/error-crypt.h>
|
---|
36 |
|
---|
37 | #ifdef HAVE_ECC_ENCRYPT
|
---|
38 | #include <wolfssl/wolfcrypt/hmac.h>
|
---|
39 | #include <wolfssl/wolfcrypt/aes.h>
|
---|
40 | #endif
|
---|
41 |
|
---|
42 | #ifdef NO_INLINE
|
---|
43 | #include <wolfssl/wolfcrypt/misc.h>
|
---|
44 | #else
|
---|
45 | #include <wolfcrypt/src/misc.c>
|
---|
46 | #endif
|
---|
47 |
|
---|
48 | /* map
|
---|
49 |
|
---|
50 | ptmul -> mulmod
|
---|
51 |
|
---|
52 | */
|
---|
53 |
|
---|
54 |
|
---|
55 | /* p256 curve on by default whether user curves or not */
|
---|
56 | #if defined(HAVE_ECC112) || defined(HAVE_ALL_CURVES)
|
---|
57 | #define ECC112
|
---|
58 | #endif
|
---|
59 | #if defined(HAVE_ECC128) || defined(HAVE_ALL_CURVES)
|
---|
60 | #define ECC128
|
---|
61 | #endif
|
---|
62 | #if defined(HAVE_ECC160) || defined(HAVE_ALL_CURVES)
|
---|
63 | #define ECC160
|
---|
64 | #endif
|
---|
65 | #if defined(HAVE_ECC192) || defined(HAVE_ALL_CURVES)
|
---|
66 | #define ECC192
|
---|
67 | #endif
|
---|
68 | #if defined(HAVE_ECC224) || defined(HAVE_ALL_CURVES)
|
---|
69 | #define ECC224
|
---|
70 | #endif
|
---|
71 | #if !defined(NO_ECC256) || defined(HAVE_ALL_CURVES)
|
---|
72 | #define ECC256
|
---|
73 | #endif
|
---|
74 | #if defined(HAVE_ECC384) || defined(HAVE_ALL_CURVES)
|
---|
75 | #define ECC384
|
---|
76 | #endif
|
---|
77 | #if defined(HAVE_ECC521) || defined(HAVE_ALL_CURVES)
|
---|
78 | #define ECC521
|
---|
79 | #endif
|
---|
80 |
|
---|
81 |
|
---|
82 |
|
---|
83 | /* This holds the key settings. ***MUST*** be organized by size from
|
---|
84 | smallest to largest. */
|
---|
85 |
|
---|
86 | const ecc_set_type ecc_sets[] = {
|
---|
87 | #ifdef ECC112
|
---|
88 | {
|
---|
89 | 14,
|
---|
90 | NID_secp111r1,
|
---|
91 | "SECP112R1",
|
---|
92 | "DB7C2ABF62E35E668076BEAD208B",
|
---|
93 | "DB7C2ABF62E35E668076BEAD2088",
|
---|
94 | "659EF8BA043916EEDE8911702B22",
|
---|
95 | "DB7C2ABF62E35E7628DFAC6561C5",
|
---|
96 | "09487239995A5EE76B55F9C2F098",
|
---|
97 | "A89CE5AF8724C0A23E0E0FF77500"
|
---|
98 | },
|
---|
99 | #endif
|
---|
100 | #ifdef ECC128
|
---|
101 | {
|
---|
102 | 16,
|
---|
103 | NID_secp128r1,
|
---|
104 | "SECP128R1",
|
---|
105 | "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF",
|
---|
106 | "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC",
|
---|
107 | "E87579C11079F43DD824993C2CEE5ED3",
|
---|
108 | "FFFFFFFE0000000075A30D1B9038A115",
|
---|
109 | "161FF7528B899B2D0C28607CA52C5B86",
|
---|
110 | "CF5AC8395BAFEB13C02DA292DDED7A83",
|
---|
111 | },
|
---|
112 | #endif
|
---|
113 | #ifdef ECC160
|
---|
114 | {
|
---|
115 | 20,
|
---|
116 | NID_secp160r1,
|
---|
117 | "SECP160R1",
|
---|
118 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF",
|
---|
119 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC",
|
---|
120 | "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45",
|
---|
121 | "0100000000000000000001F4C8F927AED3CA752257",
|
---|
122 | "4A96B5688EF573284664698968C38BB913CBFC82",
|
---|
123 | "23A628553168947D59DCC912042351377AC5FB32",
|
---|
124 | },
|
---|
125 | #endif
|
---|
126 | #ifdef ECC192
|
---|
127 | {
|
---|
128 | 24,
|
---|
129 | NID_cert192,
|
---|
130 | "ECC-192",
|
---|
131 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
|
---|
132 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
|
---|
133 | "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1",
|
---|
134 | "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",
|
---|
135 | "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012",
|
---|
136 | "7192B95FFC8DA78631011ED6B24CDD573F977A11E794811",
|
---|
137 | },
|
---|
138 | #endif
|
---|
139 | #ifdef ECC224
|
---|
140 | {
|
---|
141 | 28,
|
---|
142 | NID_cert224,
|
---|
143 | "ECC-224",
|
---|
144 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
|
---|
145 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
|
---|
146 | "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
|
---|
147 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
|
---|
148 | "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
|
---|
149 | "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
|
---|
150 | },
|
---|
151 | #endif
|
---|
152 | #ifdef ECC256
|
---|
153 | {
|
---|
154 | 32,
|
---|
155 | NID_X9_62_prime256v1,
|
---|
156 | "nistp256",
|
---|
157 | "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",
|
---|
158 | "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",
|
---|
159 | "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",
|
---|
160 | "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",
|
---|
161 | "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296",
|
---|
162 | "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5",
|
---|
163 | },
|
---|
164 | #endif
|
---|
165 | #ifdef ECC384
|
---|
166 | {
|
---|
167 | 48,
|
---|
168 | NID_secp384r1,
|
---|
169 | "nistp384",
|
---|
170 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF",
|
---|
171 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC",
|
---|
172 | "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF",
|
---|
173 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973",
|
---|
174 | "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7",
|
---|
175 | "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F",
|
---|
176 | },
|
---|
177 | #endif
|
---|
178 | #ifdef ECC521
|
---|
179 | {
|
---|
180 | 66,
|
---|
181 | NID_secp521r1,
|
---|
182 | "nistp521",
|
---|
183 | "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
|
---|
184 | "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC",
|
---|
185 | "51953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00",
|
---|
186 | "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",
|
---|
187 | "C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66",
|
---|
188 | "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650",
|
---|
189 | },
|
---|
190 | #endif
|
---|
191 | {
|
---|
192 | 0, -1,
|
---|
193 | NULL, NULL, NULL, NULL, NULL, NULL, NULL
|
---|
194 | }
|
---|
195 | };
|
---|
196 |
|
---|
197 |
|
---|
198 | int ecc_map(ecc_point*, mp_int*, mp_digit*);
|
---|
199 | int ecc_projective_add_point(ecc_point* P, ecc_point* Q, ecc_point* R,
|
---|
200 | mp_int* modulus, mp_digit* mp);
|
---|
201 | int ecc_projective_dbl_point(ecc_point* P, ecc_point* R, mp_int* modulus,
|
---|
202 | mp_digit* mp);
|
---|
203 | static int ecc_check_pubkey_order(ecc_key* key, mp_int* prime, mp_int* order);
|
---|
204 | #ifdef ECC_SHAMIR
|
---|
205 | static int ecc_mul2add(ecc_point* A, mp_int* kA, ecc_point* B, mp_int* kB,
|
---|
206 | ecc_point* C, mp_int* modulus);
|
---|
207 | #endif
|
---|
208 |
|
---|
209 | int mp_jacobi(mp_int* a, mp_int* p, int* c);
|
---|
210 | int mp_sqrtmod_prime(mp_int* n, mp_int* prime, mp_int* ret);
|
---|
211 | int mp_submod(mp_int* a, mp_int* b, mp_int* c, mp_int* d);
|
---|
212 |
|
---|
213 | #ifdef HAVE_COMP_KEY
|
---|
214 | static int wc_ecc_export_x963_compressed(ecc_key*, byte* out, word32* outLen);
|
---|
215 | #endif
|
---|
216 |
|
---|
217 | /* helper for either lib */
|
---|
218 | static int get_digit_count(mp_int* a)
|
---|
219 | {
|
---|
220 | if (a == NULL)
|
---|
221 | return 0;
|
---|
222 |
|
---|
223 | return a->used;
|
---|
224 | }
|
---|
225 |
|
---|
226 | /* helper for either lib */
|
---|
227 | static mp_digit get_digit(mp_int* a, int n)
|
---|
228 | {
|
---|
229 | if (a == NULL)
|
---|
230 | return 0;
|
---|
231 |
|
---|
232 | return (n >= a->used || n < 0) ? 0 : a->dp[n];
|
---|
233 | }
|
---|
234 |
|
---|
235 |
|
---|
236 | #if defined(USE_FAST_MATH)
|
---|
237 |
|
---|
238 | /* fast math accelerated version, but not for fp ecc yet */
|
---|
239 |
|
---|
240 | /**
|
---|
241 | Add two ECC points
|
---|
242 | P The point to add
|
---|
243 | Q The point to add
|
---|
244 | R [out] The destination of the double
|
---|
245 | modulus The modulus of the field the ECC curve is in
|
---|
246 | mp The "b" value from montgomery_setup()
|
---|
247 | return MP_OKAY on success
|
---|
248 | */
|
---|
249 | int ecc_projective_add_point(ecc_point *P, ecc_point *Q, ecc_point *R,
|
---|
250 | mp_int* modulus, mp_digit* mp)
|
---|
251 | {
|
---|
252 | fp_int t1, t2, x, y, z;
|
---|
253 | int err;
|
---|
254 |
|
---|
255 | if (P == NULL || Q == NULL || R == NULL || modulus == NULL || mp == NULL)
|
---|
256 | return ECC_BAD_ARG_E;
|
---|
257 |
|
---|
258 | if ((err = mp_init_multi(&t1, &t2, &x, &y, &z, NULL)) != MP_OKAY) {
|
---|
259 | return err;
|
---|
260 | }
|
---|
261 |
|
---|
262 | /* should we dbl instead? */
|
---|
263 | fp_sub(modulus, Q->y, &t1);
|
---|
264 | if ( (fp_cmp(P->x, Q->x) == FP_EQ) &&
|
---|
265 | (get_digit_count(Q->z) && fp_cmp(P->z, Q->z) == FP_EQ) &&
|
---|
266 | (fp_cmp(P->y, Q->y) == FP_EQ || fp_cmp(P->y, &t1) == FP_EQ)) {
|
---|
267 | return ecc_projective_dbl_point(P, R, modulus, mp);
|
---|
268 | }
|
---|
269 |
|
---|
270 | fp_copy(P->x, &x);
|
---|
271 | fp_copy(P->y, &y);
|
---|
272 | fp_copy(P->z, &z);
|
---|
273 |
|
---|
274 | /* if Z is one then these are no-operations */
|
---|
275 | if (get_digit_count(Q->z)) {
|
---|
276 | /* T1 = Z' * Z' */
|
---|
277 | fp_sqr(Q->z, &t1);
|
---|
278 | fp_montgomery_reduce(&t1, modulus, *mp);
|
---|
279 | /* X = X * T1 */
|
---|
280 | fp_mul(&t1, &x, &x);
|
---|
281 | fp_montgomery_reduce(&x, modulus, *mp);
|
---|
282 | /* T1 = Z' * T1 */
|
---|
283 | fp_mul(Q->z, &t1, &t1);
|
---|
284 | fp_montgomery_reduce(&t1, modulus, *mp);
|
---|
285 | /* Y = Y * T1 */
|
---|
286 | fp_mul(&t1, &y, &y);
|
---|
287 | fp_montgomery_reduce(&y, modulus, *mp);
|
---|
288 | }
|
---|
289 |
|
---|
290 | /* T1 = Z*Z */
|
---|
291 | fp_sqr(&z, &t1);
|
---|
292 | fp_montgomery_reduce(&t1, modulus, *mp);
|
---|
293 | /* T2 = X' * T1 */
|
---|
294 | fp_mul(Q->x, &t1, &t2);
|
---|
295 | fp_montgomery_reduce(&t2, modulus, *mp);
|
---|
296 | /* T1 = Z * T1 */
|
---|
297 | fp_mul(&z, &t1, &t1);
|
---|
298 | fp_montgomery_reduce(&t1, modulus, *mp);
|
---|
299 | /* T1 = Y' * T1 */
|
---|
300 | fp_mul(Q->y, &t1, &t1);
|
---|
301 | fp_montgomery_reduce(&t1, modulus, *mp);
|
---|
302 |
|
---|
303 | /* Y = Y - T1 */
|
---|
304 | fp_sub(&y, &t1, &y);
|
---|
305 | if (fp_cmp_d(&y, 0) == FP_LT) {
|
---|
306 | fp_add(&y, modulus, &y);
|
---|
307 | }
|
---|
308 | /* T1 = 2T1 */
|
---|
309 | fp_add(&t1, &t1, &t1);
|
---|
310 | if (fp_cmp(&t1, modulus) != FP_LT) {
|
---|
311 | fp_sub(&t1, modulus, &t1);
|
---|
312 | }
|
---|
313 | /* T1 = Y + T1 */
|
---|
314 | fp_add(&t1, &y, &t1);
|
---|
315 | if (fp_cmp(&t1, modulus) != FP_LT) {
|
---|
316 | fp_sub(&t1, modulus, &t1);
|
---|
317 | }
|
---|
318 | /* X = X - T2 */
|
---|
319 | fp_sub(&x, &t2, &x);
|
---|
320 | if (fp_cmp_d(&x, 0) == FP_LT) {
|
---|
321 | fp_add(&x, modulus, &x);
|
---|
322 | }
|
---|
323 | /* T2 = 2T2 */
|
---|
324 | fp_add(&t2, &t2, &t2);
|
---|
325 | if (fp_cmp(&t2, modulus) != FP_LT) {
|
---|
326 | fp_sub(&t2, modulus, &t2);
|
---|
327 | }
|
---|
328 | /* T2 = X + T2 */
|
---|
329 | fp_add(&t2, &x, &t2);
|
---|
330 | if (fp_cmp(&t2, modulus) != FP_LT) {
|
---|
331 | fp_sub(&t2, modulus, &t2);
|
---|
332 | }
|
---|
333 |
|
---|
334 | /* if Z' != 1 */
|
---|
335 | if (get_digit_count(Q->z)) {
|
---|
336 | /* Z = Z * Z' */
|
---|
337 | fp_mul(&z, Q->z, &z);
|
---|
338 | fp_montgomery_reduce(&z, modulus, *mp);
|
---|
339 | }
|
---|
340 |
|
---|
341 | /* Z = Z * X */
|
---|
342 | fp_mul(&z, &x, &z);
|
---|
343 | fp_montgomery_reduce(&z, modulus, *mp);
|
---|
344 |
|
---|
345 | /* T1 = T1 * X */
|
---|
346 | fp_mul(&t1, &x, &t1);
|
---|
347 | fp_montgomery_reduce(&t1, modulus, *mp);
|
---|
348 | /* X = X * X */
|
---|
349 | fp_sqr(&x, &x);
|
---|
350 | fp_montgomery_reduce(&x, modulus, *mp);
|
---|
351 | /* T2 = T2 * x */
|
---|
352 | fp_mul(&t2, &x, &t2);
|
---|
353 | fp_montgomery_reduce(&t2, modulus, *mp);
|
---|
354 | /* T1 = T1 * X */
|
---|
355 | fp_mul(&t1, &x, &t1);
|
---|
356 | fp_montgomery_reduce(&t1, modulus, *mp);
|
---|
357 |
|
---|
358 | /* X = Y*Y */
|
---|
359 | fp_sqr(&y, &x);
|
---|
360 | fp_montgomery_reduce(&x, modulus, *mp);
|
---|
361 | /* X = X - T2 */
|
---|
362 | fp_sub(&x, &t2, &x);
|
---|
363 | if (fp_cmp_d(&x, 0) == FP_LT) {
|
---|
364 | fp_add(&x, modulus, &x);
|
---|
365 | }
|
---|
366 |
|
---|
367 | /* T2 = T2 - X */
|
---|
368 | fp_sub(&t2, &x, &t2);
|
---|
369 | if (fp_cmp_d(&t2, 0) == FP_LT) {
|
---|
370 | fp_add(&t2, modulus, &t2);
|
---|
371 | }
|
---|
372 | /* T2 = T2 - X */
|
---|
373 | fp_sub(&t2, &x, &t2);
|
---|
374 | if (fp_cmp_d(&t2, 0) == FP_LT) {
|
---|
375 | fp_add(&t2, modulus, &t2);
|
---|
376 | }
|
---|
377 | /* T2 = T2 * Y */
|
---|
378 | fp_mul(&t2, &y, &t2);
|
---|
379 | fp_montgomery_reduce(&t2, modulus, *mp);
|
---|
380 | /* Y = T2 - T1 */
|
---|
381 | fp_sub(&t2, &t1, &y);
|
---|
382 | if (fp_cmp_d(&y, 0) == FP_LT) {
|
---|
383 | fp_add(&y, modulus, &y);
|
---|
384 | }
|
---|
385 | /* Y = Y/2 */
|
---|
386 | if (fp_isodd(&y)) {
|
---|
387 | fp_add(&y, modulus, &y);
|
---|
388 | }
|
---|
389 | fp_div_2(&y, &y);
|
---|
390 |
|
---|
391 | fp_copy(&x, R->x);
|
---|
392 | fp_copy(&y, R->y);
|
---|
393 | fp_copy(&z, R->z);
|
---|
394 |
|
---|
395 | return MP_OKAY;
|
---|
396 | }
|
---|
397 |
|
---|
398 |
|
---|
399 | /**
|
---|
400 | Double an ECC point
|
---|
401 | P The point to double
|
---|
402 | R [out] The destination of the double
|
---|
403 | modulus The modulus of the field the ECC curve is in
|
---|
404 | mp The "b" value from montgomery_setup()
|
---|
405 | return MP_OKAY on success
|
---|
406 | */
|
---|
407 | int ecc_projective_dbl_point(ecc_point *P, ecc_point *R, mp_int* modulus,
|
---|
408 | mp_digit* mp)
|
---|
409 | {
|
---|
410 | fp_int t1, t2;
|
---|
411 | int err;
|
---|
412 |
|
---|
413 | if (P == NULL || R == NULL || modulus == NULL || mp == NULL)
|
---|
414 | return ECC_BAD_ARG_E;
|
---|
415 |
|
---|
416 | if (P != R) {
|
---|
417 | fp_copy(P->x, R->x);
|
---|
418 | fp_copy(P->y, R->y);
|
---|
419 | fp_copy(P->z, R->z);
|
---|
420 | }
|
---|
421 |
|
---|
422 | if ((err = mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
|
---|
423 | return err;
|
---|
424 | }
|
---|
425 |
|
---|
426 | /* t1 = Z * Z */
|
---|
427 | fp_sqr(R->z, &t1);
|
---|
428 | fp_montgomery_reduce(&t1, modulus, *mp);
|
---|
429 | /* Z = Y * Z */
|
---|
430 | fp_mul(R->z, R->y, R->z);
|
---|
431 | fp_montgomery_reduce(R->z, modulus, *mp);
|
---|
432 | /* Z = 2Z */
|
---|
433 | fp_add(R->z, R->z, R->z);
|
---|
434 | if (fp_cmp(R->z, modulus) != FP_LT) {
|
---|
435 | fp_sub(R->z, modulus, R->z);
|
---|
436 | }
|
---|
437 |
|
---|
438 | /* &t2 = X - T1 */
|
---|
439 | fp_sub(R->x, &t1, &t2);
|
---|
440 | if (fp_cmp_d(&t2, 0) == FP_LT) {
|
---|
441 | fp_add(&t2, modulus, &t2);
|
---|
442 | }
|
---|
443 | /* T1 = X + T1 */
|
---|
444 | fp_add(&t1, R->x, &t1);
|
---|
445 | if (fp_cmp(&t1, modulus) != FP_LT) {
|
---|
446 | fp_sub(&t1, modulus, &t1);
|
---|
447 | }
|
---|
448 | /* T2 = T1 * T2 */
|
---|
449 | fp_mul(&t1, &t2, &t2);
|
---|
450 | fp_montgomery_reduce(&t2, modulus, *mp);
|
---|
451 | /* T1 = 2T2 */
|
---|
452 | fp_add(&t2, &t2, &t1);
|
---|
453 | if (fp_cmp(&t1, modulus) != FP_LT) {
|
---|
454 | fp_sub(&t1, modulus, &t1);
|
---|
455 | }
|
---|
456 | /* T1 = T1 + T2 */
|
---|
457 | fp_add(&t1, &t2, &t1);
|
---|
458 | if (fp_cmp(&t1, modulus) != FP_LT) {
|
---|
459 | fp_sub(&t1, modulus, &t1);
|
---|
460 | }
|
---|
461 |
|
---|
462 | /* Y = 2Y */
|
---|
463 | fp_add(R->y, R->y, R->y);
|
---|
464 | if (fp_cmp(R->y, modulus) != FP_LT) {
|
---|
465 | fp_sub(R->y, modulus, R->y);
|
---|
466 | }
|
---|
467 | /* Y = Y * Y */
|
---|
468 | fp_sqr(R->y, R->y);
|
---|
469 | fp_montgomery_reduce(R->y, modulus, *mp);
|
---|
470 | /* T2 = Y * Y */
|
---|
471 | fp_sqr(R->y, &t2);
|
---|
472 | fp_montgomery_reduce(&t2, modulus, *mp);
|
---|
473 | /* T2 = T2/2 */
|
---|
474 | if (fp_isodd(&t2)) {
|
---|
475 | fp_add(&t2, modulus, &t2);
|
---|
476 | }
|
---|
477 | fp_div_2(&t2, &t2);
|
---|
478 | /* Y = Y * X */
|
---|
479 | fp_mul(R->y, R->x, R->y);
|
---|
480 | fp_montgomery_reduce(R->y, modulus, *mp);
|
---|
481 |
|
---|
482 | /* X = T1 * T1 */
|
---|
483 | fp_sqr(&t1, R->x);
|
---|
484 | fp_montgomery_reduce(R->x, modulus, *mp);
|
---|
485 | /* X = X - Y */
|
---|
486 | fp_sub(R->x, R->y, R->x);
|
---|
487 | if (fp_cmp_d(R->x, 0) == FP_LT) {
|
---|
488 | fp_add(R->x, modulus, R->x);
|
---|
489 | }
|
---|
490 | /* X = X - Y */
|
---|
491 | fp_sub(R->x, R->y, R->x);
|
---|
492 | if (fp_cmp_d(R->x, 0) == FP_LT) {
|
---|
493 | fp_add(R->x, modulus, R->x);
|
---|
494 | }
|
---|
495 |
|
---|
496 | /* Y = Y - X */
|
---|
497 | fp_sub(R->y, R->x, R->y);
|
---|
498 | if (fp_cmp_d(R->y, 0) == FP_LT) {
|
---|
499 | fp_add(R->y, modulus, R->y);
|
---|
500 | }
|
---|
501 | /* Y = Y * T1 */
|
---|
502 | fp_mul(R->y, &t1, R->y);
|
---|
503 | fp_montgomery_reduce(R->y, modulus, *mp);
|
---|
504 | /* Y = Y - T2 */
|
---|
505 | fp_sub(R->y, &t2, R->y);
|
---|
506 | if (fp_cmp_d(R->y, 0) == FP_LT) {
|
---|
507 | fp_add(R->y, modulus, R->y);
|
---|
508 | }
|
---|
509 |
|
---|
510 | return MP_OKAY;
|
---|
511 | }
|
---|
512 |
|
---|
513 | #else /* USE_FAST_MATH */
|
---|
514 |
|
---|
515 | /**
|
---|
516 | Add two ECC points
|
---|
517 | P The point to add
|
---|
518 | Q The point to add
|
---|
519 | R [out] The destination of the double
|
---|
520 | modulus The modulus of the field the ECC curve is in
|
---|
521 | mp The "b" value from montgomery_setup()
|
---|
522 | return MP_OKAY on success
|
---|
523 | */
|
---|
524 | int ecc_projective_add_point(ecc_point* P, ecc_point* Q, ecc_point* R,
|
---|
525 | mp_int* modulus, mp_digit* mp)
|
---|
526 | {
|
---|
527 | mp_int t1;
|
---|
528 | mp_int t2;
|
---|
529 | mp_int x;
|
---|
530 | mp_int y;
|
---|
531 | mp_int z;
|
---|
532 | int err;
|
---|
533 |
|
---|
534 | if (P == NULL || Q == NULL || R == NULL || modulus == NULL || mp == NULL)
|
---|
535 | return ECC_BAD_ARG_E;
|
---|
536 |
|
---|
537 | if ((err = mp_init_multi(&t1, &t2, &x, &y, &z, NULL)) != MP_OKAY) {
|
---|
538 | return err;
|
---|
539 | }
|
---|
540 |
|
---|
541 | /* should we dbl instead? */
|
---|
542 | err = mp_sub(modulus, Q->y, &t1);
|
---|
543 |
|
---|
544 | if (err == MP_OKAY) {
|
---|
545 | if ( (mp_cmp(P->x, Q->x) == MP_EQ) &&
|
---|
546 | (get_digit_count(Q->z) && mp_cmp(P->z, Q->z) == MP_EQ) &&
|
---|
547 | (mp_cmp(P->y, Q->y) == MP_EQ || mp_cmp(P->y, &t1) == MP_EQ)) {
|
---|
548 | mp_clear(&t1);
|
---|
549 | mp_clear(&t2);
|
---|
550 | mp_clear(&x);
|
---|
551 | mp_clear(&y);
|
---|
552 | mp_clear(&z);
|
---|
553 |
|
---|
554 | return ecc_projective_dbl_point(P, R, modulus, mp);
|
---|
555 | }
|
---|
556 | }
|
---|
557 |
|
---|
558 | if (err == MP_OKAY)
|
---|
559 | err = mp_copy(P->x, &x);
|
---|
560 | if (err == MP_OKAY)
|
---|
561 | err = mp_copy(P->y, &y);
|
---|
562 | if (err == MP_OKAY)
|
---|
563 | err = mp_copy(P->z, &z);
|
---|
564 |
|
---|
565 | /* if Z is one then these are no-operations */
|
---|
566 | if (err == MP_OKAY) {
|
---|
567 | if (get_digit_count(Q->z)) {
|
---|
568 | /* T1 = Z' * Z' */
|
---|
569 | err = mp_sqr(Q->z, &t1);
|
---|
570 | if (err == MP_OKAY)
|
---|
571 | err = mp_montgomery_reduce(&t1, modulus, *mp);
|
---|
572 |
|
---|
573 | /* X = X * T1 */
|
---|
574 | if (err == MP_OKAY)
|
---|
575 | err = mp_mul(&t1, &x, &x);
|
---|
576 | if (err == MP_OKAY)
|
---|
577 | err = mp_montgomery_reduce(&x, modulus, *mp);
|
---|
578 |
|
---|
579 | /* T1 = Z' * T1 */
|
---|
580 | if (err == MP_OKAY)
|
---|
581 | err = mp_mul(Q->z, &t1, &t1);
|
---|
582 | if (err == MP_OKAY)
|
---|
583 | err = mp_montgomery_reduce(&t1, modulus, *mp);
|
---|
584 |
|
---|
585 | /* Y = Y * T1 */
|
---|
586 | if (err == MP_OKAY)
|
---|
587 | err = mp_mul(&t1, &y, &y);
|
---|
588 | if (err == MP_OKAY)
|
---|
589 | err = mp_montgomery_reduce(&y, modulus, *mp);
|
---|
590 | }
|
---|
591 | }
|
---|
592 |
|
---|
593 | /* T1 = Z*Z */
|
---|
594 | if (err == MP_OKAY)
|
---|
595 | err = mp_sqr(&z, &t1);
|
---|
596 | if (err == MP_OKAY)
|
---|
597 | err = mp_montgomery_reduce(&t1, modulus, *mp);
|
---|
598 |
|
---|
599 | /* T2 = X' * T1 */
|
---|
600 | if (err == MP_OKAY)
|
---|
601 | err = mp_mul(Q->x, &t1, &t2);
|
---|
602 | if (err == MP_OKAY)
|
---|
603 | err = mp_montgomery_reduce(&t2, modulus, *mp);
|
---|
604 |
|
---|
605 | /* T1 = Z * T1 */
|
---|
606 | if (err == MP_OKAY)
|
---|
607 | err = mp_mul(&z, &t1, &t1);
|
---|
608 | if (err == MP_OKAY)
|
---|
609 | err = mp_montgomery_reduce(&t1, modulus, *mp);
|
---|
610 |
|
---|
611 | /* T1 = Y' * T1 */
|
---|
612 | if (err == MP_OKAY)
|
---|
613 | err = mp_mul(Q->y, &t1, &t1);
|
---|
614 | if (err == MP_OKAY)
|
---|
615 | err = mp_montgomery_reduce(&t1, modulus, *mp);
|
---|
616 |
|
---|
617 | /* Y = Y - T1 */
|
---|
618 | if (err == MP_OKAY)
|
---|
619 | err = mp_sub(&y, &t1, &y);
|
---|
620 | if (err == MP_OKAY) {
|
---|
621 | if (mp_cmp_d(&y, 0) == MP_LT)
|
---|
622 | err = mp_add(&y, modulus, &y);
|
---|
623 | }
|
---|
624 | /* T1 = 2T1 */
|
---|
625 | if (err == MP_OKAY)
|
---|
626 | err = mp_add(&t1, &t1, &t1);
|
---|
627 | if (err == MP_OKAY) {
|
---|
628 | if (mp_cmp(&t1, modulus) != MP_LT)
|
---|
629 | err = mp_sub(&t1, modulus, &t1);
|
---|
630 | }
|
---|
631 | /* T1 = Y + T1 */
|
---|
632 | if (err == MP_OKAY)
|
---|
633 | err = mp_add(&t1, &y, &t1);
|
---|
634 | if (err == MP_OKAY) {
|
---|
635 | if (mp_cmp(&t1, modulus) != MP_LT)
|
---|
636 | err = mp_sub(&t1, modulus, &t1);
|
---|
637 | }
|
---|
638 | /* X = X - T2 */
|
---|
639 | if (err == MP_OKAY)
|
---|
640 | err = mp_sub(&x, &t2, &x);
|
---|
641 | if (err == MP_OKAY) {
|
---|
642 | if (mp_cmp_d(&x, 0) == MP_LT)
|
---|
643 | err = mp_add(&x, modulus, &x);
|
---|
644 | }
|
---|
645 | /* T2 = 2T2 */
|
---|
646 | if (err == MP_OKAY)
|
---|
647 | err = mp_add(&t2, &t2, &t2);
|
---|
648 | if (err == MP_OKAY) {
|
---|
649 | if (mp_cmp(&t2, modulus) != MP_LT)
|
---|
650 | err = mp_sub(&t2, modulus, &t2);
|
---|
651 | }
|
---|
652 | /* T2 = X + T2 */
|
---|
653 | if (err == MP_OKAY)
|
---|
654 | err = mp_add(&t2, &x, &t2);
|
---|
655 | if (err == MP_OKAY) {
|
---|
656 | if (mp_cmp(&t2, modulus) != MP_LT)
|
---|
657 | err = mp_sub(&t2, modulus, &t2);
|
---|
658 | }
|
---|
659 |
|
---|
660 | if (err == MP_OKAY) {
|
---|
661 | if (get_digit_count(Q->z)) {
|
---|
662 | /* Z = Z * Z' */
|
---|
663 | err = mp_mul(&z, Q->z, &z);
|
---|
664 | if (err == MP_OKAY)
|
---|
665 | err = mp_montgomery_reduce(&z, modulus, *mp);
|
---|
666 | }
|
---|
667 | }
|
---|
668 |
|
---|
669 | /* Z = Z * X */
|
---|
670 | if (err == MP_OKAY)
|
---|
671 | err = mp_mul(&z, &x, &z);
|
---|
672 | if (err == MP_OKAY)
|
---|
673 | err = mp_montgomery_reduce(&z, modulus, *mp);
|
---|
674 |
|
---|
675 | /* T1 = T1 * X */
|
---|
676 | if (err == MP_OKAY)
|
---|
677 | err = mp_mul(&t1, &x, &t1);
|
---|
678 | if (err == MP_OKAY)
|
---|
679 | err = mp_montgomery_reduce(&t1, modulus, *mp);
|
---|
680 |
|
---|
681 | /* X = X * X */
|
---|
682 | if (err == MP_OKAY)
|
---|
683 | err = mp_sqr(&x, &x);
|
---|
684 | if (err == MP_OKAY)
|
---|
685 | err = mp_montgomery_reduce(&x, modulus, *mp);
|
---|
686 |
|
---|
687 | /* T2 = T2 * x */
|
---|
688 | if (err == MP_OKAY)
|
---|
689 | err = mp_mul(&t2, &x, &t2);
|
---|
690 | if (err == MP_OKAY)
|
---|
691 | err = mp_montgomery_reduce(&t2, modulus, *mp);
|
---|
692 |
|
---|
693 | /* T1 = T1 * X */
|
---|
694 | if (err == MP_OKAY)
|
---|
695 | err = mp_mul(&t1, &x, &t1);
|
---|
696 | if (err == MP_OKAY)
|
---|
697 | err = mp_montgomery_reduce(&t1, modulus, *mp);
|
---|
698 |
|
---|
699 | /* X = Y*Y */
|
---|
700 | if (err == MP_OKAY)
|
---|
701 | err = mp_sqr(&y, &x);
|
---|
702 | if (err == MP_OKAY)
|
---|
703 | err = mp_montgomery_reduce(&x, modulus, *mp);
|
---|
704 |
|
---|
705 | /* X = X - T2 */
|
---|
706 | if (err == MP_OKAY)
|
---|
707 | err = mp_sub(&x, &t2, &x);
|
---|
708 | if (err == MP_OKAY) {
|
---|
709 | if (mp_cmp_d(&x, 0) == MP_LT)
|
---|
710 | err = mp_add(&x, modulus, &x);
|
---|
711 | }
|
---|
712 | /* T2 = T2 - X */
|
---|
713 | if (err == MP_OKAY)
|
---|
714 | err = mp_sub(&t2, &x, &t2);
|
---|
715 | if (err == MP_OKAY) {
|
---|
716 | if (mp_cmp_d(&t2, 0) == MP_LT)
|
---|
717 | err = mp_add(&t2, modulus, &t2);
|
---|
718 | }
|
---|
719 | /* T2 = T2 - X */
|
---|
720 | if (err == MP_OKAY)
|
---|
721 | err = mp_sub(&t2, &x, &t2);
|
---|
722 | if (err == MP_OKAY) {
|
---|
723 | if (mp_cmp_d(&t2, 0) == MP_LT)
|
---|
724 | err = mp_add(&t2, modulus, &t2);
|
---|
725 | }
|
---|
726 | /* T2 = T2 * Y */
|
---|
727 | if (err == MP_OKAY)
|
---|
728 | err = mp_mul(&t2, &y, &t2);
|
---|
729 | if (err == MP_OKAY)
|
---|
730 | err = mp_montgomery_reduce(&t2, modulus, *mp);
|
---|
731 |
|
---|
732 | /* Y = T2 - T1 */
|
---|
733 | if (err == MP_OKAY)
|
---|
734 | err = mp_sub(&t2, &t1, &y);
|
---|
735 | if (err == MP_OKAY) {
|
---|
736 | if (mp_cmp_d(&y, 0) == MP_LT)
|
---|
737 | err = mp_add(&y, modulus, &y);
|
---|
738 | }
|
---|
739 | /* Y = Y/2 */
|
---|
740 | if (err == MP_OKAY) {
|
---|
741 | if (mp_isodd(&y))
|
---|
742 | err = mp_add(&y, modulus, &y);
|
---|
743 | }
|
---|
744 | if (err == MP_OKAY)
|
---|
745 | err = mp_div_2(&y, &y);
|
---|
746 |
|
---|
747 | if (err == MP_OKAY)
|
---|
748 | err = mp_copy(&x, R->x);
|
---|
749 | if (err == MP_OKAY)
|
---|
750 | err = mp_copy(&y, R->y);
|
---|
751 | if (err == MP_OKAY)
|
---|
752 | err = mp_copy(&z, R->z);
|
---|
753 |
|
---|
754 | /* clean up */
|
---|
755 | mp_clear(&t1);
|
---|
756 | mp_clear(&t2);
|
---|
757 | mp_clear(&x);
|
---|
758 | mp_clear(&y);
|
---|
759 | mp_clear(&z);
|
---|
760 |
|
---|
761 | return err;
|
---|
762 | }
|
---|
763 |
|
---|
764 |
|
---|
765 | /**
|
---|
766 | Double an ECC point
|
---|
767 | P The point to double
|
---|
768 | R [out] The destination of the double
|
---|
769 | modulus The modulus of the field the ECC curve is in
|
---|
770 | mp The "b" value from montgomery_setup()
|
---|
771 | return MP_OKAY on success
|
---|
772 | */
|
---|
773 | int ecc_projective_dbl_point(ecc_point *P, ecc_point *R, mp_int* modulus,
|
---|
774 | mp_digit* mp)
|
---|
775 | {
|
---|
776 | mp_int t1;
|
---|
777 | mp_int t2;
|
---|
778 | int err;
|
---|
779 |
|
---|
780 | if (P == NULL || R == NULL || modulus == NULL || mp == NULL)
|
---|
781 | return ECC_BAD_ARG_E;
|
---|
782 |
|
---|
783 | if ((err = mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
|
---|
784 | return err;
|
---|
785 | }
|
---|
786 |
|
---|
787 | if (P != R) {
|
---|
788 | err = mp_copy(P->x, R->x);
|
---|
789 | if (err == MP_OKAY)
|
---|
790 | err = mp_copy(P->y, R->y);
|
---|
791 | if (err == MP_OKAY)
|
---|
792 | err = mp_copy(P->z, R->z);
|
---|
793 | }
|
---|
794 |
|
---|
795 | /* t1 = Z * Z */
|
---|
796 | if (err == MP_OKAY)
|
---|
797 | err = mp_sqr(R->z, &t1);
|
---|
798 | if (err == MP_OKAY)
|
---|
799 | err = mp_montgomery_reduce(&t1, modulus, *mp);
|
---|
800 |
|
---|
801 | /* Z = Y * Z */
|
---|
802 | if (err == MP_OKAY)
|
---|
803 | err = mp_mul(R->z, R->y, R->z);
|
---|
804 | if (err == MP_OKAY)
|
---|
805 | err = mp_montgomery_reduce(R->z, modulus, *mp);
|
---|
806 |
|
---|
807 | /* Z = 2Z */
|
---|
808 | if (err == MP_OKAY)
|
---|
809 | err = mp_add(R->z, R->z, R->z);
|
---|
810 | if (err == MP_OKAY) {
|
---|
811 | if (mp_cmp(R->z, modulus) != MP_LT)
|
---|
812 | err = mp_sub(R->z, modulus, R->z);
|
---|
813 | }
|
---|
814 |
|
---|
815 | /* T2 = X - T1 */
|
---|
816 | if (err == MP_OKAY)
|
---|
817 | err = mp_sub(R->x, &t1, &t2);
|
---|
818 | if (err == MP_OKAY) {
|
---|
819 | if (mp_cmp_d(&t2, 0) == MP_LT)
|
---|
820 | err = mp_add(&t2, modulus, &t2);
|
---|
821 | }
|
---|
822 | /* T1 = X + T1 */
|
---|
823 | if (err == MP_OKAY)
|
---|
824 | err = mp_add(&t1, R->x, &t1);
|
---|
825 | if (err == MP_OKAY) {
|
---|
826 | if (mp_cmp(&t1, modulus) != MP_LT)
|
---|
827 | err = mp_sub(&t1, modulus, &t1);
|
---|
828 | }
|
---|
829 | /* T2 = T1 * T2 */
|
---|
830 | if (err == MP_OKAY)
|
---|
831 | err = mp_mul(&t1, &t2, &t2);
|
---|
832 | if (err == MP_OKAY)
|
---|
833 | err = mp_montgomery_reduce(&t2, modulus, *mp);
|
---|
834 |
|
---|
835 | /* T1 = 2T2 */
|
---|
836 | if (err == MP_OKAY)
|
---|
837 | err = mp_add(&t2, &t2, &t1);
|
---|
838 | if (err == MP_OKAY) {
|
---|
839 | if (mp_cmp(&t1, modulus) != MP_LT)
|
---|
840 | err = mp_sub(&t1, modulus, &t1);
|
---|
841 | }
|
---|
842 | /* T1 = T1 + T2 */
|
---|
843 | if (err == MP_OKAY)
|
---|
844 | err = mp_add(&t1, &t2, &t1);
|
---|
845 | if (err == MP_OKAY) {
|
---|
846 | if (mp_cmp(&t1, modulus) != MP_LT)
|
---|
847 | err = mp_sub(&t1, modulus, &t1);
|
---|
848 | }
|
---|
849 | /* Y = 2Y */
|
---|
850 | if (err == MP_OKAY)
|
---|
851 | err = mp_add(R->y, R->y, R->y);
|
---|
852 | if (err == MP_OKAY) {
|
---|
853 | if (mp_cmp(R->y, modulus) != MP_LT)
|
---|
854 | err = mp_sub(R->y, modulus, R->y);
|
---|
855 | }
|
---|
856 | /* Y = Y * Y */
|
---|
857 | if (err == MP_OKAY)
|
---|
858 | err = mp_sqr(R->y, R->y);
|
---|
859 | if (err == MP_OKAY)
|
---|
860 | err = mp_montgomery_reduce(R->y, modulus, *mp);
|
---|
861 |
|
---|
862 | /* T2 = Y * Y */
|
---|
863 | if (err == MP_OKAY)
|
---|
864 | err = mp_sqr(R->y, &t2);
|
---|
865 | if (err == MP_OKAY)
|
---|
866 | err = mp_montgomery_reduce(&t2, modulus, *mp);
|
---|
867 |
|
---|
868 | /* T2 = T2/2 */
|
---|
869 | if (err == MP_OKAY) {
|
---|
870 | if (mp_isodd(&t2))
|
---|
871 | err = mp_add(&t2, modulus, &t2);
|
---|
872 | }
|
---|
873 | if (err == MP_OKAY)
|
---|
874 | err = mp_div_2(&t2, &t2);
|
---|
875 |
|
---|
876 | /* Y = Y * X */
|
---|
877 | if (err == MP_OKAY)
|
---|
878 | err = mp_mul(R->y, R->x, R->y);
|
---|
879 | if (err == MP_OKAY)
|
---|
880 | err = mp_montgomery_reduce(R->y, modulus, *mp);
|
---|
881 |
|
---|
882 | /* X = T1 * T1 */
|
---|
883 | if (err == MP_OKAY)
|
---|
884 | err = mp_sqr(&t1, R->x);
|
---|
885 | if (err == MP_OKAY)
|
---|
886 | err = mp_montgomery_reduce(R->x, modulus, *mp);
|
---|
887 |
|
---|
888 | /* X = X - Y */
|
---|
889 | if (err == MP_OKAY)
|
---|
890 | err = mp_sub(R->x, R->y, R->x);
|
---|
891 | if (err == MP_OKAY) {
|
---|
892 | if (mp_cmp_d(R->x, 0) == MP_LT)
|
---|
893 | err = mp_add(R->x, modulus, R->x);
|
---|
894 | }
|
---|
895 | /* X = X - Y */
|
---|
896 | if (err == MP_OKAY)
|
---|
897 | err = mp_sub(R->x, R->y, R->x);
|
---|
898 | if (err == MP_OKAY) {
|
---|
899 | if (mp_cmp_d(R->x, 0) == MP_LT)
|
---|
900 | err = mp_add(R->x, modulus, R->x);
|
---|
901 | }
|
---|
902 | /* Y = Y - X */
|
---|
903 | if (err == MP_OKAY)
|
---|
904 | err = mp_sub(R->y, R->x, R->y);
|
---|
905 | if (err == MP_OKAY) {
|
---|
906 | if (mp_cmp_d(R->y, 0) == MP_LT)
|
---|
907 | err = mp_add(R->y, modulus, R->y);
|
---|
908 | }
|
---|
909 | /* Y = Y * T1 */
|
---|
910 | if (err == MP_OKAY)
|
---|
911 | err = mp_mul(R->y, &t1, R->y);
|
---|
912 | if (err == MP_OKAY)
|
---|
913 | err = mp_montgomery_reduce(R->y, modulus, *mp);
|
---|
914 |
|
---|
915 | /* Y = Y - T2 */
|
---|
916 | if (err == MP_OKAY)
|
---|
917 | err = mp_sub(R->y, &t2, R->y);
|
---|
918 | if (err == MP_OKAY) {
|
---|
919 | if (mp_cmp_d(R->y, 0) == MP_LT)
|
---|
920 | err = mp_add(R->y, modulus, R->y);
|
---|
921 | }
|
---|
922 |
|
---|
923 | /* clean up */
|
---|
924 | mp_clear(&t1);
|
---|
925 | mp_clear(&t2);
|
---|
926 |
|
---|
927 | return err;
|
---|
928 | }
|
---|
929 |
|
---|
930 | #endif /* USE_FAST_MATH */
|
---|
931 |
|
---|
932 | /**
|
---|
933 | Map a projective jacbobian point back to affine space
|
---|
934 | P [in/out] The point to map
|
---|
935 | modulus The modulus of the field the ECC curve is in
|
---|
936 | mp The "b" value from montgomery_setup()
|
---|
937 | return MP_OKAY on success
|
---|
938 | */
|
---|
939 | int ecc_map(ecc_point* P, mp_int* modulus, mp_digit* mp)
|
---|
940 | {
|
---|
941 | mp_int t1;
|
---|
942 | mp_int t2;
|
---|
943 | int err;
|
---|
944 |
|
---|
945 | if (P == NULL || mp == NULL || modulus == NULL)
|
---|
946 | return ECC_BAD_ARG_E;
|
---|
947 |
|
---|
948 | /* special case for point at infinity */
|
---|
949 | if (mp_cmp_d(P->z, 0) == MP_EQ) {
|
---|
950 | mp_set(P->x, 0);
|
---|
951 | mp_set(P->y, 0);
|
---|
952 | mp_set(P->z, 1);
|
---|
953 | return MP_OKAY;
|
---|
954 | }
|
---|
955 |
|
---|
956 | if ((err = mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
|
---|
957 | return MEMORY_E;
|
---|
958 | }
|
---|
959 |
|
---|
960 | /* first map z back to normal */
|
---|
961 | err = mp_montgomery_reduce(P->z, modulus, *mp);
|
---|
962 |
|
---|
963 | /* get 1/z */
|
---|
964 | if (err == MP_OKAY)
|
---|
965 | err = mp_invmod(P->z, modulus, &t1);
|
---|
966 |
|
---|
967 | /* get 1/z^2 and 1/z^3 */
|
---|
968 | if (err == MP_OKAY)
|
---|
969 | err = mp_sqr(&t1, &t2);
|
---|
970 | if (err == MP_OKAY)
|
---|
971 | err = mp_mod(&t2, modulus, &t2);
|
---|
972 | if (err == MP_OKAY)
|
---|
973 | err = mp_mul(&t1, &t2, &t1);
|
---|
974 | if (err == MP_OKAY)
|
---|
975 | err = mp_mod(&t1, modulus, &t1);
|
---|
976 |
|
---|
977 | /* multiply against x/y */
|
---|
978 | if (err == MP_OKAY)
|
---|
979 | err = mp_mul(P->x, &t2, P->x);
|
---|
980 | if (err == MP_OKAY)
|
---|
981 | err = mp_montgomery_reduce(P->x, modulus, *mp);
|
---|
982 | if (err == MP_OKAY)
|
---|
983 | err = mp_mul(P->y, &t1, P->y);
|
---|
984 | if (err == MP_OKAY)
|
---|
985 | err = mp_montgomery_reduce(P->y, modulus, *mp);
|
---|
986 |
|
---|
987 | if (err == MP_OKAY)
|
---|
988 | mp_set(P->z, 1);
|
---|
989 |
|
---|
990 | /* clean up */
|
---|
991 | mp_clear(&t1);
|
---|
992 | mp_clear(&t2);
|
---|
993 |
|
---|
994 | return err;
|
---|
995 | }
|
---|
996 |
|
---|
997 |
|
---|
998 | #ifndef ECC_TIMING_RESISTANT
|
---|
999 |
|
---|
1000 | /* size of sliding window, don't change this! */
|
---|
1001 | #define WINSIZE 4
|
---|
1002 |
|
---|
1003 | /**
|
---|
1004 | Perform a point multiplication
|
---|
1005 | k The scalar to multiply by
|
---|
1006 | G The base point
|
---|
1007 | R [out] Destination for kG
|
---|
1008 | modulus The modulus of the field the ECC curve is in
|
---|
1009 | map Boolean whether to map back to affine or not
|
---|
1010 | (1==map, 0 == leave in projective)
|
---|
1011 | return MP_OKAY on success
|
---|
1012 | */
|
---|
1013 | #ifdef FP_ECC
|
---|
1014 | static int normal_ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R,
|
---|
1015 | mp_int* modulus, int map)
|
---|
1016 | #else
|
---|
1017 | int wc_ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R, mp_int* modulus,
|
---|
1018 | int map)
|
---|
1019 | #endif
|
---|
1020 | {
|
---|
1021 | ecc_point *tG, *M[8];
|
---|
1022 | int i, j, err;
|
---|
1023 | mp_int mu;
|
---|
1024 | mp_digit mp;
|
---|
1025 | mp_digit buf;
|
---|
1026 | int first = 1, bitbuf = 0, bitcpy = 0, bitcnt = 0, mode = 0,
|
---|
1027 | digidx = 0;
|
---|
1028 |
|
---|
1029 | if (k == NULL || G == NULL || R == NULL || modulus == NULL)
|
---|
1030 | return ECC_BAD_ARG_E;
|
---|
1031 |
|
---|
1032 | /* init montgomery reduction */
|
---|
1033 | if ((err = mp_montgomery_setup(modulus, &mp)) != MP_OKAY) {
|
---|
1034 | return err;
|
---|
1035 | }
|
---|
1036 | if ((err = mp_init(&mu)) != MP_OKAY) {
|
---|
1037 | return err;
|
---|
1038 | }
|
---|
1039 | if ((err = mp_montgomery_calc_normalization(&mu, modulus)) != MP_OKAY) {
|
---|
1040 | mp_clear(&mu);
|
---|
1041 | return err;
|
---|
1042 | }
|
---|
1043 |
|
---|
1044 | /* alloc ram for window temps */
|
---|
1045 | for (i = 0; i < 8; i++) {
|
---|
1046 | M[i] = wc_ecc_new_point();
|
---|
1047 | if (M[i] == NULL) {
|
---|
1048 | for (j = 0; j < i; j++) {
|
---|
1049 | wc_ecc_del_point(M[j]);
|
---|
1050 | }
|
---|
1051 | mp_clear(&mu);
|
---|
1052 | return MEMORY_E;
|
---|
1053 | }
|
---|
1054 | }
|
---|
1055 |
|
---|
1056 | /* make a copy of G incase R==G */
|
---|
1057 | tG = wc_ecc_new_point();
|
---|
1058 | if (tG == NULL)
|
---|
1059 | err = MEMORY_E;
|
---|
1060 |
|
---|
1061 | /* tG = G and convert to montgomery */
|
---|
1062 | if (err == MP_OKAY) {
|
---|
1063 | if (mp_cmp_d(&mu, 1) == MP_EQ) {
|
---|
1064 | err = mp_copy(G->x, tG->x);
|
---|
1065 | if (err == MP_OKAY)
|
---|
1066 | err = mp_copy(G->y, tG->y);
|
---|
1067 | if (err == MP_OKAY)
|
---|
1068 | err = mp_copy(G->z, tG->z);
|
---|
1069 | } else {
|
---|
1070 | err = mp_mulmod(G->x, &mu, modulus, tG->x);
|
---|
1071 | if (err == MP_OKAY)
|
---|
1072 | err = mp_mulmod(G->y, &mu, modulus, tG->y);
|
---|
1073 | if (err == MP_OKAY)
|
---|
1074 | err = mp_mulmod(G->z, &mu, modulus, tG->z);
|
---|
1075 | }
|
---|
1076 | }
|
---|
1077 | mp_clear(&mu);
|
---|
1078 |
|
---|
1079 | /* calc the M tab, which holds kG for k==8..15 */
|
---|
1080 | /* M[0] == 8G */
|
---|
1081 | if (err == MP_OKAY)
|
---|
1082 | err = ecc_projective_dbl_point(tG, M[0], modulus, &mp);
|
---|
1083 | if (err == MP_OKAY)
|
---|
1084 | err = ecc_projective_dbl_point(M[0], M[0], modulus, &mp);
|
---|
1085 | if (err == MP_OKAY)
|
---|
1086 | err = ecc_projective_dbl_point(M[0], M[0], modulus, &mp);
|
---|
1087 |
|
---|
1088 | /* now find (8+k)G for k=1..7 */
|
---|
1089 | if (err == MP_OKAY)
|
---|
1090 | for (j = 9; j < 16; j++) {
|
---|
1091 | err = ecc_projective_add_point(M[j-9], tG, M[j-8], modulus, &mp);
|
---|
1092 | if (err != MP_OKAY) break;
|
---|
1093 | }
|
---|
1094 |
|
---|
1095 | /* setup sliding window */
|
---|
1096 | if (err == MP_OKAY) {
|
---|
1097 | mode = 0;
|
---|
1098 | bitcnt = 1;
|
---|
1099 | buf = 0;
|
---|
1100 | digidx = get_digit_count(k) - 1;
|
---|
1101 | bitcpy = bitbuf = 0;
|
---|
1102 | first = 1;
|
---|
1103 |
|
---|
1104 | /* perform ops */
|
---|
1105 | for (;;) {
|
---|
1106 | /* grab next digit as required */
|
---|
1107 | if (--bitcnt == 0) {
|
---|
1108 | if (digidx == -1) {
|
---|
1109 | break;
|
---|
1110 | }
|
---|
1111 | buf = get_digit(k, digidx);
|
---|
1112 | bitcnt = (int) DIGIT_BIT;
|
---|
1113 | --digidx;
|
---|
1114 | }
|
---|
1115 |
|
---|
1116 | /* grab the next msb from the ltiplicand */
|
---|
1117 | i = (int)(buf >> (DIGIT_BIT - 1)) & 1;
|
---|
1118 | buf <<= 1;
|
---|
1119 |
|
---|
1120 | /* skip leading zero bits */
|
---|
1121 | if (mode == 0 && i == 0)
|
---|
1122 | continue;
|
---|
1123 |
|
---|
1124 | /* if the bit is zero and mode == 1 then we double */
|
---|
1125 | if (mode == 1 && i == 0) {
|
---|
1126 | err = ecc_projective_dbl_point(R, R, modulus, &mp);
|
---|
1127 | if (err != MP_OKAY) break;
|
---|
1128 | continue;
|
---|
1129 | }
|
---|
1130 |
|
---|
1131 | /* else we add it to the window */
|
---|
1132 | bitbuf |= (i << (WINSIZE - ++bitcpy));
|
---|
1133 | mode = 2;
|
---|
1134 |
|
---|
1135 | if (bitcpy == WINSIZE) {
|
---|
1136 | /* if this is the first window we do a simple copy */
|
---|
1137 | if (first == 1) {
|
---|
1138 | /* R = kG [k = first window] */
|
---|
1139 | err = mp_copy(M[bitbuf-8]->x, R->x);
|
---|
1140 | if (err != MP_OKAY) break;
|
---|
1141 |
|
---|
1142 | err = mp_copy(M[bitbuf-8]->y, R->y);
|
---|
1143 | if (err != MP_OKAY) break;
|
---|
1144 |
|
---|
1145 | err = mp_copy(M[bitbuf-8]->z, R->z);
|
---|
1146 | first = 0;
|
---|
1147 | } else {
|
---|
1148 | /* normal window */
|
---|
1149 | /* ok window is filled so double as required and add */
|
---|
1150 | /* double first */
|
---|
1151 | for (j = 0; j < WINSIZE; j++) {
|
---|
1152 | err = ecc_projective_dbl_point(R, R, modulus, &mp);
|
---|
1153 | if (err != MP_OKAY) break;
|
---|
1154 | }
|
---|
1155 | if (err != MP_OKAY) break; /* out of first for(;;) */
|
---|
1156 |
|
---|
1157 | /* then add, bitbuf will be 8..15 [8..2^WINSIZE] guaranted */
|
---|
1158 | err = ecc_projective_add_point(R,M[bitbuf-8],R,modulus,&mp);
|
---|
1159 | }
|
---|
1160 | if (err != MP_OKAY) break;
|
---|
1161 | /* empty window and reset */
|
---|
1162 | bitcpy = bitbuf = 0;
|
---|
1163 | mode = 1;
|
---|
1164 | }
|
---|
1165 | }
|
---|
1166 | }
|
---|
1167 |
|
---|
1168 | /* if bits remain then double/add */
|
---|
1169 | if (err == MP_OKAY) {
|
---|
1170 | if (mode == 2 && bitcpy > 0) {
|
---|
1171 | /* double then add */
|
---|
1172 | for (j = 0; j < bitcpy; j++) {
|
---|
1173 | /* only double if we have had at least one add first */
|
---|
1174 | if (first == 0) {
|
---|
1175 | err = ecc_projective_dbl_point(R, R, modulus, &mp);
|
---|
1176 | if (err != MP_OKAY) break;
|
---|
1177 | }
|
---|
1178 |
|
---|
1179 | bitbuf <<= 1;
|
---|
1180 | if ((bitbuf & (1 << WINSIZE)) != 0) {
|
---|
1181 | if (first == 1) {
|
---|
1182 | /* first add, so copy */
|
---|
1183 | err = mp_copy(tG->x, R->x);
|
---|
1184 | if (err != MP_OKAY) break;
|
---|
1185 |
|
---|
1186 | err = mp_copy(tG->y, R->y);
|
---|
1187 | if (err != MP_OKAY) break;
|
---|
1188 |
|
---|
1189 | err = mp_copy(tG->z, R->z);
|
---|
1190 | if (err != MP_OKAY) break;
|
---|
1191 | first = 0;
|
---|
1192 | } else {
|
---|
1193 | /* then add */
|
---|
1194 | err = ecc_projective_add_point(R, tG, R, modulus, &mp);
|
---|
1195 | if (err != MP_OKAY) break;
|
---|
1196 | }
|
---|
1197 | }
|
---|
1198 | }
|
---|
1199 | }
|
---|
1200 | }
|
---|
1201 |
|
---|
1202 | /* map R back from projective space */
|
---|
1203 | if (err == MP_OKAY && map)
|
---|
1204 | err = ecc_map(R, modulus, &mp);
|
---|
1205 |
|
---|
1206 | mp_clear(&mu);
|
---|
1207 | wc_ecc_del_point(tG);
|
---|
1208 | for (i = 0; i < 8; i++) {
|
---|
1209 | wc_ecc_del_point(M[i]);
|
---|
1210 | }
|
---|
1211 | return err;
|
---|
1212 | }
|
---|
1213 |
|
---|
1214 | #undef WINSIZE
|
---|
1215 |
|
---|
1216 | #else /* ECC_TIMING_RESISTANT */
|
---|
1217 |
|
---|
1218 | /**
|
---|
1219 | Perform a point multiplication (timing resistant)
|
---|
1220 | k The scalar to multiply by
|
---|
1221 | G The base point
|
---|
1222 | R [out] Destination for kG
|
---|
1223 | modulus The modulus of the field the ECC curve is in
|
---|
1224 | map Boolean whether to map back to affine or not
|
---|
1225 | (1==map, 0 == leave in projective)
|
---|
1226 | return MP_OKAY on success
|
---|
1227 | */
|
---|
1228 | #ifdef FP_ECC
|
---|
1229 | static int normal_ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R,
|
---|
1230 | mp_int* modulus, int map)
|
---|
1231 | #else
|
---|
1232 | int wc_ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R, mp_int* modulus,
|
---|
1233 | int map)
|
---|
1234 | #endif
|
---|
1235 | {
|
---|
1236 | ecc_point *tG, *M[3];
|
---|
1237 | int i, j, err;
|
---|
1238 | mp_int mu;
|
---|
1239 | mp_digit mp;
|
---|
1240 | mp_digit buf;
|
---|
1241 | int bitcnt = 0, mode = 0, digidx = 0;
|
---|
1242 |
|
---|
1243 | if (k == NULL || G == NULL || R == NULL || modulus == NULL)
|
---|
1244 | return ECC_BAD_ARG_E;
|
---|
1245 |
|
---|
1246 | /* init montgomery reduction */
|
---|
1247 | if ((err = mp_montgomery_setup(modulus, &mp)) != MP_OKAY) {
|
---|
1248 | return err;
|
---|
1249 | }
|
---|
1250 | if ((err = mp_init(&mu)) != MP_OKAY) {
|
---|
1251 | return err;
|
---|
1252 | }
|
---|
1253 | if ((err = mp_montgomery_calc_normalization(&mu, modulus)) != MP_OKAY) {
|
---|
1254 | mp_clear(&mu);
|
---|
1255 | return err;
|
---|
1256 | }
|
---|
1257 |
|
---|
1258 | /* alloc ram for window temps */
|
---|
1259 | for (i = 0; i < 3; i++) {
|
---|
1260 | M[i] = wc_ecc_new_point();
|
---|
1261 | if (M[i] == NULL) {
|
---|
1262 | for (j = 0; j < i; j++) {
|
---|
1263 | wc_ecc_del_point(M[j]);
|
---|
1264 | }
|
---|
1265 | mp_clear(&mu);
|
---|
1266 | return MEMORY_E;
|
---|
1267 | }
|
---|
1268 | }
|
---|
1269 |
|
---|
1270 | /* make a copy of G incase R==G */
|
---|
1271 | tG = wc_ecc_new_point();
|
---|
1272 | if (tG == NULL)
|
---|
1273 | err = MEMORY_E;
|
---|
1274 |
|
---|
1275 | /* tG = G and convert to montgomery */
|
---|
1276 | if (err == MP_OKAY) {
|
---|
1277 | err = mp_mulmod(G->x, &mu, modulus, tG->x);
|
---|
1278 | if (err == MP_OKAY)
|
---|
1279 | err = mp_mulmod(G->y, &mu, modulus, tG->y);
|
---|
1280 | if (err == MP_OKAY)
|
---|
1281 | err = mp_mulmod(G->z, &mu, modulus, tG->z);
|
---|
1282 | }
|
---|
1283 | mp_clear(&mu);
|
---|
1284 |
|
---|
1285 | /* calc the M tab */
|
---|
1286 | /* M[0] == G */
|
---|
1287 | if (err == MP_OKAY)
|
---|
1288 | err = mp_copy(tG->x, M[0]->x);
|
---|
1289 | if (err == MP_OKAY)
|
---|
1290 | err = mp_copy(tG->y, M[0]->y);
|
---|
1291 | if (err == MP_OKAY)
|
---|
1292 | err = mp_copy(tG->z, M[0]->z);
|
---|
1293 |
|
---|
1294 | /* M[1] == 2G */
|
---|
1295 | if (err == MP_OKAY)
|
---|
1296 | err = ecc_projective_dbl_point(tG, M[1], modulus, &mp);
|
---|
1297 |
|
---|
1298 | /* setup sliding window */
|
---|
1299 | mode = 0;
|
---|
1300 | bitcnt = 1;
|
---|
1301 | buf = 0;
|
---|
1302 | digidx = get_digit_count(k) - 1;
|
---|
1303 |
|
---|
1304 | /* perform ops */
|
---|
1305 | if (err == MP_OKAY) {
|
---|
1306 | for (;;) {
|
---|
1307 | /* grab next digit as required */
|
---|
1308 | if (--bitcnt == 0) {
|
---|
1309 | if (digidx == -1) {
|
---|
1310 | break;
|
---|
1311 | }
|
---|
1312 | buf = get_digit(k, digidx);
|
---|
1313 | bitcnt = (int) DIGIT_BIT;
|
---|
1314 | --digidx;
|
---|
1315 | }
|
---|
1316 |
|
---|
1317 | /* grab the next msb from the ltiplicand */
|
---|
1318 | i = (buf >> (DIGIT_BIT - 1)) & 1;
|
---|
1319 | buf <<= 1;
|
---|
1320 |
|
---|
1321 | if (mode == 0 && i == 0) {
|
---|
1322 | /* dummy operations */
|
---|
1323 | if (err == MP_OKAY)
|
---|
1324 | err = ecc_projective_add_point(M[0], M[1], M[2], modulus,
|
---|
1325 | &mp);
|
---|
1326 | if (err == MP_OKAY)
|
---|
1327 | err = ecc_projective_dbl_point(M[1], M[2], modulus, &mp);
|
---|
1328 | if (err == MP_OKAY)
|
---|
1329 | continue;
|
---|
1330 | }
|
---|
1331 |
|
---|
1332 | if (mode == 0 && i == 1) {
|
---|
1333 | mode = 1;
|
---|
1334 | /* dummy operations */
|
---|
1335 | if (err == MP_OKAY)
|
---|
1336 | err = ecc_projective_add_point(M[0], M[1], M[2], modulus,
|
---|
1337 | &mp);
|
---|
1338 | if (err == MP_OKAY)
|
---|
1339 | err = ecc_projective_dbl_point(M[1], M[2], modulus, &mp);
|
---|
1340 | if (err == MP_OKAY)
|
---|
1341 | continue;
|
---|
1342 | }
|
---|
1343 |
|
---|
1344 | if (err == MP_OKAY)
|
---|
1345 | err = ecc_projective_add_point(M[0], M[1], M[i^1], modulus, &mp);
|
---|
1346 | if (err == MP_OKAY)
|
---|
1347 | err = ecc_projective_dbl_point(M[i], M[i], modulus, &mp);
|
---|
1348 | if (err != MP_OKAY)
|
---|
1349 | break;
|
---|
1350 | } /* end for */
|
---|
1351 | }
|
---|
1352 |
|
---|
1353 | /* copy result out */
|
---|
1354 | if (err == MP_OKAY)
|
---|
1355 | err = mp_copy(M[0]->x, R->x);
|
---|
1356 | if (err == MP_OKAY)
|
---|
1357 | err = mp_copy(M[0]->y, R->y);
|
---|
1358 | if (err == MP_OKAY)
|
---|
1359 | err = mp_copy(M[0]->z, R->z);
|
---|
1360 |
|
---|
1361 | /* map R back from projective space */
|
---|
1362 | if (err == MP_OKAY && map)
|
---|
1363 | err = ecc_map(R, modulus, &mp);
|
---|
1364 |
|
---|
1365 | /* done */
|
---|
1366 | mp_clear(&mu);
|
---|
1367 | wc_ecc_del_point(tG);
|
---|
1368 | for (i = 0; i < 3; i++) {
|
---|
1369 | wc_ecc_del_point(M[i]);
|
---|
1370 | }
|
---|
1371 | return err;
|
---|
1372 | }
|
---|
1373 |
|
---|
1374 | #endif /* ECC_TIMING_RESISTANT */
|
---|
1375 |
|
---|
1376 |
|
---|
1377 | #ifdef ALT_ECC_SIZE
|
---|
1378 |
|
---|
1379 | static void alt_fp_init(fp_int* a)
|
---|
1380 | {
|
---|
1381 | a->size = FP_SIZE_ECC;
|
---|
1382 | fp_zero(a);
|
---|
1383 | }
|
---|
1384 |
|
---|
1385 | #endif /* ALT_ECC_SIZE */
|
---|
1386 |
|
---|
1387 |
|
---|
1388 | /**
|
---|
1389 | Allocate a new ECC point
|
---|
1390 | return A newly allocated point or NULL on error
|
---|
1391 | */
|
---|
1392 | ecc_point* wc_ecc_new_point(void)
|
---|
1393 | {
|
---|
1394 | ecc_point* p;
|
---|
1395 |
|
---|
1396 | p = (ecc_point*)XMALLOC(sizeof(ecc_point), 0, DYNAMIC_TYPE_ECC);
|
---|
1397 | if (p == NULL) {
|
---|
1398 | return NULL;
|
---|
1399 | }
|
---|
1400 | XMEMSET(p, 0, sizeof(ecc_point));
|
---|
1401 |
|
---|
1402 | #ifndef USE_FAST_MATH
|
---|
1403 | p->x->dp = NULL;
|
---|
1404 | p->y->dp = NULL;
|
---|
1405 | p->z->dp = NULL;
|
---|
1406 | #endif
|
---|
1407 |
|
---|
1408 | #ifndef ALT_ECC_SIZE
|
---|
1409 | if (mp_init_multi(p->x, p->y, p->z, NULL, NULL, NULL) != MP_OKAY) {
|
---|
1410 | XFREE(p, 0, DYNAMIC_TYPE_ECC);
|
---|
1411 | return NULL;
|
---|
1412 | }
|
---|
1413 | #else
|
---|
1414 | p->x = (mp_int*)&p->xyz[0];
|
---|
1415 | p->y = (mp_int*)&p->xyz[1];
|
---|
1416 | p->z = (mp_int*)&p->xyz[2];
|
---|
1417 | alt_fp_init(p->x);
|
---|
1418 | alt_fp_init(p->y);
|
---|
1419 | alt_fp_init(p->z);
|
---|
1420 | #endif
|
---|
1421 |
|
---|
1422 | return p;
|
---|
1423 | }
|
---|
1424 |
|
---|
1425 | /** Free an ECC point from memory
|
---|
1426 | p The point to free
|
---|
1427 | */
|
---|
1428 | void wc_ecc_del_point(ecc_point* p)
|
---|
1429 | {
|
---|
1430 | /* prevents free'ing null arguments */
|
---|
1431 | if (p != NULL) {
|
---|
1432 | mp_clear(p->x);
|
---|
1433 | mp_clear(p->y);
|
---|
1434 | mp_clear(p->z);
|
---|
1435 | XFREE(p, 0, DYNAMIC_TYPE_ECC);
|
---|
1436 | }
|
---|
1437 | }
|
---|
1438 |
|
---|
1439 | /** Copy the value of a point to an other one
|
---|
1440 | p The point to copy
|
---|
1441 | r The created point
|
---|
1442 | */
|
---|
1443 | int wc_ecc_copy_point(ecc_point* p, ecc_point *r)
|
---|
1444 | {
|
---|
1445 | int ret;
|
---|
1446 |
|
---|
1447 | /* prevents null arguments */
|
---|
1448 | if (p == NULL || r == NULL)
|
---|
1449 | return ECC_BAD_ARG_E;
|
---|
1450 |
|
---|
1451 | ret = mp_copy(p->x, r->x);
|
---|
1452 | if (ret != MP_OKAY)
|
---|
1453 | return ret;
|
---|
1454 | ret = mp_copy(p->y, r->y);
|
---|
1455 | if (ret != MP_OKAY)
|
---|
1456 | return ret;
|
---|
1457 | ret = mp_copy(p->z, r->z);
|
---|
1458 | if (ret != MP_OKAY)
|
---|
1459 | return ret;
|
---|
1460 |
|
---|
1461 | return MP_OKAY;
|
---|
1462 | }
|
---|
1463 |
|
---|
1464 | /** Compare the value of a point with an other one
|
---|
1465 | a The point to compare
|
---|
1466 | b The othe point to compare
|
---|
1467 |
|
---|
1468 | return MP_EQ if equal, MP_LT/MP_GT if not, < 0 in case of error
|
---|
1469 | */
|
---|
1470 | int wc_ecc_cmp_point(ecc_point* a, ecc_point *b)
|
---|
1471 | {
|
---|
1472 | int ret;
|
---|
1473 |
|
---|
1474 | /* prevents null arguments */
|
---|
1475 | if (a == NULL || b == NULL)
|
---|
1476 | return BAD_FUNC_ARG;
|
---|
1477 |
|
---|
1478 | ret = mp_cmp(a->x, b->x);
|
---|
1479 | if (ret != MP_EQ)
|
---|
1480 | return ret;
|
---|
1481 | ret = mp_cmp(a->y, b->y);
|
---|
1482 | if (ret != MP_EQ)
|
---|
1483 | return ret;
|
---|
1484 | ret = mp_cmp(a->z, b->z);
|
---|
1485 | if (ret != MP_EQ)
|
---|
1486 | return ret;
|
---|
1487 |
|
---|
1488 | return MP_EQ;
|
---|
1489 | }
|
---|
1490 |
|
---|
1491 | /** Returns whether an ECC idx is valid or not
|
---|
1492 | n The idx number to check
|
---|
1493 | return 1 if valid, 0 if not
|
---|
1494 | */
|
---|
1495 | int wc_ecc_is_valid_idx(int n)
|
---|
1496 | {
|
---|
1497 | int x;
|
---|
1498 |
|
---|
1499 | for (x = 0; ecc_sets[x].size != 0; x++)
|
---|
1500 | ;
|
---|
1501 | /* -1 is a valid index --- indicating that the domain params
|
---|
1502 | were supplied by the user */
|
---|
1503 | if ((n >= -1) && (n < x)) {
|
---|
1504 | return 1;
|
---|
1505 | }
|
---|
1506 | return 0;
|
---|
1507 | }
|
---|
1508 |
|
---|
1509 |
|
---|
1510 | /**
|
---|
1511 | Create an ECC shared secret between two keys
|
---|
1512 | private_key The private ECC key
|
---|
1513 | public_key The public key
|
---|
1514 | out [out] Destination of the shared secret
|
---|
1515 | Conforms to EC-DH from ANSI X9.63
|
---|
1516 | outlen [in/out] The max size and resulting size of the shared secret
|
---|
1517 | return MP_OKAY if successful
|
---|
1518 | */
|
---|
1519 | int wc_ecc_shared_secret(ecc_key* private_key, ecc_key* public_key, byte* out,
|
---|
1520 | word32* outlen)
|
---|
1521 | {
|
---|
1522 | word32 x = 0;
|
---|
1523 | ecc_point* result;
|
---|
1524 | mp_int prime;
|
---|
1525 | int err;
|
---|
1526 |
|
---|
1527 | if (private_key == NULL || public_key == NULL || out == NULL ||
|
---|
1528 | outlen == NULL)
|
---|
1529 | return BAD_FUNC_ARG;
|
---|
1530 |
|
---|
1531 | /* type valid? */
|
---|
1532 | if (private_key->type != ECC_PRIVATEKEY) {
|
---|
1533 | return ECC_BAD_ARG_E;
|
---|
1534 | }
|
---|
1535 |
|
---|
1536 | if (wc_ecc_is_valid_idx(private_key->idx) == 0 ||
|
---|
1537 | wc_ecc_is_valid_idx(public_key->idx) == 0)
|
---|
1538 | return ECC_BAD_ARG_E;
|
---|
1539 |
|
---|
1540 | if (XSTRNCMP(private_key->dp->name, public_key->dp->name, ECC_MAXNAME) != 0)
|
---|
1541 | return ECC_BAD_ARG_E;
|
---|
1542 |
|
---|
1543 | /* make new point */
|
---|
1544 | result = wc_ecc_new_point();
|
---|
1545 | if (result == NULL) {
|
---|
1546 | return MEMORY_E;
|
---|
1547 | }
|
---|
1548 |
|
---|
1549 | if ((err = mp_init(&prime)) != MP_OKAY) {
|
---|
1550 | wc_ecc_del_point(result);
|
---|
1551 | return err;
|
---|
1552 | }
|
---|
1553 |
|
---|
1554 | err = mp_read_radix(&prime, (char *)private_key->dp->prime, 16);
|
---|
1555 |
|
---|
1556 | if (err == MP_OKAY)
|
---|
1557 | err = wc_ecc_mulmod(&private_key->k, &public_key->pubkey, result, &prime,1);
|
---|
1558 |
|
---|
1559 | if (err == MP_OKAY) {
|
---|
1560 | x = mp_unsigned_bin_size(&prime);
|
---|
1561 | if (*outlen < x)
|
---|
1562 | err = BUFFER_E;
|
---|
1563 | }
|
---|
1564 |
|
---|
1565 | if (err == MP_OKAY) {
|
---|
1566 | XMEMSET(out, 0, x);
|
---|
1567 | err = mp_to_unsigned_bin(result->x,out + (x -
|
---|
1568 | mp_unsigned_bin_size(result->x)));
|
---|
1569 | *outlen = x;
|
---|
1570 | }
|
---|
1571 |
|
---|
1572 | mp_clear(&prime);
|
---|
1573 | wc_ecc_del_point(result);
|
---|
1574 |
|
---|
1575 | return err;
|
---|
1576 | }
|
---|
1577 |
|
---|
1578 | /**
|
---|
1579 | Create an ECC shared secret between two keys
|
---|
1580 | private_key The private ECC key
|
---|
1581 | point The point to use (public key)
|
---|
1582 | out [out] Destination of the shared secret
|
---|
1583 | Conforms to EC-DH from ANSI X9.63
|
---|
1584 | outlen [in/out] The max size and resulting size of the shared secret
|
---|
1585 | return MP_OKAY if successful
|
---|
1586 | */
|
---|
1587 | int wc_ecc_shared_secret_ssh(ecc_key* private_key, ecc_point* point,
|
---|
1588 | byte* out, word32 *outlen)
|
---|
1589 | {
|
---|
1590 | word32 x = 0;
|
---|
1591 | ecc_point* result;
|
---|
1592 | mp_int prime;
|
---|
1593 | int err;
|
---|
1594 |
|
---|
1595 | if (private_key == NULL || point == NULL || out == NULL || outlen == NULL)
|
---|
1596 | return BAD_FUNC_ARG;
|
---|
1597 |
|
---|
1598 | /* type valid? */
|
---|
1599 | if (private_key->type != ECC_PRIVATEKEY) {
|
---|
1600 | return ECC_BAD_ARG_E;
|
---|
1601 | }
|
---|
1602 |
|
---|
1603 | if (wc_ecc_is_valid_idx(private_key->idx) == 0)
|
---|
1604 | return ECC_BAD_ARG_E;
|
---|
1605 |
|
---|
1606 | /* make new point */
|
---|
1607 | result = wc_ecc_new_point();
|
---|
1608 | if (result == NULL) {
|
---|
1609 | return MEMORY_E;
|
---|
1610 | }
|
---|
1611 |
|
---|
1612 | if ((err = mp_init(&prime)) != MP_OKAY) {
|
---|
1613 | wc_ecc_del_point(result);
|
---|
1614 | return err;
|
---|
1615 | }
|
---|
1616 |
|
---|
1617 | err = mp_read_radix(&prime, (char *)private_key->dp->prime, 16);
|
---|
1618 |
|
---|
1619 | if (err == MP_OKAY)
|
---|
1620 | err = wc_ecc_mulmod(&private_key->k, point, result, &prime, 1);
|
---|
1621 |
|
---|
1622 | if (err == MP_OKAY) {
|
---|
1623 | x = mp_unsigned_bin_size(&prime);
|
---|
1624 | if (*outlen < x)
|
---|
1625 | err = BUFFER_E;
|
---|
1626 | }
|
---|
1627 |
|
---|
1628 | if (err == MP_OKAY) {
|
---|
1629 | XMEMSET(out, 0, x);
|
---|
1630 | err = mp_to_unsigned_bin(result->x,out +
|
---|
1631 | (x - mp_unsigned_bin_size(result->x)));
|
---|
1632 | *outlen = x;
|
---|
1633 | }
|
---|
1634 |
|
---|
1635 | mp_clear(&prime);
|
---|
1636 | wc_ecc_del_point(result);
|
---|
1637 |
|
---|
1638 | return err;
|
---|
1639 | }
|
---|
1640 |
|
---|
1641 |
|
---|
1642 | /* return 1 if point is at infinity, 0 if not, < 0 on error */
|
---|
1643 | int wc_ecc_point_is_at_infinity(ecc_point* p)
|
---|
1644 | {
|
---|
1645 | if (p == NULL)
|
---|
1646 | return BAD_FUNC_ARG;
|
---|
1647 |
|
---|
1648 | if (get_digit_count(p->x) == 0 && get_digit_count(p->y) == 0)
|
---|
1649 | return 1;
|
---|
1650 |
|
---|
1651 | return 0;
|
---|
1652 | }
|
---|
1653 |
|
---|
1654 |
|
---|
1655 | static int wc_ecc_make_key_ex(WC_RNG* rng, ecc_key* key, const ecc_set_type* dp)
|
---|
1656 | {
|
---|
1657 | int err;
|
---|
1658 | ecc_point* base;
|
---|
1659 | mp_int prime;
|
---|
1660 | mp_int order;
|
---|
1661 | #ifdef WOLFSSL_SMALL_STACK
|
---|
1662 | byte* buf;
|
---|
1663 | #else
|
---|
1664 | byte buf[ECC_MAXSIZE_GEN];
|
---|
1665 | #endif
|
---|
1666 | int keysize;
|
---|
1667 | int po_init = 0; /* prime order Init flag for clear */
|
---|
1668 |
|
---|
1669 | if (key == NULL || rng == NULL || dp == NULL)
|
---|
1670 | return ECC_BAD_ARG_E;
|
---|
1671 |
|
---|
1672 | #ifdef WOLFSSL_SMALL_STACK
|
---|
1673 | buf = (byte*)XMALLOC(ECC_MAXSIZE_GEN, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
1674 | if (buf == NULL)
|
---|
1675 | return MEMORY_E;
|
---|
1676 | #endif
|
---|
1677 |
|
---|
1678 | key->idx = -1;
|
---|
1679 | key->dp = dp;
|
---|
1680 |
|
---|
1681 | /*generate 8 extra bytes to mitigate bias from the modulo operation below*/
|
---|
1682 | /*see section A.1.2 in 'Suite B Implementor's Guide to FIPS 186-3 (ECDSA)'*/
|
---|
1683 | keysize = dp->size + 8;
|
---|
1684 |
|
---|
1685 | /* allocate ram */
|
---|
1686 | base = NULL;
|
---|
1687 |
|
---|
1688 | /* make up random string */
|
---|
1689 | err = wc_RNG_GenerateBlock(rng, buf, keysize);
|
---|
1690 |
|
---|
1691 | /* setup the key variables */
|
---|
1692 | if (err == 0) {
|
---|
1693 | #ifndef ALT_ECC_SIZE
|
---|
1694 | err = mp_init_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z,
|
---|
1695 | &key->k, &prime, &order);
|
---|
1696 | #else
|
---|
1697 | key->pubkey.x = (mp_int*)&key->pubkey.xyz[0];
|
---|
1698 | key->pubkey.y = (mp_int*)&key->pubkey.xyz[1];
|
---|
1699 | key->pubkey.z = (mp_int*)&key->pubkey.xyz[2];
|
---|
1700 | alt_fp_init(key->pubkey.x);
|
---|
1701 | alt_fp_init(key->pubkey.y);
|
---|
1702 | alt_fp_init(key->pubkey.z);
|
---|
1703 | err = mp_init_multi(&key->k, &prime, &order, NULL, NULL, NULL);
|
---|
1704 | #endif
|
---|
1705 | if (err != MP_OKAY)
|
---|
1706 | err = MEMORY_E;
|
---|
1707 | else
|
---|
1708 | po_init = 1;
|
---|
1709 | }
|
---|
1710 |
|
---|
1711 | if (err == MP_OKAY) {
|
---|
1712 | base = wc_ecc_new_point();
|
---|
1713 | if (base == NULL)
|
---|
1714 | err = MEMORY_E;
|
---|
1715 | }
|
---|
1716 |
|
---|
1717 | /* read in the specs for this key */
|
---|
1718 | if (err == MP_OKAY)
|
---|
1719 | err = mp_read_radix(&prime, (char *)key->dp->prime, 16);
|
---|
1720 | if (err == MP_OKAY)
|
---|
1721 | err = mp_read_radix(&order, (char *)key->dp->order, 16);
|
---|
1722 | if (err == MP_OKAY)
|
---|
1723 | err = mp_read_radix(base->x, (char *)key->dp->Gx, 16);
|
---|
1724 | if (err == MP_OKAY)
|
---|
1725 | err = mp_read_radix(base->y, (char *)key->dp->Gy, 16);
|
---|
1726 |
|
---|
1727 | if (err == MP_OKAY)
|
---|
1728 | mp_set(base->z, 1);
|
---|
1729 | if (err == MP_OKAY)
|
---|
1730 | err = mp_read_unsigned_bin(&key->k, (byte*)buf, keysize);
|
---|
1731 |
|
---|
1732 | /* quick sanity check to make sure we're not dealing with a 0 key */
|
---|
1733 | if (err == MP_OKAY) {
|
---|
1734 | if (MP_YES == mp_iszero(&key->k))
|
---|
1735 | err = MP_ZERO_E;
|
---|
1736 | }
|
---|
1737 |
|
---|
1738 | /* the key should be smaller than the order of base point */
|
---|
1739 | if (err == MP_OKAY) {
|
---|
1740 | if (mp_cmp(&key->k, &order) != MP_LT)
|
---|
1741 | err = mp_mod(&key->k, &order, &key->k);
|
---|
1742 | }
|
---|
1743 | /* make the public key */
|
---|
1744 | if (err == MP_OKAY)
|
---|
1745 | err = wc_ecc_mulmod(&key->k, base, &key->pubkey, &prime, 1);
|
---|
1746 |
|
---|
1747 | #ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
|
---|
1748 | /* validate the public key, order * pubkey = point at infinity */
|
---|
1749 | if (err == MP_OKAY)
|
---|
1750 | err = ecc_check_pubkey_order(key, &prime, &order);
|
---|
1751 | #endif /* WOLFSSL_VALIDATE_KEYGEN */
|
---|
1752 |
|
---|
1753 | if (err == MP_OKAY)
|
---|
1754 | key->type = ECC_PRIVATEKEY;
|
---|
1755 |
|
---|
1756 | if (err != MP_OKAY) {
|
---|
1757 | /* clean up */
|
---|
1758 | mp_clear(key->pubkey.x);
|
---|
1759 | mp_clear(key->pubkey.y);
|
---|
1760 | mp_clear(key->pubkey.z);
|
---|
1761 | mp_clear(&key->k);
|
---|
1762 | }
|
---|
1763 | wc_ecc_del_point(base);
|
---|
1764 | if (po_init) {
|
---|
1765 | mp_clear(&prime);
|
---|
1766 | mp_clear(&order);
|
---|
1767 | }
|
---|
1768 |
|
---|
1769 | ForceZero(buf, ECC_MAXSIZE);
|
---|
1770 | #ifdef WOLFSSL_SMALL_STACK
|
---|
1771 | XFREE(buf, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
1772 | #endif
|
---|
1773 |
|
---|
1774 | return err;
|
---|
1775 | }
|
---|
1776 |
|
---|
1777 | /**
|
---|
1778 | Make a new ECC key
|
---|
1779 | rng An active RNG state
|
---|
1780 | keysize The keysize for the new key (in octets from 20 to 65 bytes)
|
---|
1781 | key [out] Destination of the newly created key
|
---|
1782 | return MP_OKAY if successful,
|
---|
1783 | upon error all allocated memory will be freed
|
---|
1784 | */
|
---|
1785 | int wc_ecc_make_key(WC_RNG* rng, int keysize, ecc_key* key)
|
---|
1786 | {
|
---|
1787 | int x, err;
|
---|
1788 |
|
---|
1789 | if (key == NULL || rng == NULL)
|
---|
1790 | return ECC_BAD_ARG_E;
|
---|
1791 |
|
---|
1792 | /* find key size */
|
---|
1793 | for (x = 0; (keysize > ecc_sets[x].size) && (ecc_sets[x].size != 0); x++)
|
---|
1794 | ;
|
---|
1795 | keysize = ecc_sets[x].size;
|
---|
1796 |
|
---|
1797 | if (keysize > ECC_MAXSIZE || ecc_sets[x].size == 0) {
|
---|
1798 | return BAD_FUNC_ARG;
|
---|
1799 | }
|
---|
1800 | err = wc_ecc_make_key_ex(rng, key, &ecc_sets[x]);
|
---|
1801 | key->idx = x;
|
---|
1802 |
|
---|
1803 | return err;
|
---|
1804 | }
|
---|
1805 |
|
---|
1806 | /* Setup dynamic pointers is using normal math for proper freeing */
|
---|
1807 | int wc_ecc_init(ecc_key* key)
|
---|
1808 | {
|
---|
1809 | (void)key;
|
---|
1810 |
|
---|
1811 | #ifndef USE_FAST_MATH
|
---|
1812 | key->pubkey.x->dp = NULL;
|
---|
1813 | key->pubkey.y->dp = NULL;
|
---|
1814 | key->pubkey.z->dp = NULL;
|
---|
1815 |
|
---|
1816 | key->k.dp = NULL;
|
---|
1817 | #endif
|
---|
1818 |
|
---|
1819 | #ifdef ALT_ECC_SIZE
|
---|
1820 | if (mp_init(&key->k) != MP_OKAY)
|
---|
1821 | return MEMORY_E;
|
---|
1822 |
|
---|
1823 | key->pubkey.x = (mp_int*)&key->pubkey.xyz[0];
|
---|
1824 | key->pubkey.y = (mp_int*)&key->pubkey.xyz[1];
|
---|
1825 | key->pubkey.z = (mp_int*)&key->pubkey.xyz[2];
|
---|
1826 | alt_fp_init(key->pubkey.x);
|
---|
1827 | alt_fp_init(key->pubkey.y);
|
---|
1828 | alt_fp_init(key->pubkey.z);
|
---|
1829 | #endif
|
---|
1830 |
|
---|
1831 | return MP_OKAY;
|
---|
1832 | }
|
---|
1833 |
|
---|
1834 |
|
---|
1835 | /**
|
---|
1836 | Sign a message digest
|
---|
1837 | in The message digest to sign
|
---|
1838 | inlen The length of the digest
|
---|
1839 | out [out] The destination for the signature
|
---|
1840 | outlen [in/out] The max size and resulting size of the signature
|
---|
1841 | key A private ECC key
|
---|
1842 | return MP_OKAY if successful
|
---|
1843 | */
|
---|
1844 | int wc_ecc_sign_hash(const byte* in, word32 inlen, byte* out, word32 *outlen,
|
---|
1845 | WC_RNG* rng, ecc_key* key)
|
---|
1846 | {
|
---|
1847 | mp_int r;
|
---|
1848 | mp_int s;
|
---|
1849 | int err;
|
---|
1850 |
|
---|
1851 | if (in == NULL || out == NULL || outlen == NULL ||
|
---|
1852 | key == NULL || rng == NULL)
|
---|
1853 | return ECC_BAD_ARG_E;
|
---|
1854 |
|
---|
1855 | if ((err = mp_init_multi(&r, &s, NULL, NULL, NULL, NULL)) != MP_OKAY) {
|
---|
1856 | return err;
|
---|
1857 | }
|
---|
1858 |
|
---|
1859 | err = wc_ecc_sign_hash_ex(in, inlen, rng, key, &r, &s);
|
---|
1860 | if (err == MP_OKAY)
|
---|
1861 | err = StoreECC_DSA_Sig(out, outlen, &r, &s);
|
---|
1862 |
|
---|
1863 | mp_clear(&r);
|
---|
1864 | mp_clear(&s);
|
---|
1865 |
|
---|
1866 | return err;
|
---|
1867 | }
|
---|
1868 |
|
---|
1869 | /**
|
---|
1870 | Sign a message digest
|
---|
1871 | in The message digest to sign
|
---|
1872 | inlen The length of the digest
|
---|
1873 | out [out] The destination for the signature
|
---|
1874 | outlen [in/out] The max size and resulting size of the signature
|
---|
1875 | key A private ECC key
|
---|
1876 | r [out] The destination for r component of the signature
|
---|
1877 | s [out] The destination for s component of the signature
|
---|
1878 | return MP_OKAY if successful
|
---|
1879 | */
|
---|
1880 | int wc_ecc_sign_hash_ex(const byte* in, word32 inlen, WC_RNG* rng,
|
---|
1881 | ecc_key* key, mp_int *r, mp_int *s)
|
---|
1882 | {
|
---|
1883 | mp_int e;
|
---|
1884 | mp_int p;
|
---|
1885 | int err;
|
---|
1886 |
|
---|
1887 | if (in == NULL || r == NULL || s == NULL || key == NULL || rng == NULL)
|
---|
1888 | return ECC_BAD_ARG_E;
|
---|
1889 |
|
---|
1890 | /* is this a private key? */
|
---|
1891 | if (key->type != ECC_PRIVATEKEY) {
|
---|
1892 | return ECC_BAD_ARG_E;
|
---|
1893 | }
|
---|
1894 |
|
---|
1895 | /* is the IDX valid ? */
|
---|
1896 | if (wc_ecc_is_valid_idx(key->idx) != 1) {
|
---|
1897 | return ECC_BAD_ARG_E;
|
---|
1898 | }
|
---|
1899 |
|
---|
1900 | /* get the hash and load it as a bignum into 'e' */
|
---|
1901 | /* init the bignums */
|
---|
1902 | if ((err = mp_init_multi(&p, &e, NULL, NULL, NULL, NULL)) != MP_OKAY) {
|
---|
1903 | return err;
|
---|
1904 | }
|
---|
1905 | err = mp_read_radix(&p, (char *)key->dp->order, 16);
|
---|
1906 |
|
---|
1907 | if (err == MP_OKAY) {
|
---|
1908 | /* we may need to truncate if hash is longer than key size */
|
---|
1909 | word32 orderBits = mp_count_bits(&p);
|
---|
1910 |
|
---|
1911 | /* truncate down to byte size, may be all that's needed */
|
---|
1912 | if ( (WOLFSSL_BIT_SIZE * inlen) > orderBits)
|
---|
1913 | inlen = (orderBits + WOLFSSL_BIT_SIZE - 1)/WOLFSSL_BIT_SIZE;
|
---|
1914 | err = mp_read_unsigned_bin(&e, (byte*)in, inlen);
|
---|
1915 |
|
---|
1916 | /* may still need bit truncation too */
|
---|
1917 | if (err == MP_OKAY && (WOLFSSL_BIT_SIZE * inlen) > orderBits)
|
---|
1918 | mp_rshb(&e, WOLFSSL_BIT_SIZE - (orderBits & 0x7));
|
---|
1919 | }
|
---|
1920 |
|
---|
1921 | /* make up a key and export the public copy */
|
---|
1922 | if (err == MP_OKAY) {
|
---|
1923 | int loop_check = 0;
|
---|
1924 | ecc_key pubkey;
|
---|
1925 | if (wc_ecc_init(&pubkey) == MP_OKAY) {
|
---|
1926 | for (;;) {
|
---|
1927 | if (++loop_check > 64) {
|
---|
1928 | err = RNG_FAILURE_E;
|
---|
1929 | break;
|
---|
1930 | }
|
---|
1931 | err = wc_ecc_make_key_ex(rng, &pubkey, key->dp);
|
---|
1932 | if (err != MP_OKAY) break;
|
---|
1933 |
|
---|
1934 | /* find r = x1 mod n */
|
---|
1935 | err = mp_mod(pubkey.pubkey.x, &p, r);
|
---|
1936 | if (err != MP_OKAY) break;
|
---|
1937 |
|
---|
1938 | if (mp_iszero(r) == MP_YES) {
|
---|
1939 | mp_clear(pubkey.pubkey.x);
|
---|
1940 | mp_clear(pubkey.pubkey.y);
|
---|
1941 | mp_clear(pubkey.pubkey.z);
|
---|
1942 | mp_clear(&pubkey.k);
|
---|
1943 | }
|
---|
1944 | else {
|
---|
1945 | /* find s = (e + xr)/k */
|
---|
1946 | err = mp_invmod(&pubkey.k, &p, &pubkey.k);
|
---|
1947 | if (err != MP_OKAY) break;
|
---|
1948 |
|
---|
1949 | err = mp_mulmod(&key->k, r, &p, s); /* s = xr */
|
---|
1950 | if (err != MP_OKAY) break;
|
---|
1951 |
|
---|
1952 | err = mp_add(&e, s, s); /* s = e + xr */
|
---|
1953 | if (err != MP_OKAY) break;
|
---|
1954 |
|
---|
1955 | err = mp_mod(s, &p, s); /* s = e + xr */
|
---|
1956 | if (err != MP_OKAY) break;
|
---|
1957 |
|
---|
1958 | err = mp_mulmod(s, &pubkey.k, &p, s); /* s = (e + xr)/k */
|
---|
1959 | if (err != MP_OKAY) break;
|
---|
1960 |
|
---|
1961 | if (mp_iszero(s) == MP_NO)
|
---|
1962 | break;
|
---|
1963 | }
|
---|
1964 | }
|
---|
1965 | wc_ecc_free(&pubkey);
|
---|
1966 | }
|
---|
1967 | }
|
---|
1968 |
|
---|
1969 | mp_clear(&p);
|
---|
1970 | mp_clear(&e);
|
---|
1971 |
|
---|
1972 | return err;
|
---|
1973 | }
|
---|
1974 |
|
---|
1975 |
|
---|
1976 | /**
|
---|
1977 | Free an ECC key from memory
|
---|
1978 | key The key you wish to free
|
---|
1979 | */
|
---|
1980 | void wc_ecc_free(ecc_key* key)
|
---|
1981 | {
|
---|
1982 | if (key == NULL)
|
---|
1983 | return;
|
---|
1984 |
|
---|
1985 | mp_clear(key->pubkey.x);
|
---|
1986 | mp_clear(key->pubkey.y);
|
---|
1987 | mp_clear(key->pubkey.z);
|
---|
1988 | mp_clear(&key->k);
|
---|
1989 | }
|
---|
1990 |
|
---|
1991 |
|
---|
1992 | #ifdef USE_FAST_MATH
|
---|
1993 | #define GEN_MEM_ERR FP_MEM
|
---|
1994 | #else
|
---|
1995 | #define GEN_MEM_ERR MP_MEM
|
---|
1996 | #endif
|
---|
1997 |
|
---|
1998 | #ifdef ECC_SHAMIR
|
---|
1999 |
|
---|
2000 | /** Computes kA*A + kB*B = C using Shamir's Trick
|
---|
2001 | A First point to multiply
|
---|
2002 | kA What to multiple A by
|
---|
2003 | B Second point to multiply
|
---|
2004 | kB What to multiple B by
|
---|
2005 | C [out] Destination point (can overlap with A or B)
|
---|
2006 | modulus Modulus for curve
|
---|
2007 | return MP_OKAY on success
|
---|
2008 | */
|
---|
2009 | #ifdef FP_ECC
|
---|
2010 | static int normal_ecc_mul2add(ecc_point* A, mp_int* kA,
|
---|
2011 | ecc_point* B, mp_int* kB,
|
---|
2012 | ecc_point* C, mp_int* modulus)
|
---|
2013 | #else
|
---|
2014 | static int ecc_mul2add(ecc_point* A, mp_int* kA,
|
---|
2015 | ecc_point* B, mp_int* kB,
|
---|
2016 | ecc_point* C, mp_int* modulus)
|
---|
2017 | #endif
|
---|
2018 | {
|
---|
2019 | ecc_point* precomp[16];
|
---|
2020 | unsigned bitbufA, bitbufB, lenA, lenB, len, x, y, nA, nB, nibble;
|
---|
2021 | unsigned char* tA;
|
---|
2022 | unsigned char* tB;
|
---|
2023 | int err = MP_OKAY, first;
|
---|
2024 | int muInit = 0;
|
---|
2025 | int tableInit = 0;
|
---|
2026 | mp_digit mp;
|
---|
2027 | mp_int mu;
|
---|
2028 |
|
---|
2029 | /* argchks */
|
---|
2030 | if (A == NULL || kA == NULL || B == NULL || kB == NULL || C == NULL ||
|
---|
2031 | modulus == NULL)
|
---|
2032 | return ECC_BAD_ARG_E;
|
---|
2033 |
|
---|
2034 |
|
---|
2035 | /* allocate memory */
|
---|
2036 | tA = (unsigned char*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
2037 | if (tA == NULL) {
|
---|
2038 | return GEN_MEM_ERR;
|
---|
2039 | }
|
---|
2040 | tB = (unsigned char*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
2041 | if (tB == NULL) {
|
---|
2042 | XFREE(tA, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
2043 | return GEN_MEM_ERR;
|
---|
2044 | }
|
---|
2045 | XMEMSET(tA, 0, ECC_BUFSIZE);
|
---|
2046 | XMEMSET(tB, 0, ECC_BUFSIZE);
|
---|
2047 |
|
---|
2048 | /* get sizes */
|
---|
2049 | lenA = mp_unsigned_bin_size(kA);
|
---|
2050 | lenB = mp_unsigned_bin_size(kB);
|
---|
2051 | len = MAX(lenA, lenB);
|
---|
2052 |
|
---|
2053 | /* sanity check */
|
---|
2054 | if ((lenA > ECC_BUFSIZE) || (lenB > ECC_BUFSIZE)) {
|
---|
2055 | err = BAD_FUNC_ARG;
|
---|
2056 | }
|
---|
2057 |
|
---|
2058 | if (err == MP_OKAY) {
|
---|
2059 | /* extract and justify kA */
|
---|
2060 | err = mp_to_unsigned_bin(kA, (len - lenA) + tA);
|
---|
2061 |
|
---|
2062 | /* extract and justify kB */
|
---|
2063 | if (err == MP_OKAY)
|
---|
2064 | err = mp_to_unsigned_bin(kB, (len - lenB) + tB);
|
---|
2065 |
|
---|
2066 | /* allocate the table */
|
---|
2067 | if (err == MP_OKAY) {
|
---|
2068 | for (x = 0; x < 16; x++) {
|
---|
2069 | precomp[x] = wc_ecc_new_point();
|
---|
2070 | if (precomp[x] == NULL) {
|
---|
2071 | for (y = 0; y < x; ++y) {
|
---|
2072 | wc_ecc_del_point(precomp[y]);
|
---|
2073 | }
|
---|
2074 | err = GEN_MEM_ERR;
|
---|
2075 | break;
|
---|
2076 | }
|
---|
2077 | }
|
---|
2078 | }
|
---|
2079 | }
|
---|
2080 |
|
---|
2081 | if (err == MP_OKAY)
|
---|
2082 | tableInit = 1;
|
---|
2083 |
|
---|
2084 | if (err == MP_OKAY)
|
---|
2085 | /* init montgomery reduction */
|
---|
2086 | err = mp_montgomery_setup(modulus, &mp);
|
---|
2087 |
|
---|
2088 | if (err == MP_OKAY)
|
---|
2089 | err = mp_init(&mu);
|
---|
2090 | if (err == MP_OKAY)
|
---|
2091 | muInit = 1;
|
---|
2092 |
|
---|
2093 | if (err == MP_OKAY)
|
---|
2094 | err = mp_montgomery_calc_normalization(&mu, modulus);
|
---|
2095 |
|
---|
2096 | if (err == MP_OKAY)
|
---|
2097 | /* copy ones ... */
|
---|
2098 | err = mp_mulmod(A->x, &mu, modulus, precomp[1]->x);
|
---|
2099 |
|
---|
2100 | if (err == MP_OKAY)
|
---|
2101 | err = mp_mulmod(A->y, &mu, modulus, precomp[1]->y);
|
---|
2102 | if (err == MP_OKAY)
|
---|
2103 | err = mp_mulmod(A->z, &mu, modulus, precomp[1]->z);
|
---|
2104 |
|
---|
2105 | if (err == MP_OKAY)
|
---|
2106 | err = mp_mulmod(B->x, &mu, modulus, precomp[1<<2]->x);
|
---|
2107 | if (err == MP_OKAY)
|
---|
2108 | err = mp_mulmod(B->y, &mu, modulus, precomp[1<<2]->y);
|
---|
2109 | if (err == MP_OKAY)
|
---|
2110 | err = mp_mulmod(B->z, &mu, modulus, precomp[1<<2]->z);
|
---|
2111 |
|
---|
2112 | if (err == MP_OKAY)
|
---|
2113 | /* precomp [i,0](A + B) table */
|
---|
2114 | err = ecc_projective_dbl_point(precomp[1], precomp[2], modulus, &mp);
|
---|
2115 |
|
---|
2116 | if (err == MP_OKAY)
|
---|
2117 | err = ecc_projective_add_point(precomp[1], precomp[2], precomp[3],
|
---|
2118 | modulus, &mp);
|
---|
2119 | if (err == MP_OKAY)
|
---|
2120 | /* precomp [0,i](A + B) table */
|
---|
2121 | err = ecc_projective_dbl_point(precomp[1<<2], precomp[2<<2], modulus, &mp);
|
---|
2122 |
|
---|
2123 | if (err == MP_OKAY)
|
---|
2124 | err = ecc_projective_add_point(precomp[1<<2], precomp[2<<2], precomp[3<<2],
|
---|
2125 | modulus, &mp);
|
---|
2126 |
|
---|
2127 | if (err == MP_OKAY) {
|
---|
2128 | /* precomp [i,j](A + B) table (i != 0, j != 0) */
|
---|
2129 | for (x = 1; x < 4; x++) {
|
---|
2130 | for (y = 1; y < 4; y++) {
|
---|
2131 | if (err == MP_OKAY)
|
---|
2132 | err = ecc_projective_add_point(precomp[x], precomp[(y<<2)],
|
---|
2133 | precomp[x+(y<<2)], modulus, &mp);
|
---|
2134 | }
|
---|
2135 | }
|
---|
2136 | }
|
---|
2137 |
|
---|
2138 | if (err == MP_OKAY) {
|
---|
2139 | nibble = 3;
|
---|
2140 | first = 1;
|
---|
2141 | bitbufA = tA[0];
|
---|
2142 | bitbufB = tB[0];
|
---|
2143 |
|
---|
2144 | /* for every byte of the multiplicands */
|
---|
2145 | for (x = -1;; ) {
|
---|
2146 | /* grab a nibble */
|
---|
2147 | if (++nibble == 4) {
|
---|
2148 | ++x; if (x == len) break;
|
---|
2149 | bitbufA = tA[x];
|
---|
2150 | bitbufB = tB[x];
|
---|
2151 | nibble = 0;
|
---|
2152 | }
|
---|
2153 |
|
---|
2154 | /* extract two bits from both, shift/update */
|
---|
2155 | nA = (bitbufA >> 6) & 0x03;
|
---|
2156 | nB = (bitbufB >> 6) & 0x03;
|
---|
2157 | bitbufA = (bitbufA << 2) & 0xFF;
|
---|
2158 | bitbufB = (bitbufB << 2) & 0xFF;
|
---|
2159 |
|
---|
2160 | /* if both zero, if first, continue */
|
---|
2161 | if ((nA == 0) && (nB == 0) && (first == 1)) {
|
---|
2162 | continue;
|
---|
2163 | }
|
---|
2164 |
|
---|
2165 | /* double twice, only if this isn't the first */
|
---|
2166 | if (first == 0) {
|
---|
2167 | /* double twice */
|
---|
2168 | if (err == MP_OKAY)
|
---|
2169 | err = ecc_projective_dbl_point(C, C, modulus, &mp);
|
---|
2170 | if (err == MP_OKAY)
|
---|
2171 | err = ecc_projective_dbl_point(C, C, modulus, &mp);
|
---|
2172 | else
|
---|
2173 | break;
|
---|
2174 | }
|
---|
2175 |
|
---|
2176 | /* if not both zero */
|
---|
2177 | if ((nA != 0) || (nB != 0)) {
|
---|
2178 | if (first == 1) {
|
---|
2179 | /* if first, copy from table */
|
---|
2180 | first = 0;
|
---|
2181 | if (err == MP_OKAY)
|
---|
2182 | err = mp_copy(precomp[nA + (nB<<2)]->x, C->x);
|
---|
2183 |
|
---|
2184 | if (err == MP_OKAY)
|
---|
2185 | err = mp_copy(precomp[nA + (nB<<2)]->y, C->y);
|
---|
2186 |
|
---|
2187 | if (err == MP_OKAY)
|
---|
2188 | err = mp_copy(precomp[nA + (nB<<2)]->z, C->z);
|
---|
2189 | else
|
---|
2190 | break;
|
---|
2191 | } else {
|
---|
2192 | /* if not first, add from table */
|
---|
2193 | if (err == MP_OKAY)
|
---|
2194 | err = ecc_projective_add_point(C, precomp[nA + (nB<<2)], C,
|
---|
2195 | modulus, &mp);
|
---|
2196 | else
|
---|
2197 | break;
|
---|
2198 | }
|
---|
2199 | }
|
---|
2200 | }
|
---|
2201 | }
|
---|
2202 |
|
---|
2203 | if (err == MP_OKAY)
|
---|
2204 | /* reduce to affine */
|
---|
2205 | err = ecc_map(C, modulus, &mp);
|
---|
2206 |
|
---|
2207 | /* clean up */
|
---|
2208 | if (muInit)
|
---|
2209 | mp_clear(&mu);
|
---|
2210 |
|
---|
2211 | if (tableInit) {
|
---|
2212 | for (x = 0; x < 16; x++) {
|
---|
2213 | wc_ecc_del_point(precomp[x]);
|
---|
2214 | }
|
---|
2215 | }
|
---|
2216 | ForceZero(tA, ECC_BUFSIZE);
|
---|
2217 | ForceZero(tB, ECC_BUFSIZE);
|
---|
2218 | XFREE(tA, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
2219 | XFREE(tB, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
2220 |
|
---|
2221 | return err;
|
---|
2222 | }
|
---|
2223 |
|
---|
2224 |
|
---|
2225 | #endif /* ECC_SHAMIR */
|
---|
2226 |
|
---|
2227 |
|
---|
2228 |
|
---|
2229 | /* verify
|
---|
2230 | *
|
---|
2231 | * w = s^-1 mod n
|
---|
2232 | * u1 = xw
|
---|
2233 | * u2 = rw
|
---|
2234 | * X = u1*G + u2*Q
|
---|
2235 | * v = X_x1 mod n
|
---|
2236 | * accept if v == r
|
---|
2237 | */
|
---|
2238 |
|
---|
2239 | /**
|
---|
2240 | Verify an ECC signature
|
---|
2241 | sig The signature to verify
|
---|
2242 | siglen The length of the signature (octets)
|
---|
2243 | hash The hash (message digest) that was signed
|
---|
2244 | hashlen The length of the hash (octets)
|
---|
2245 | stat Result of signature, 1==valid, 0==invalid
|
---|
2246 | key The corresponding public ECC key
|
---|
2247 | return MP_OKAY if successful (even if the signature is not valid)
|
---|
2248 | */
|
---|
2249 | int wc_ecc_verify_hash(const byte* sig, word32 siglen, const byte* hash,
|
---|
2250 | word32 hashlen, int* stat, ecc_key* key)
|
---|
2251 | {
|
---|
2252 | mp_int r;
|
---|
2253 | mp_int s;
|
---|
2254 | int err;
|
---|
2255 |
|
---|
2256 | if (sig == NULL || hash == NULL || stat == NULL || key == NULL)
|
---|
2257 | return ECC_BAD_ARG_E;
|
---|
2258 |
|
---|
2259 | /* default to invalid signature */
|
---|
2260 | *stat = 0;
|
---|
2261 |
|
---|
2262 | /* Note, DecodeECC_DSA_Sig() calls mp_init() on r and s.
|
---|
2263 | * If either of those don't allocate correctly, none of
|
---|
2264 | * the rest of this function will execute, and everything
|
---|
2265 | * gets cleaned up at the end. */
|
---|
2266 | XMEMSET(&r, 0, sizeof(r));
|
---|
2267 | XMEMSET(&s, 0, sizeof(s));
|
---|
2268 |
|
---|
2269 | err = DecodeECC_DSA_Sig(sig, siglen, &r, &s);
|
---|
2270 |
|
---|
2271 | if (err == MP_OKAY)
|
---|
2272 | err = wc_ecc_verify_hash_ex(&r, &s, hash, hashlen, stat, key);
|
---|
2273 |
|
---|
2274 | mp_clear(&r);
|
---|
2275 | mp_clear(&s);
|
---|
2276 |
|
---|
2277 | return err;
|
---|
2278 | }
|
---|
2279 |
|
---|
2280 | /**
|
---|
2281 | Verify an ECC signature
|
---|
2282 | r The signature R component to verify
|
---|
2283 | s The signature S component to verify
|
---|
2284 | hash The hash (message digest) that was signed
|
---|
2285 | hashlen The length of the hash (octets)
|
---|
2286 | stat Result of signature, 1==valid, 0==invalid
|
---|
2287 | key The corresponding public ECC key
|
---|
2288 | return MP_OKAY if successful (even if the signature is not valid)
|
---|
2289 | */
|
---|
2290 | int wc_ecc_verify_hash_ex(mp_int *r, mp_int *s, const byte* hash,
|
---|
2291 | word32 hashlen, int* stat, ecc_key* key)
|
---|
2292 | {
|
---|
2293 | ecc_point *mG, *mQ;
|
---|
2294 | mp_int v;
|
---|
2295 | mp_int w;
|
---|
2296 | mp_int u1;
|
---|
2297 | mp_int u2;
|
---|
2298 | mp_int e;
|
---|
2299 | mp_int p;
|
---|
2300 | mp_int m;
|
---|
2301 | int err;
|
---|
2302 |
|
---|
2303 | if (r == NULL || s == NULL || hash == NULL || stat == NULL || key == NULL)
|
---|
2304 | return ECC_BAD_ARG_E;
|
---|
2305 |
|
---|
2306 | /* default to invalid signature */
|
---|
2307 | *stat = 0;
|
---|
2308 |
|
---|
2309 | /* is the IDX valid ? */
|
---|
2310 | if (wc_ecc_is_valid_idx(key->idx) != 1) {
|
---|
2311 | return ECC_BAD_ARG_E;
|
---|
2312 | }
|
---|
2313 |
|
---|
2314 | /* allocate ints */
|
---|
2315 | if ((err = mp_init_multi(&v, &w, &u1, &u2, &p, &e)) != MP_OKAY) {
|
---|
2316 | return MEMORY_E;
|
---|
2317 | }
|
---|
2318 |
|
---|
2319 | if ((err = mp_init(&m)) != MP_OKAY) {
|
---|
2320 | mp_clear(&v);
|
---|
2321 | mp_clear(&w);
|
---|
2322 | mp_clear(&u1);
|
---|
2323 | mp_clear(&u2);
|
---|
2324 | mp_clear(&p);
|
---|
2325 | mp_clear(&e);
|
---|
2326 | return MEMORY_E;
|
---|
2327 | }
|
---|
2328 |
|
---|
2329 | /* allocate points */
|
---|
2330 | mG = wc_ecc_new_point();
|
---|
2331 | mQ = wc_ecc_new_point();
|
---|
2332 | if (mQ == NULL || mG == NULL)
|
---|
2333 | err = MEMORY_E;
|
---|
2334 |
|
---|
2335 | /* get the order */
|
---|
2336 | if (err == MP_OKAY)
|
---|
2337 | err = mp_read_radix(&p, (char *)key->dp->order, 16);
|
---|
2338 |
|
---|
2339 | /* get the modulus */
|
---|
2340 | if (err == MP_OKAY)
|
---|
2341 | err = mp_read_radix(&m, (char *)key->dp->prime, 16);
|
---|
2342 |
|
---|
2343 | /* check for zero */
|
---|
2344 | if (err == MP_OKAY) {
|
---|
2345 | if (mp_iszero(r) || mp_iszero(s) || mp_cmp(r, &p) != MP_LT ||
|
---|
2346 | mp_cmp(s, &p) != MP_LT)
|
---|
2347 | err = MP_ZERO_E;
|
---|
2348 | }
|
---|
2349 | /* read hash */
|
---|
2350 | if (err == MP_OKAY) {
|
---|
2351 | /* we may need to truncate if hash is longer than key size */
|
---|
2352 | unsigned int orderBits = mp_count_bits(&p);
|
---|
2353 |
|
---|
2354 | /* truncate down to byte size, may be all that's needed */
|
---|
2355 | if ( (WOLFSSL_BIT_SIZE * hashlen) > orderBits)
|
---|
2356 | hashlen = (orderBits + WOLFSSL_BIT_SIZE - 1)/WOLFSSL_BIT_SIZE;
|
---|
2357 | err = mp_read_unsigned_bin(&e, hash, hashlen);
|
---|
2358 |
|
---|
2359 | /* may still need bit truncation too */
|
---|
2360 | if (err == MP_OKAY && (WOLFSSL_BIT_SIZE * hashlen) > orderBits)
|
---|
2361 | mp_rshb(&e, WOLFSSL_BIT_SIZE - (orderBits & 0x7));
|
---|
2362 | }
|
---|
2363 |
|
---|
2364 | /* w = s^-1 mod n */
|
---|
2365 | if (err == MP_OKAY)
|
---|
2366 | err = mp_invmod(s, &p, &w);
|
---|
2367 |
|
---|
2368 | /* u1 = ew */
|
---|
2369 | if (err == MP_OKAY)
|
---|
2370 | err = mp_mulmod(&e, &w, &p, &u1);
|
---|
2371 |
|
---|
2372 | /* u2 = rw */
|
---|
2373 | if (err == MP_OKAY)
|
---|
2374 | err = mp_mulmod(r, &w, &p, &u2);
|
---|
2375 |
|
---|
2376 | /* find mG and mQ */
|
---|
2377 | if (err == MP_OKAY)
|
---|
2378 | err = mp_read_radix(mG->x, (char *)key->dp->Gx, 16);
|
---|
2379 |
|
---|
2380 | if (err == MP_OKAY)
|
---|
2381 | err = mp_read_radix(mG->y, (char *)key->dp->Gy, 16);
|
---|
2382 | if (err == MP_OKAY)
|
---|
2383 | mp_set(mG->z, 1);
|
---|
2384 |
|
---|
2385 | if (err == MP_OKAY)
|
---|
2386 | err = mp_copy(key->pubkey.x, mQ->x);
|
---|
2387 | if (err == MP_OKAY)
|
---|
2388 | err = mp_copy(key->pubkey.y, mQ->y);
|
---|
2389 | if (err == MP_OKAY)
|
---|
2390 | err = mp_copy(key->pubkey.z, mQ->z);
|
---|
2391 |
|
---|
2392 | #ifndef ECC_SHAMIR
|
---|
2393 | {
|
---|
2394 | mp_digit mp;
|
---|
2395 |
|
---|
2396 | /* compute u1*mG + u2*mQ = mG */
|
---|
2397 | if (err == MP_OKAY)
|
---|
2398 | err = wc_ecc_mulmod(&u1, mG, mG, &m, 0);
|
---|
2399 | if (err == MP_OKAY)
|
---|
2400 | err = wc_ecc_mulmod(&u2, mQ, mQ, &m, 0);
|
---|
2401 |
|
---|
2402 | /* find the montgomery mp */
|
---|
2403 | if (err == MP_OKAY)
|
---|
2404 | err = mp_montgomery_setup(&m, &mp);
|
---|
2405 |
|
---|
2406 | /* add them */
|
---|
2407 | if (err == MP_OKAY)
|
---|
2408 | err = ecc_projective_add_point(mQ, mG, mG, &m, &mp);
|
---|
2409 |
|
---|
2410 | /* reduce */
|
---|
2411 | if (err == MP_OKAY)
|
---|
2412 | err = ecc_map(mG, &m, &mp);
|
---|
2413 | }
|
---|
2414 | #else
|
---|
2415 | /* use Shamir's trick to compute u1*mG + u2*mQ using half the doubles */
|
---|
2416 | if (err == MP_OKAY)
|
---|
2417 | err = ecc_mul2add(mG, &u1, mQ, &u2, mG, &m);
|
---|
2418 | #endif /* ECC_SHAMIR */
|
---|
2419 |
|
---|
2420 | /* v = X_x1 mod n */
|
---|
2421 | if (err == MP_OKAY)
|
---|
2422 | err = mp_mod(mG->x, &p, &v);
|
---|
2423 |
|
---|
2424 | /* does v == r */
|
---|
2425 | if (err == MP_OKAY) {
|
---|
2426 | if (mp_cmp(&v, r) == MP_EQ)
|
---|
2427 | *stat = 1;
|
---|
2428 | }
|
---|
2429 |
|
---|
2430 | wc_ecc_del_point(mG);
|
---|
2431 | wc_ecc_del_point(mQ);
|
---|
2432 |
|
---|
2433 | mp_clear(&v);
|
---|
2434 | mp_clear(&w);
|
---|
2435 | mp_clear(&u1);
|
---|
2436 | mp_clear(&u2);
|
---|
2437 | mp_clear(&p);
|
---|
2438 | mp_clear(&e);
|
---|
2439 | mp_clear(&m);
|
---|
2440 |
|
---|
2441 | return err;
|
---|
2442 | }
|
---|
2443 |
|
---|
2444 | /* import point from der */
|
---|
2445 | int wc_ecc_import_point_der(byte* in, word32 inLen, const int curve_idx,
|
---|
2446 | ecc_point* point)
|
---|
2447 | {
|
---|
2448 | int err = 0;
|
---|
2449 | int compressed = 0;
|
---|
2450 |
|
---|
2451 | if (in == NULL || point == NULL || (curve_idx < 0) ||
|
---|
2452 | (wc_ecc_is_valid_idx(curve_idx) == 0))
|
---|
2453 | return ECC_BAD_ARG_E;
|
---|
2454 |
|
---|
2455 | /* must be odd */
|
---|
2456 | if ((inLen & 1) == 0) {
|
---|
2457 | return ECC_BAD_ARG_E;
|
---|
2458 | }
|
---|
2459 |
|
---|
2460 | /* init point */
|
---|
2461 | #ifdef ALT_ECC_SIZE
|
---|
2462 | point->x = (mp_int*)&point->xyz[0];
|
---|
2463 | point->y = (mp_int*)&point->xyz[1];
|
---|
2464 | point->z = (mp_int*)&point->xyz[2];
|
---|
2465 | alt_fp_init(point->x);
|
---|
2466 | alt_fp_init(point->y);
|
---|
2467 | alt_fp_init(point->z);
|
---|
2468 | #else
|
---|
2469 | err = mp_init_multi(point->x, point->y, point->z, NULL, NULL, NULL);
|
---|
2470 | #endif
|
---|
2471 | if (err != MP_OKAY)
|
---|
2472 | return MEMORY_E;
|
---|
2473 |
|
---|
2474 | /* check for 4, 2, or 3 */
|
---|
2475 | if (in[0] != 0x04 && in[0] != 0x02 && in[0] != 0x03) {
|
---|
2476 | err = ASN_PARSE_E;
|
---|
2477 | }
|
---|
2478 |
|
---|
2479 | if (in[0] == 0x02 || in[0] == 0x03) {
|
---|
2480 | #ifdef HAVE_COMP_KEY
|
---|
2481 | compressed = 1;
|
---|
2482 | #else
|
---|
2483 | err = NOT_COMPILED_IN;
|
---|
2484 | #endif
|
---|
2485 | }
|
---|
2486 |
|
---|
2487 | /* read data */
|
---|
2488 | if (err == MP_OKAY)
|
---|
2489 | err = mp_read_unsigned_bin(point->x, (byte*)in+1, (inLen-1)>>1);
|
---|
2490 |
|
---|
2491 | #ifdef HAVE_COMP_KEY
|
---|
2492 | if (err == MP_OKAY && compressed == 1) { /* build y */
|
---|
2493 | mp_int t1, t2, prime, a, b;
|
---|
2494 |
|
---|
2495 | if (mp_init_multi(&t1, &t2, &prime, &a, &b, NULL) != MP_OKAY)
|
---|
2496 | err = MEMORY_E;
|
---|
2497 |
|
---|
2498 | /* load prime */
|
---|
2499 | if (err == MP_OKAY)
|
---|
2500 | err = mp_read_radix(&prime, (char *)ecc_sets[curve_idx].prime, 16);
|
---|
2501 |
|
---|
2502 | /* load a */
|
---|
2503 | if (err == MP_OKAY)
|
---|
2504 | err = mp_read_radix(&a, (char *)ecc_sets[curve_idx].Af, 16);
|
---|
2505 |
|
---|
2506 | /* load b */
|
---|
2507 | if (err == MP_OKAY)
|
---|
2508 | err = mp_read_radix(&b, (char *)ecc_sets[curve_idx].Bf, 16);
|
---|
2509 |
|
---|
2510 | /* compute x^3 */
|
---|
2511 | if (err == MP_OKAY)
|
---|
2512 | err = mp_sqr(point->x, &t1);
|
---|
2513 |
|
---|
2514 | if (err == MP_OKAY)
|
---|
2515 | err = mp_mulmod(&t1, point->x, &prime, &t1);
|
---|
2516 |
|
---|
2517 | /* compute x^3 + a*x */
|
---|
2518 | if (err == MP_OKAY)
|
---|
2519 | err = mp_mulmod(&a, point->x, &prime, &t2);
|
---|
2520 |
|
---|
2521 | if (err == MP_OKAY)
|
---|
2522 | err = mp_add(&t1, &t2, &t1);
|
---|
2523 |
|
---|
2524 | /* compute x^3 + a*x + b */
|
---|
2525 | if (err == MP_OKAY)
|
---|
2526 | err = mp_add(&t1, &b, &t1);
|
---|
2527 |
|
---|
2528 | /* compute sqrt(x^3 + a*x + b) */
|
---|
2529 | if (err == MP_OKAY)
|
---|
2530 | err = mp_sqrtmod_prime(&t1, &prime, &t2);
|
---|
2531 |
|
---|
2532 | /* adjust y */
|
---|
2533 | if (err == MP_OKAY) {
|
---|
2534 | if ((mp_isodd(&t2) && in[0] == 0x03) ||
|
---|
2535 | (!mp_isodd(&t2) && in[0] == 0x02)) {
|
---|
2536 | err = mp_mod(&t2, &prime, point->y);
|
---|
2537 | }
|
---|
2538 | else {
|
---|
2539 | err = mp_submod(&prime, &t2, &prime, point->y);
|
---|
2540 | }
|
---|
2541 | }
|
---|
2542 |
|
---|
2543 | mp_clear(&a);
|
---|
2544 | mp_clear(&b);
|
---|
2545 | mp_clear(&prime);
|
---|
2546 | mp_clear(&t2);
|
---|
2547 | mp_clear(&t1);
|
---|
2548 | }
|
---|
2549 | #endif
|
---|
2550 |
|
---|
2551 | if (err == MP_OKAY && compressed == 0)
|
---|
2552 | err = mp_read_unsigned_bin(point->y,
|
---|
2553 | (byte*)in+1+((inLen-1)>>1), (inLen-1)>>1);
|
---|
2554 | if (err == MP_OKAY)
|
---|
2555 | mp_set(point->z, 1);
|
---|
2556 |
|
---|
2557 | if (err != MP_OKAY) {
|
---|
2558 | mp_clear(point->x);
|
---|
2559 | mp_clear(point->y);
|
---|
2560 | mp_clear(point->z);
|
---|
2561 | }
|
---|
2562 |
|
---|
2563 | return err;
|
---|
2564 | }
|
---|
2565 |
|
---|
2566 | /* export point to der */
|
---|
2567 | int wc_ecc_export_point_der(const int curve_idx, ecc_point* point, byte* out,
|
---|
2568 | word32* outLen)
|
---|
2569 | {
|
---|
2570 | #ifdef WOLFSSL_SMALL_STACK
|
---|
2571 | byte* buf;
|
---|
2572 | #else
|
---|
2573 | byte buf[ECC_BUFSIZE];
|
---|
2574 | #endif
|
---|
2575 | word32 numlen;
|
---|
2576 | int ret = MP_OKAY;
|
---|
2577 |
|
---|
2578 | if ((curve_idx < 0) || (wc_ecc_is_valid_idx(curve_idx) == 0))
|
---|
2579 | return ECC_BAD_ARG_E;
|
---|
2580 |
|
---|
2581 | /* return length needed only */
|
---|
2582 | if (point != NULL && out == NULL && outLen != NULL) {
|
---|
2583 | numlen = ecc_sets[curve_idx].size;
|
---|
2584 | *outLen = 1 + 2*numlen;
|
---|
2585 | return LENGTH_ONLY_E;
|
---|
2586 | }
|
---|
2587 |
|
---|
2588 | if (point == NULL || out == NULL || outLen == NULL)
|
---|
2589 | return ECC_BAD_ARG_E;
|
---|
2590 |
|
---|
2591 | numlen = ecc_sets[curve_idx].size;
|
---|
2592 |
|
---|
2593 | if (*outLen < (1 + 2*numlen)) {
|
---|
2594 | *outLen = 1 + 2*numlen;
|
---|
2595 | return BUFFER_E;
|
---|
2596 | }
|
---|
2597 |
|
---|
2598 | /* store byte 0x04 */
|
---|
2599 | out[0] = 0x04;
|
---|
2600 |
|
---|
2601 | #ifdef WOLFSSL_SMALL_STACK
|
---|
2602 | buf = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
2603 | if (buf == NULL)
|
---|
2604 | return MEMORY_E;
|
---|
2605 | #endif
|
---|
2606 |
|
---|
2607 | /* pad and store x */
|
---|
2608 | XMEMSET(buf, 0, ECC_BUFSIZE);
|
---|
2609 | ret = mp_to_unsigned_bin(point->x, buf +
|
---|
2610 | (numlen - mp_unsigned_bin_size(point->x)));
|
---|
2611 | if (ret != MP_OKAY)
|
---|
2612 | goto done;
|
---|
2613 | XMEMCPY(out+1, buf, numlen);
|
---|
2614 |
|
---|
2615 | /* pad and store y */
|
---|
2616 | XMEMSET(buf, 0, ECC_BUFSIZE);
|
---|
2617 | ret = mp_to_unsigned_bin(point->y, buf +
|
---|
2618 | (numlen - mp_unsigned_bin_size(point->y)));
|
---|
2619 | if (ret != MP_OKAY)
|
---|
2620 | goto done;
|
---|
2621 | XMEMCPY(out+1+numlen, buf, numlen);
|
---|
2622 |
|
---|
2623 | *outLen = 1 + 2*numlen;
|
---|
2624 |
|
---|
2625 | done:
|
---|
2626 | #ifdef WOLFSSL_SMALL_STACK
|
---|
2627 | XFREE(buf, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
2628 | #endif
|
---|
2629 |
|
---|
2630 | return ret;
|
---|
2631 | }
|
---|
2632 |
|
---|
2633 |
|
---|
2634 | /* export public ECC key in ANSI X9.63 format */
|
---|
2635 | int wc_ecc_export_x963(ecc_key* key, byte* out, word32* outLen)
|
---|
2636 | {
|
---|
2637 | #ifdef WOLFSSL_SMALL_STACK
|
---|
2638 | byte* buf;
|
---|
2639 | #else
|
---|
2640 | byte buf[ECC_BUFSIZE];
|
---|
2641 | #endif
|
---|
2642 | word32 numlen;
|
---|
2643 | int ret = MP_OKAY;
|
---|
2644 |
|
---|
2645 | /* return length needed only */
|
---|
2646 | if (key != NULL && out == NULL && outLen != NULL) {
|
---|
2647 | numlen = key->dp->size;
|
---|
2648 | *outLen = 1 + 2*numlen;
|
---|
2649 | return LENGTH_ONLY_E;
|
---|
2650 | }
|
---|
2651 |
|
---|
2652 | if (key == NULL || out == NULL || outLen == NULL)
|
---|
2653 | return ECC_BAD_ARG_E;
|
---|
2654 |
|
---|
2655 | if (wc_ecc_is_valid_idx(key->idx) == 0) {
|
---|
2656 | return ECC_BAD_ARG_E;
|
---|
2657 | }
|
---|
2658 | numlen = key->dp->size;
|
---|
2659 |
|
---|
2660 | if (*outLen < (1 + 2*numlen)) {
|
---|
2661 | *outLen = 1 + 2*numlen;
|
---|
2662 | return BUFFER_E;
|
---|
2663 | }
|
---|
2664 |
|
---|
2665 | /* store byte 0x04 */
|
---|
2666 | out[0] = 0x04;
|
---|
2667 |
|
---|
2668 | #ifdef WOLFSSL_SMALL_STACK
|
---|
2669 | buf = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
2670 | if (buf == NULL)
|
---|
2671 | return MEMORY_E;
|
---|
2672 | #endif
|
---|
2673 |
|
---|
2674 | /* pad and store x */
|
---|
2675 | XMEMSET(buf, 0, ECC_BUFSIZE);
|
---|
2676 | ret = mp_to_unsigned_bin(key->pubkey.x,
|
---|
2677 | buf + (numlen - mp_unsigned_bin_size(key->pubkey.x)));
|
---|
2678 | if (ret != MP_OKAY)
|
---|
2679 | goto done;
|
---|
2680 | XMEMCPY(out+1, buf, numlen);
|
---|
2681 |
|
---|
2682 | /* pad and store y */
|
---|
2683 | XMEMSET(buf, 0, ECC_BUFSIZE);
|
---|
2684 | ret = mp_to_unsigned_bin(key->pubkey.y,
|
---|
2685 | buf + (numlen - mp_unsigned_bin_size(key->pubkey.y)));
|
---|
2686 | if (ret != MP_OKAY)
|
---|
2687 | goto done;
|
---|
2688 | XMEMCPY(out+1+numlen, buf, numlen);
|
---|
2689 |
|
---|
2690 | *outLen = 1 + 2*numlen;
|
---|
2691 |
|
---|
2692 | done:
|
---|
2693 | #ifdef WOLFSSL_SMALL_STACK
|
---|
2694 | XFREE(buf, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
2695 | #endif
|
---|
2696 |
|
---|
2697 | return ret;
|
---|
2698 | }
|
---|
2699 |
|
---|
2700 |
|
---|
2701 | /* export public ECC key in ANSI X9.63 format, extended with
|
---|
2702 | * compression option */
|
---|
2703 | int wc_ecc_export_x963_ex(ecc_key* key, byte* out, word32* outLen,
|
---|
2704 | int compressed)
|
---|
2705 | {
|
---|
2706 | if (compressed == 0)
|
---|
2707 | return wc_ecc_export_x963(key, out, outLen);
|
---|
2708 | #ifdef HAVE_COMP_KEY
|
---|
2709 | else
|
---|
2710 | return wc_ecc_export_x963_compressed(key, out, outLen);
|
---|
2711 | #endif
|
---|
2712 |
|
---|
2713 | return NOT_COMPILED_IN;
|
---|
2714 | }
|
---|
2715 |
|
---|
2716 |
|
---|
2717 | /* is ec point on curve descriped by dp ? */
|
---|
2718 | static int ecc_is_point(const ecc_set_type* dp, ecc_point* ecp, mp_int* prime)
|
---|
2719 | {
|
---|
2720 | mp_int b, t1, t2;
|
---|
2721 | int err;
|
---|
2722 |
|
---|
2723 | if ((err = mp_init_multi(&b, &t1, &t2, NULL, NULL, NULL)) != MP_OKAY) {
|
---|
2724 | return err;
|
---|
2725 | }
|
---|
2726 |
|
---|
2727 | /* load b */
|
---|
2728 | err = mp_read_radix(&b, dp->Bf, 16);
|
---|
2729 |
|
---|
2730 | /* compute y^2 */
|
---|
2731 | if (err == MP_OKAY)
|
---|
2732 | err = mp_sqr(ecp->y, &t1);
|
---|
2733 |
|
---|
2734 | /* compute x^3 */
|
---|
2735 | if (err == MP_OKAY)
|
---|
2736 | err = mp_sqr(ecp->x, &t2);
|
---|
2737 | if (err == MP_OKAY)
|
---|
2738 | err = mp_mod(&t2, prime, &t2);
|
---|
2739 | if (err == MP_OKAY)
|
---|
2740 | err = mp_mul(ecp->x, &t2, &t2);
|
---|
2741 |
|
---|
2742 | /* compute y^2 - x^3 */
|
---|
2743 | if (err == MP_OKAY)
|
---|
2744 | err = mp_sub(&t1, &t2, &t1);
|
---|
2745 |
|
---|
2746 | /* compute y^2 - x^3 + 3x */
|
---|
2747 | if (err == MP_OKAY)
|
---|
2748 | err = mp_add(&t1, ecp->x, &t1);
|
---|
2749 | if (err == MP_OKAY)
|
---|
2750 | err = mp_add(&t1, ecp->x, &t1);
|
---|
2751 | if (err == MP_OKAY)
|
---|
2752 | err = mp_add(&t1, ecp->x, &t1);
|
---|
2753 | if (err == MP_OKAY)
|
---|
2754 | err = mp_mod(&t1, prime, &t1);
|
---|
2755 |
|
---|
2756 | while (err == MP_OKAY && mp_cmp_d(&t1, 0) == MP_LT) {
|
---|
2757 | err = mp_add(&t1, prime, &t1);
|
---|
2758 | }
|
---|
2759 | while (err == MP_OKAY && mp_cmp(&t1, prime) != MP_LT) {
|
---|
2760 | err = mp_sub(&t1, prime, &t1);
|
---|
2761 | }
|
---|
2762 |
|
---|
2763 | /* compare to b */
|
---|
2764 | if (err == MP_OKAY) {
|
---|
2765 | if (mp_cmp(&t1, &b) != MP_EQ) {
|
---|
2766 | err = MP_VAL;
|
---|
2767 | } else {
|
---|
2768 | err = MP_OKAY;
|
---|
2769 | }
|
---|
2770 | }
|
---|
2771 |
|
---|
2772 | mp_clear(&b);
|
---|
2773 | mp_clear(&t1);
|
---|
2774 | mp_clear(&t2);
|
---|
2775 |
|
---|
2776 | return err;
|
---|
2777 | }
|
---|
2778 |
|
---|
2779 |
|
---|
2780 | /* validate privkey * generator == pubkey, 0 on success */
|
---|
2781 | static int ecc_check_privkey_gen(ecc_key* key, mp_int* prime)
|
---|
2782 | {
|
---|
2783 | ecc_point* base = NULL;
|
---|
2784 | ecc_point* res = NULL;
|
---|
2785 | int err;
|
---|
2786 |
|
---|
2787 | if (key == NULL)
|
---|
2788 | return BAD_FUNC_ARG;
|
---|
2789 |
|
---|
2790 | base = wc_ecc_new_point();
|
---|
2791 | if (base == NULL)
|
---|
2792 | return MEMORY_E;
|
---|
2793 |
|
---|
2794 | /* set up base generator */
|
---|
2795 | err = mp_read_radix(base->x, (char*)key->dp->Gx, 16);
|
---|
2796 | if (err == MP_OKAY)
|
---|
2797 | err = mp_read_radix(base->y, (char*)key->dp->Gy, 16);
|
---|
2798 | if (err == MP_OKAY)
|
---|
2799 | mp_set(base->z, 1);
|
---|
2800 |
|
---|
2801 | if (err == MP_OKAY) {
|
---|
2802 | res = wc_ecc_new_point();
|
---|
2803 | if (res == NULL)
|
---|
2804 | err = MEMORY_E;
|
---|
2805 | else {
|
---|
2806 | err = wc_ecc_mulmod(&key->k, base, res, prime, 1);
|
---|
2807 | if (err == MP_OKAY) {
|
---|
2808 | /* compare result to public key */
|
---|
2809 | if (mp_cmp(res->x, key->pubkey.x) != MP_EQ ||
|
---|
2810 | mp_cmp(res->y, key->pubkey.y) != MP_EQ ||
|
---|
2811 | mp_cmp(res->z, key->pubkey.z) != MP_EQ) {
|
---|
2812 | /* didn't match */
|
---|
2813 | err = ECC_PRIV_KEY_E;
|
---|
2814 | }
|
---|
2815 | }
|
---|
2816 | }
|
---|
2817 | }
|
---|
2818 |
|
---|
2819 | wc_ecc_del_point(res);
|
---|
2820 | wc_ecc_del_point(base);
|
---|
2821 |
|
---|
2822 | return err;
|
---|
2823 | }
|
---|
2824 |
|
---|
2825 |
|
---|
2826 | #ifdef WOLFSSL_VALIDATE_ECC_IMPORT
|
---|
2827 |
|
---|
2828 | /* check privkey generator helper, creates prime needed */
|
---|
2829 | static int ecc_check_privkey_gen_helper(ecc_key* key)
|
---|
2830 | {
|
---|
2831 | mp_int prime;
|
---|
2832 | int err;
|
---|
2833 |
|
---|
2834 | if (key == NULL)
|
---|
2835 | return BAD_FUNC_ARG;
|
---|
2836 |
|
---|
2837 | err = mp_init(&prime);
|
---|
2838 | if (err != MP_OKAY)
|
---|
2839 | return err;
|
---|
2840 |
|
---|
2841 | err = mp_read_radix(&prime, (char*)key->dp->prime, 16);
|
---|
2842 |
|
---|
2843 | if (err == MP_OKAY);
|
---|
2844 | err = ecc_check_privkey_gen(key, &prime);
|
---|
2845 |
|
---|
2846 | mp_clear(&prime);
|
---|
2847 |
|
---|
2848 | return err;
|
---|
2849 | }
|
---|
2850 |
|
---|
2851 | #endif /* WOLFSSL_VALIDATE_ECC_IMPORT */
|
---|
2852 |
|
---|
2853 |
|
---|
2854 | /* validate order * pubkey = point at infinity, 0 on success */
|
---|
2855 | static int ecc_check_pubkey_order(ecc_key* key, mp_int* prime, mp_int* order)
|
---|
2856 | {
|
---|
2857 | ecc_point* inf = NULL;
|
---|
2858 | int err;
|
---|
2859 |
|
---|
2860 | if (key == NULL)
|
---|
2861 | return BAD_FUNC_ARG;
|
---|
2862 |
|
---|
2863 | inf = wc_ecc_new_point();
|
---|
2864 | if (inf == NULL)
|
---|
2865 | err = MEMORY_E;
|
---|
2866 | else {
|
---|
2867 | err = wc_ecc_mulmod(order, &key->pubkey, inf, prime, 1);
|
---|
2868 | if (err == MP_OKAY && !wc_ecc_point_is_at_infinity(inf))
|
---|
2869 | err = ECC_INF_E;
|
---|
2870 | }
|
---|
2871 |
|
---|
2872 | wc_ecc_del_point(inf);
|
---|
2873 |
|
---|
2874 | return err;
|
---|
2875 | }
|
---|
2876 |
|
---|
2877 |
|
---|
2878 | /* perform sanity checks on ec key validity, 0 on success */
|
---|
2879 | int wc_ecc_check_key(ecc_key* key)
|
---|
2880 | {
|
---|
2881 | mp_int prime; /* used by multiple calls so let's cache */
|
---|
2882 | mp_int order; /* other callers have, so let's gen here */
|
---|
2883 | int err;
|
---|
2884 |
|
---|
2885 | if (key == NULL)
|
---|
2886 | return BAD_FUNC_ARG;
|
---|
2887 |
|
---|
2888 | /* pubkey point cannot be at inifinity */
|
---|
2889 | if (wc_ecc_point_is_at_infinity(&key->pubkey))
|
---|
2890 | return ECC_INF_E;
|
---|
2891 |
|
---|
2892 | err = mp_init_multi(&prime, &order, NULL, NULL, NULL, NULL);
|
---|
2893 | if (err != MP_OKAY)
|
---|
2894 | return err;
|
---|
2895 |
|
---|
2896 | err = mp_read_radix(&prime, (char*)key->dp->prime, 16);
|
---|
2897 |
|
---|
2898 | /* make sure point is actually on curve */
|
---|
2899 | if (err == MP_OKAY)
|
---|
2900 | err = ecc_is_point(key->dp, &key->pubkey, &prime);
|
---|
2901 |
|
---|
2902 | if (err == MP_OKAY)
|
---|
2903 | err = mp_read_radix(&order, (char*)key->dp->order, 16);
|
---|
2904 |
|
---|
2905 | /* pubkey * order must be at infinity */
|
---|
2906 | if (err == MP_OKAY)
|
---|
2907 | err = ecc_check_pubkey_order(key, &prime, &order);
|
---|
2908 |
|
---|
2909 | /* private * base generator must equal pubkey */
|
---|
2910 | if (err == MP_OKAY && key->type == ECC_PRIVATEKEY)
|
---|
2911 | err = ecc_check_privkey_gen(key, &prime);
|
---|
2912 |
|
---|
2913 | mp_clear(&order);
|
---|
2914 | mp_clear(&prime);
|
---|
2915 |
|
---|
2916 | return err;
|
---|
2917 | }
|
---|
2918 |
|
---|
2919 |
|
---|
2920 | /* import public ECC key in ANSI X9.63 format */
|
---|
2921 | int wc_ecc_import_x963(const byte* in, word32 inLen, ecc_key* key)
|
---|
2922 | {
|
---|
2923 | int x, err;
|
---|
2924 | int compressed = 0;
|
---|
2925 |
|
---|
2926 | if (in == NULL || key == NULL)
|
---|
2927 | return ECC_BAD_ARG_E;
|
---|
2928 |
|
---|
2929 | /* must be odd */
|
---|
2930 | if ((inLen & 1) == 0) {
|
---|
2931 | return ECC_BAD_ARG_E;
|
---|
2932 | }
|
---|
2933 |
|
---|
2934 | /* init key */
|
---|
2935 | #ifdef ALT_ECC_SIZE
|
---|
2936 | key->pubkey.x = (mp_int*)&key->pubkey.xyz[0];
|
---|
2937 | key->pubkey.y = (mp_int*)&key->pubkey.xyz[1];
|
---|
2938 | key->pubkey.z = (mp_int*)&key->pubkey.xyz[2];
|
---|
2939 | alt_fp_init(key->pubkey.x);
|
---|
2940 | alt_fp_init(key->pubkey.y);
|
---|
2941 | alt_fp_init(key->pubkey.z);
|
---|
2942 | err = mp_init(&key->k);
|
---|
2943 | #else
|
---|
2944 | err = mp_init_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z, &key->k,
|
---|
2945 | NULL, NULL);
|
---|
2946 | #endif
|
---|
2947 | if (err != MP_OKAY)
|
---|
2948 | return MEMORY_E;
|
---|
2949 |
|
---|
2950 | /* check for 4, 2, or 3 */
|
---|
2951 | if (in[0] != 0x04 && in[0] != 0x02 && in[0] != 0x03) {
|
---|
2952 | err = ASN_PARSE_E;
|
---|
2953 | }
|
---|
2954 |
|
---|
2955 | if (in[0] == 0x02 || in[0] == 0x03) {
|
---|
2956 | #ifdef HAVE_COMP_KEY
|
---|
2957 | compressed = 1;
|
---|
2958 | #else
|
---|
2959 | err = NOT_COMPILED_IN;
|
---|
2960 | #endif
|
---|
2961 | }
|
---|
2962 |
|
---|
2963 | if (err == MP_OKAY) {
|
---|
2964 | /* determine the idx */
|
---|
2965 |
|
---|
2966 | if (compressed)
|
---|
2967 | inLen = (inLen-1)*2 + 1; /* used uncompressed len */
|
---|
2968 |
|
---|
2969 | for (x = 0; ecc_sets[x].size != 0; x++) {
|
---|
2970 | if ((unsigned)ecc_sets[x].size >= ((inLen-1)>>1)) {
|
---|
2971 | break;
|
---|
2972 | }
|
---|
2973 | }
|
---|
2974 | if (ecc_sets[x].size == 0) {
|
---|
2975 | err = ASN_PARSE_E;
|
---|
2976 | } else {
|
---|
2977 | /* set the idx */
|
---|
2978 | key->idx = x;
|
---|
2979 | key->dp = &ecc_sets[x];
|
---|
2980 | key->type = ECC_PUBLICKEY;
|
---|
2981 | }
|
---|
2982 | }
|
---|
2983 |
|
---|
2984 | /* read data */
|
---|
2985 | if (err == MP_OKAY)
|
---|
2986 | err = mp_read_unsigned_bin(key->pubkey.x, (byte*)in+1, (inLen-1)>>1);
|
---|
2987 |
|
---|
2988 | #ifdef HAVE_COMP_KEY
|
---|
2989 | if (err == MP_OKAY && compressed == 1) { /* build y */
|
---|
2990 | mp_int t1, t2, prime, a, b;
|
---|
2991 |
|
---|
2992 | if (mp_init_multi(&t1, &t2, &prime, &a, &b, NULL) != MP_OKAY)
|
---|
2993 | err = MEMORY_E;
|
---|
2994 |
|
---|
2995 | /* load prime */
|
---|
2996 | if (err == MP_OKAY)
|
---|
2997 | err = mp_read_radix(&prime, (char *)key->dp->prime, 16);
|
---|
2998 |
|
---|
2999 | /* load a */
|
---|
3000 | if (err == MP_OKAY)
|
---|
3001 | err = mp_read_radix(&a, (char *)key->dp->Af, 16);
|
---|
3002 |
|
---|
3003 | /* load b */
|
---|
3004 | if (err == MP_OKAY)
|
---|
3005 | err = mp_read_radix(&b, (char *)key->dp->Bf, 16);
|
---|
3006 |
|
---|
3007 | /* compute x^3 */
|
---|
3008 | if (err == MP_OKAY)
|
---|
3009 | err = mp_sqr(key->pubkey.x, &t1);
|
---|
3010 |
|
---|
3011 | if (err == MP_OKAY)
|
---|
3012 | err = mp_mulmod(&t1, key->pubkey.x, &prime, &t1);
|
---|
3013 |
|
---|
3014 | /* compute x^3 + a*x */
|
---|
3015 | if (err == MP_OKAY)
|
---|
3016 | err = mp_mulmod(&a, key->pubkey.x, &prime, &t2);
|
---|
3017 |
|
---|
3018 | if (err == MP_OKAY)
|
---|
3019 | err = mp_add(&t1, &t2, &t1);
|
---|
3020 |
|
---|
3021 | /* compute x^3 + a*x + b */
|
---|
3022 | if (err == MP_OKAY)
|
---|
3023 | err = mp_add(&t1, &b, &t1);
|
---|
3024 |
|
---|
3025 | /* compute sqrt(x^3 + a*x + b) */
|
---|
3026 | if (err == MP_OKAY)
|
---|
3027 | err = mp_sqrtmod_prime(&t1, &prime, &t2);
|
---|
3028 |
|
---|
3029 | /* adjust y */
|
---|
3030 | if (err == MP_OKAY) {
|
---|
3031 | if ((mp_isodd(&t2) && in[0] == 0x03) ||
|
---|
3032 | (!mp_isodd(&t2) && in[0] == 0x02)) {
|
---|
3033 | err = mp_mod(&t2, &prime, key->pubkey.y);
|
---|
3034 | }
|
---|
3035 | else {
|
---|
3036 | err = mp_submod(&prime, &t2, &prime, key->pubkey.y);
|
---|
3037 | }
|
---|
3038 | }
|
---|
3039 |
|
---|
3040 | mp_clear(&a);
|
---|
3041 | mp_clear(&b);
|
---|
3042 | mp_clear(&prime);
|
---|
3043 | mp_clear(&t2);
|
---|
3044 | mp_clear(&t1);
|
---|
3045 | }
|
---|
3046 | #endif
|
---|
3047 |
|
---|
3048 | if (err == MP_OKAY && compressed == 0)
|
---|
3049 | err = mp_read_unsigned_bin(key->pubkey.y, (byte*)in+1+((inLen-1)>>1),
|
---|
3050 | (inLen-1)>>1);
|
---|
3051 | if (err == MP_OKAY)
|
---|
3052 | mp_set(key->pubkey.z, 1);
|
---|
3053 |
|
---|
3054 | #ifdef WOLFSSL_VALIDATE_ECC_IMPORT
|
---|
3055 | if (err == MP_OKAY)
|
---|
3056 | err = wc_ecc_check_key(key);
|
---|
3057 | #endif
|
---|
3058 |
|
---|
3059 | if (err != MP_OKAY) {
|
---|
3060 | mp_clear(key->pubkey.x);
|
---|
3061 | mp_clear(key->pubkey.y);
|
---|
3062 | mp_clear(key->pubkey.z);
|
---|
3063 | mp_clear(&key->k);
|
---|
3064 | }
|
---|
3065 |
|
---|
3066 | return err;
|
---|
3067 | }
|
---|
3068 |
|
---|
3069 |
|
---|
3070 | /* export ecc private key only raw, outLen is in/out size
|
---|
3071 | return MP_OKAY on success */
|
---|
3072 | int wc_ecc_export_private_only(ecc_key* key, byte* out, word32* outLen)
|
---|
3073 | {
|
---|
3074 | word32 numlen;
|
---|
3075 |
|
---|
3076 | if (key == NULL || out == NULL || outLen == NULL)
|
---|
3077 | return ECC_BAD_ARG_E;
|
---|
3078 |
|
---|
3079 | if (wc_ecc_is_valid_idx(key->idx) == 0) {
|
---|
3080 | return ECC_BAD_ARG_E;
|
---|
3081 | }
|
---|
3082 | numlen = key->dp->size;
|
---|
3083 |
|
---|
3084 | if (*outLen < numlen) {
|
---|
3085 | *outLen = numlen;
|
---|
3086 | return BUFFER_E;
|
---|
3087 | }
|
---|
3088 | *outLen = numlen;
|
---|
3089 | XMEMSET(out, 0, *outLen);
|
---|
3090 | return mp_to_unsigned_bin(&key->k, out + (numlen -
|
---|
3091 | mp_unsigned_bin_size(&key->k)));
|
---|
3092 | }
|
---|
3093 |
|
---|
3094 |
|
---|
3095 | /* ecc private key import, public key in ANSI X9.63 format, private raw */
|
---|
3096 | int wc_ecc_import_private_key(const byte* priv, word32 privSz, const byte* pub,
|
---|
3097 | word32 pubSz, ecc_key* key)
|
---|
3098 | {
|
---|
3099 | int ret = wc_ecc_import_x963(pub, pubSz, key);
|
---|
3100 | if (ret != 0)
|
---|
3101 | return ret;
|
---|
3102 |
|
---|
3103 | key->type = ECC_PRIVATEKEY;
|
---|
3104 |
|
---|
3105 | ret = mp_read_unsigned_bin(&key->k, priv, privSz);
|
---|
3106 |
|
---|
3107 | #ifdef WOLFSSL_VALIDATE_ECC_IMPORT
|
---|
3108 | if (ret == MP_OKAY)
|
---|
3109 | ret = ecc_check_privkey_gen_helper(key);
|
---|
3110 | #endif
|
---|
3111 |
|
---|
3112 | return ret;
|
---|
3113 | }
|
---|
3114 |
|
---|
3115 | /**
|
---|
3116 | Convert ECC R,S to signature
|
---|
3117 | r R component of signature
|
---|
3118 | s S component of signature
|
---|
3119 | out DER-encoded ECDSA signature
|
---|
3120 | outlen [in/out] output buffer size, output signature size
|
---|
3121 | return MP_OKAY on success
|
---|
3122 | */
|
---|
3123 | int wc_ecc_rs_to_sig(const char* r, const char* s, byte* out, word32* outlen)
|
---|
3124 | {
|
---|
3125 | int err;
|
---|
3126 | mp_int rtmp;
|
---|
3127 | mp_int stmp;
|
---|
3128 |
|
---|
3129 | if (r == NULL || s == NULL || out == NULL || outlen == NULL)
|
---|
3130 | return ECC_BAD_ARG_E;
|
---|
3131 |
|
---|
3132 | err = mp_init_multi(&rtmp, &stmp, NULL, NULL, NULL, NULL);
|
---|
3133 | if (err != MP_OKAY)
|
---|
3134 | return err;
|
---|
3135 |
|
---|
3136 | err = mp_read_radix(&rtmp, r, 16);
|
---|
3137 | if (err == MP_OKAY)
|
---|
3138 | err = mp_read_radix(&stmp, s, 16);
|
---|
3139 |
|
---|
3140 | /* convert mp_ints to ECDSA sig, initializes rtmp and stmp internally */
|
---|
3141 | if (err == MP_OKAY)
|
---|
3142 | err = StoreECC_DSA_Sig(out, outlen, &rtmp, &stmp);
|
---|
3143 |
|
---|
3144 | if (err == MP_OKAY) {
|
---|
3145 | if (mp_iszero(&rtmp) || mp_iszero(&stmp))
|
---|
3146 | err = MP_ZERO_E;
|
---|
3147 | }
|
---|
3148 |
|
---|
3149 | mp_clear(&rtmp);
|
---|
3150 | mp_clear(&stmp);
|
---|
3151 |
|
---|
3152 | return err;
|
---|
3153 | }
|
---|
3154 |
|
---|
3155 | /**
|
---|
3156 | Import raw ECC key
|
---|
3157 | key The destination ecc_key structure
|
---|
3158 | qx x component of base point, as ASCII hex string
|
---|
3159 | qy y component of base point, as ASCII hex string
|
---|
3160 | d private key, as ASCII hex string
|
---|
3161 | curveName ECC curve name, from ecc_sets[]
|
---|
3162 | return MP_OKAY on success
|
---|
3163 | */
|
---|
3164 | int wc_ecc_import_raw(ecc_key* key, const char* qx, const char* qy,
|
---|
3165 | const char* d, const char* curveName)
|
---|
3166 | {
|
---|
3167 | int err, x;
|
---|
3168 |
|
---|
3169 | if (key == NULL || qx == NULL || qy == NULL || d == NULL ||
|
---|
3170 | curveName == NULL)
|
---|
3171 | return ECC_BAD_ARG_E;
|
---|
3172 |
|
---|
3173 | /* init key */
|
---|
3174 | #ifdef ALT_ECC_SIZE
|
---|
3175 | key->pubkey.x = (mp_int*)&key->pubkey.xyz[0];
|
---|
3176 | key->pubkey.y = (mp_int*)&key->pubkey.xyz[1];
|
---|
3177 | key->pubkey.z = (mp_int*)&key->pubkey.xyz[2];
|
---|
3178 | alt_fp_init(key->pubkey.x);
|
---|
3179 | alt_fp_init(key->pubkey.y);
|
---|
3180 | alt_fp_init(key->pubkey.z);
|
---|
3181 | err = mp_init(&key->k);
|
---|
3182 | #else
|
---|
3183 | err = mp_init_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z, &key->k,
|
---|
3184 | NULL, NULL);
|
---|
3185 | #endif
|
---|
3186 | if (err != MP_OKAY)
|
---|
3187 | return MEMORY_E;
|
---|
3188 |
|
---|
3189 | /* read Qx */
|
---|
3190 | if (err == MP_OKAY)
|
---|
3191 | err = mp_read_radix(key->pubkey.x, qx, 16);
|
---|
3192 |
|
---|
3193 | /* read Qy */
|
---|
3194 | if (err == MP_OKAY)
|
---|
3195 | err = mp_read_radix(key->pubkey.y, qy, 16);
|
---|
3196 |
|
---|
3197 | if (err == MP_OKAY)
|
---|
3198 | mp_set(key->pubkey.z, 1);
|
---|
3199 |
|
---|
3200 | /* read and set the curve */
|
---|
3201 | if (err == MP_OKAY) {
|
---|
3202 | for (x = 0; ecc_sets[x].size != 0; x++) {
|
---|
3203 | if (XSTRNCMP(ecc_sets[x].name, curveName,
|
---|
3204 | XSTRLEN(curveName)) == 0) {
|
---|
3205 | break;
|
---|
3206 | }
|
---|
3207 | }
|
---|
3208 | if (ecc_sets[x].size == 0) {
|
---|
3209 | err = ASN_PARSE_E;
|
---|
3210 | } else {
|
---|
3211 | /* set the curve */
|
---|
3212 | key->idx = x;
|
---|
3213 | key->dp = &ecc_sets[x];
|
---|
3214 | key->type = ECC_PUBLICKEY;
|
---|
3215 | }
|
---|
3216 | }
|
---|
3217 |
|
---|
3218 | /* import private key */
|
---|
3219 | if (err == MP_OKAY) {
|
---|
3220 | key->type = ECC_PRIVATEKEY;
|
---|
3221 | err = mp_read_radix(&key->k, d, 16);
|
---|
3222 | }
|
---|
3223 |
|
---|
3224 | #ifdef WOLFSSL_VALIDATE_ECC_IMPORT
|
---|
3225 | if (err == MP_OKAY)
|
---|
3226 | err = wc_ecc_check_key(key);
|
---|
3227 | #endif
|
---|
3228 |
|
---|
3229 | if (err != MP_OKAY) {
|
---|
3230 | mp_clear(key->pubkey.x);
|
---|
3231 | mp_clear(key->pubkey.y);
|
---|
3232 | mp_clear(key->pubkey.z);
|
---|
3233 | mp_clear(&key->k);
|
---|
3234 | }
|
---|
3235 |
|
---|
3236 | return err;
|
---|
3237 | }
|
---|
3238 |
|
---|
3239 |
|
---|
3240 | /* key size in octets */
|
---|
3241 | int wc_ecc_size(ecc_key* key)
|
---|
3242 | {
|
---|
3243 | if (key == NULL) return 0;
|
---|
3244 |
|
---|
3245 | return key->dp->size;
|
---|
3246 | }
|
---|
3247 |
|
---|
3248 |
|
---|
3249 | /* worst case estimate, check actual return from wc_ecc_sign_hash for actual
|
---|
3250 | value of signature size in octets */
|
---|
3251 | int wc_ecc_sig_size(ecc_key* key)
|
---|
3252 | {
|
---|
3253 | int sz = wc_ecc_size(key);
|
---|
3254 | if (sz <= 0)
|
---|
3255 | return sz;
|
---|
3256 |
|
---|
3257 | return sz * 2 + SIG_HEADER_SZ + 4; /* (4) worst case estimate */
|
---|
3258 | }
|
---|
3259 |
|
---|
3260 |
|
---|
3261 | #ifdef FP_ECC
|
---|
3262 |
|
---|
3263 | /* fixed point ECC cache */
|
---|
3264 | /* number of entries in the cache */
|
---|
3265 | #ifndef FP_ENTRIES
|
---|
3266 | #define FP_ENTRIES 16
|
---|
3267 | #endif
|
---|
3268 |
|
---|
3269 | /* number of bits in LUT */
|
---|
3270 | #ifndef FP_LUT
|
---|
3271 | #define FP_LUT 8U
|
---|
3272 | #endif
|
---|
3273 |
|
---|
3274 | #ifdef ECC_SHAMIR
|
---|
3275 | /* Sharmir requires a bigger LUT, TAO */
|
---|
3276 | #if (FP_LUT > 12) || (FP_LUT < 4)
|
---|
3277 | #error FP_LUT must be between 4 and 12 inclusively
|
---|
3278 | #endif
|
---|
3279 | #else
|
---|
3280 | #if (FP_LUT > 12) || (FP_LUT < 2)
|
---|
3281 | #error FP_LUT must be between 2 and 12 inclusively
|
---|
3282 | #endif
|
---|
3283 | #endif
|
---|
3284 |
|
---|
3285 |
|
---|
3286 | /** Our FP cache */
|
---|
3287 | typedef struct {
|
---|
3288 | ecc_point* g; /* cached COPY of base point */
|
---|
3289 | ecc_point* LUT[1U<<FP_LUT]; /* fixed point lookup */
|
---|
3290 | mp_int mu; /* copy of the montgomery constant */
|
---|
3291 | int lru_count; /* amount of times this entry has been used */
|
---|
3292 | int lock; /* flag to indicate cache eviction */
|
---|
3293 | /* permitted (0) or not (1) */
|
---|
3294 | } fp_cache_t;
|
---|
3295 |
|
---|
3296 | /* if HAVE_THREAD_LS this cache is per thread, no locking needed */
|
---|
3297 | static THREAD_LS_T fp_cache_t fp_cache[FP_ENTRIES];
|
---|
3298 |
|
---|
3299 | #ifndef HAVE_THREAD_LS
|
---|
3300 | static volatile int initMutex = 0; /* prevent multiple mutex inits */
|
---|
3301 | static wolfSSL_Mutex ecc_fp_lock;
|
---|
3302 | #endif /* HAVE_THREAD_LS */
|
---|
3303 |
|
---|
3304 | /* simple table to help direct the generation of the LUT */
|
---|
3305 | static const struct {
|
---|
3306 | int ham, terma, termb;
|
---|
3307 | } lut_orders[] = {
|
---|
3308 | { 0, 0, 0 }, { 1, 0, 0 }, { 1, 0, 0 }, { 2, 1, 2 }, { 1, 0, 0 }, { 2, 1, 4 }, { 2, 2, 4 }, { 3, 3, 4 },
|
---|
3309 | { 1, 0, 0 }, { 2, 1, 8 }, { 2, 2, 8 }, { 3, 3, 8 }, { 2, 4, 8 }, { 3, 5, 8 }, { 3, 6, 8 }, { 4, 7, 8 },
|
---|
3310 | { 1, 0, 0 }, { 2, 1, 16 }, { 2, 2, 16 }, { 3, 3, 16 }, { 2, 4, 16 }, { 3, 5, 16 }, { 3, 6, 16 }, { 4, 7, 16 },
|
---|
3311 | { 2, 8, 16 }, { 3, 9, 16 }, { 3, 10, 16 }, { 4, 11, 16 }, { 3, 12, 16 }, { 4, 13, 16 }, { 4, 14, 16 }, { 5, 15, 16 },
|
---|
3312 | { 1, 0, 0 }, { 2, 1, 32 }, { 2, 2, 32 }, { 3, 3, 32 }, { 2, 4, 32 }, { 3, 5, 32 }, { 3, 6, 32 }, { 4, 7, 32 },
|
---|
3313 | { 2, 8, 32 }, { 3, 9, 32 }, { 3, 10, 32 }, { 4, 11, 32 }, { 3, 12, 32 }, { 4, 13, 32 }, { 4, 14, 32 }, { 5, 15, 32 },
|
---|
3314 | { 2, 16, 32 }, { 3, 17, 32 }, { 3, 18, 32 }, { 4, 19, 32 }, { 3, 20, 32 }, { 4, 21, 32 }, { 4, 22, 32 }, { 5, 23, 32 },
|
---|
3315 | { 3, 24, 32 }, { 4, 25, 32 }, { 4, 26, 32 }, { 5, 27, 32 }, { 4, 28, 32 }, { 5, 29, 32 }, { 5, 30, 32 }, { 6, 31, 32 },
|
---|
3316 | #if FP_LUT > 6
|
---|
3317 | { 1, 0, 0 }, { 2, 1, 64 }, { 2, 2, 64 }, { 3, 3, 64 }, { 2, 4, 64 }, { 3, 5, 64 }, { 3, 6, 64 }, { 4, 7, 64 },
|
---|
3318 | { 2, 8, 64 }, { 3, 9, 64 }, { 3, 10, 64 }, { 4, 11, 64 }, { 3, 12, 64 }, { 4, 13, 64 }, { 4, 14, 64 }, { 5, 15, 64 },
|
---|
3319 | { 2, 16, 64 }, { 3, 17, 64 }, { 3, 18, 64 }, { 4, 19, 64 }, { 3, 20, 64 }, { 4, 21, 64 }, { 4, 22, 64 }, { 5, 23, 64 },
|
---|
3320 | { 3, 24, 64 }, { 4, 25, 64 }, { 4, 26, 64 }, { 5, 27, 64 }, { 4, 28, 64 }, { 5, 29, 64 }, { 5, 30, 64 }, { 6, 31, 64 },
|
---|
3321 | { 2, 32, 64 }, { 3, 33, 64 }, { 3, 34, 64 }, { 4, 35, 64 }, { 3, 36, 64 }, { 4, 37, 64 }, { 4, 38, 64 }, { 5, 39, 64 },
|
---|
3322 | { 3, 40, 64 }, { 4, 41, 64 }, { 4, 42, 64 }, { 5, 43, 64 }, { 4, 44, 64 }, { 5, 45, 64 }, { 5, 46, 64 }, { 6, 47, 64 },
|
---|
3323 | { 3, 48, 64 }, { 4, 49, 64 }, { 4, 50, 64 }, { 5, 51, 64 }, { 4, 52, 64 }, { 5, 53, 64 }, { 5, 54, 64 }, { 6, 55, 64 },
|
---|
3324 | { 4, 56, 64 }, { 5, 57, 64 }, { 5, 58, 64 }, { 6, 59, 64 }, { 5, 60, 64 }, { 6, 61, 64 }, { 6, 62, 64 }, { 7, 63, 64 },
|
---|
3325 | #if FP_LUT > 7
|
---|
3326 | { 1, 0, 0 }, { 2, 1, 128 }, { 2, 2, 128 }, { 3, 3, 128 }, { 2, 4, 128 }, { 3, 5, 128 }, { 3, 6, 128 }, { 4, 7, 128 },
|
---|
3327 | { 2, 8, 128 }, { 3, 9, 128 }, { 3, 10, 128 }, { 4, 11, 128 }, { 3, 12, 128 }, { 4, 13, 128 }, { 4, 14, 128 }, { 5, 15, 128 },
|
---|
3328 | { 2, 16, 128 }, { 3, 17, 128 }, { 3, 18, 128 }, { 4, 19, 128 }, { 3, 20, 128 }, { 4, 21, 128 }, { 4, 22, 128 }, { 5, 23, 128 },
|
---|
3329 | { 3, 24, 128 }, { 4, 25, 128 }, { 4, 26, 128 }, { 5, 27, 128 }, { 4, 28, 128 }, { 5, 29, 128 }, { 5, 30, 128 }, { 6, 31, 128 },
|
---|
3330 | { 2, 32, 128 }, { 3, 33, 128 }, { 3, 34, 128 }, { 4, 35, 128 }, { 3, 36, 128 }, { 4, 37, 128 }, { 4, 38, 128 }, { 5, 39, 128 },
|
---|
3331 | { 3, 40, 128 }, { 4, 41, 128 }, { 4, 42, 128 }, { 5, 43, 128 }, { 4, 44, 128 }, { 5, 45, 128 }, { 5, 46, 128 }, { 6, 47, 128 },
|
---|
3332 | { 3, 48, 128 }, { 4, 49, 128 }, { 4, 50, 128 }, { 5, 51, 128 }, { 4, 52, 128 }, { 5, 53, 128 }, { 5, 54, 128 }, { 6, 55, 128 },
|
---|
3333 | { 4, 56, 128 }, { 5, 57, 128 }, { 5, 58, 128 }, { 6, 59, 128 }, { 5, 60, 128 }, { 6, 61, 128 }, { 6, 62, 128 }, { 7, 63, 128 },
|
---|
3334 | { 2, 64, 128 }, { 3, 65, 128 }, { 3, 66, 128 }, { 4, 67, 128 }, { 3, 68, 128 }, { 4, 69, 128 }, { 4, 70, 128 }, { 5, 71, 128 },
|
---|
3335 | { 3, 72, 128 }, { 4, 73, 128 }, { 4, 74, 128 }, { 5, 75, 128 }, { 4, 76, 128 }, { 5, 77, 128 }, { 5, 78, 128 }, { 6, 79, 128 },
|
---|
3336 | { 3, 80, 128 }, { 4, 81, 128 }, { 4, 82, 128 }, { 5, 83, 128 }, { 4, 84, 128 }, { 5, 85, 128 }, { 5, 86, 128 }, { 6, 87, 128 },
|
---|
3337 | { 4, 88, 128 }, { 5, 89, 128 }, { 5, 90, 128 }, { 6, 91, 128 }, { 5, 92, 128 }, { 6, 93, 128 }, { 6, 94, 128 }, { 7, 95, 128 },
|
---|
3338 | { 3, 96, 128 }, { 4, 97, 128 }, { 4, 98, 128 }, { 5, 99, 128 }, { 4, 100, 128 }, { 5, 101, 128 }, { 5, 102, 128 }, { 6, 103, 128 },
|
---|
3339 | { 4, 104, 128 }, { 5, 105, 128 }, { 5, 106, 128 }, { 6, 107, 128 }, { 5, 108, 128 }, { 6, 109, 128 }, { 6, 110, 128 }, { 7, 111, 128 },
|
---|
3340 | { 4, 112, 128 }, { 5, 113, 128 }, { 5, 114, 128 }, { 6, 115, 128 }, { 5, 116, 128 }, { 6, 117, 128 }, { 6, 118, 128 }, { 7, 119, 128 },
|
---|
3341 | { 5, 120, 128 }, { 6, 121, 128 }, { 6, 122, 128 }, { 7, 123, 128 }, { 6, 124, 128 }, { 7, 125, 128 }, { 7, 126, 128 }, { 8, 127, 128 },
|
---|
3342 | #if FP_LUT > 8
|
---|
3343 | { 1, 0, 0 }, { 2, 1, 256 }, { 2, 2, 256 }, { 3, 3, 256 }, { 2, 4, 256 }, { 3, 5, 256 }, { 3, 6, 256 }, { 4, 7, 256 },
|
---|
3344 | { 2, 8, 256 }, { 3, 9, 256 }, { 3, 10, 256 }, { 4, 11, 256 }, { 3, 12, 256 }, { 4, 13, 256 }, { 4, 14, 256 }, { 5, 15, 256 },
|
---|
3345 | { 2, 16, 256 }, { 3, 17, 256 }, { 3, 18, 256 }, { 4, 19, 256 }, { 3, 20, 256 }, { 4, 21, 256 }, { 4, 22, 256 }, { 5, 23, 256 },
|
---|
3346 | { 3, 24, 256 }, { 4, 25, 256 }, { 4, 26, 256 }, { 5, 27, 256 }, { 4, 28, 256 }, { 5, 29, 256 }, { 5, 30, 256 }, { 6, 31, 256 },
|
---|
3347 | { 2, 32, 256 }, { 3, 33, 256 }, { 3, 34, 256 }, { 4, 35, 256 }, { 3, 36, 256 }, { 4, 37, 256 }, { 4, 38, 256 }, { 5, 39, 256 },
|
---|
3348 | { 3, 40, 256 }, { 4, 41, 256 }, { 4, 42, 256 }, { 5, 43, 256 }, { 4, 44, 256 }, { 5, 45, 256 }, { 5, 46, 256 }, { 6, 47, 256 },
|
---|
3349 | { 3, 48, 256 }, { 4, 49, 256 }, { 4, 50, 256 }, { 5, 51, 256 }, { 4, 52, 256 }, { 5, 53, 256 }, { 5, 54, 256 }, { 6, 55, 256 },
|
---|
3350 | { 4, 56, 256 }, { 5, 57, 256 }, { 5, 58, 256 }, { 6, 59, 256 }, { 5, 60, 256 }, { 6, 61, 256 }, { 6, 62, 256 }, { 7, 63, 256 },
|
---|
3351 | { 2, 64, 256 }, { 3, 65, 256 }, { 3, 66, 256 }, { 4, 67, 256 }, { 3, 68, 256 }, { 4, 69, 256 }, { 4, 70, 256 }, { 5, 71, 256 },
|
---|
3352 | { 3, 72, 256 }, { 4, 73, 256 }, { 4, 74, 256 }, { 5, 75, 256 }, { 4, 76, 256 }, { 5, 77, 256 }, { 5, 78, 256 }, { 6, 79, 256 },
|
---|
3353 | { 3, 80, 256 }, { 4, 81, 256 }, { 4, 82, 256 }, { 5, 83, 256 }, { 4, 84, 256 }, { 5, 85, 256 }, { 5, 86, 256 }, { 6, 87, 256 },
|
---|
3354 | { 4, 88, 256 }, { 5, 89, 256 }, { 5, 90, 256 }, { 6, 91, 256 }, { 5, 92, 256 }, { 6, 93, 256 }, { 6, 94, 256 }, { 7, 95, 256 },
|
---|
3355 | { 3, 96, 256 }, { 4, 97, 256 }, { 4, 98, 256 }, { 5, 99, 256 }, { 4, 100, 256 }, { 5, 101, 256 }, { 5, 102, 256 }, { 6, 103, 256 },
|
---|
3356 | { 4, 104, 256 }, { 5, 105, 256 }, { 5, 106, 256 }, { 6, 107, 256 }, { 5, 108, 256 }, { 6, 109, 256 }, { 6, 110, 256 }, { 7, 111, 256 },
|
---|
3357 | { 4, 112, 256 }, { 5, 113, 256 }, { 5, 114, 256 }, { 6, 115, 256 }, { 5, 116, 256 }, { 6, 117, 256 }, { 6, 118, 256 }, { 7, 119, 256 },
|
---|
3358 | { 5, 120, 256 }, { 6, 121, 256 }, { 6, 122, 256 }, { 7, 123, 256 }, { 6, 124, 256 }, { 7, 125, 256 }, { 7, 126, 256 }, { 8, 127, 256 },
|
---|
3359 | { 2, 128, 256 }, { 3, 129, 256 }, { 3, 130, 256 }, { 4, 131, 256 }, { 3, 132, 256 }, { 4, 133, 256 }, { 4, 134, 256 }, { 5, 135, 256 },
|
---|
3360 | { 3, 136, 256 }, { 4, 137, 256 }, { 4, 138, 256 }, { 5, 139, 256 }, { 4, 140, 256 }, { 5, 141, 256 }, { 5, 142, 256 }, { 6, 143, 256 },
|
---|
3361 | { 3, 144, 256 }, { 4, 145, 256 }, { 4, 146, 256 }, { 5, 147, 256 }, { 4, 148, 256 }, { 5, 149, 256 }, { 5, 150, 256 }, { 6, 151, 256 },
|
---|
3362 | { 4, 152, 256 }, { 5, 153, 256 }, { 5, 154, 256 }, { 6, 155, 256 }, { 5, 156, 256 }, { 6, 157, 256 }, { 6, 158, 256 }, { 7, 159, 256 },
|
---|
3363 | { 3, 160, 256 }, { 4, 161, 256 }, { 4, 162, 256 }, { 5, 163, 256 }, { 4, 164, 256 }, { 5, 165, 256 }, { 5, 166, 256 }, { 6, 167, 256 },
|
---|
3364 | { 4, 168, 256 }, { 5, 169, 256 }, { 5, 170, 256 }, { 6, 171, 256 }, { 5, 172, 256 }, { 6, 173, 256 }, { 6, 174, 256 }, { 7, 175, 256 },
|
---|
3365 | { 4, 176, 256 }, { 5, 177, 256 }, { 5, 178, 256 }, { 6, 179, 256 }, { 5, 180, 256 }, { 6, 181, 256 }, { 6, 182, 256 }, { 7, 183, 256 },
|
---|
3366 | { 5, 184, 256 }, { 6, 185, 256 }, { 6, 186, 256 }, { 7, 187, 256 }, { 6, 188, 256 }, { 7, 189, 256 }, { 7, 190, 256 }, { 8, 191, 256 },
|
---|
3367 | { 3, 192, 256 }, { 4, 193, 256 }, { 4, 194, 256 }, { 5, 195, 256 }, { 4, 196, 256 }, { 5, 197, 256 }, { 5, 198, 256 }, { 6, 199, 256 },
|
---|
3368 | { 4, 200, 256 }, { 5, 201, 256 }, { 5, 202, 256 }, { 6, 203, 256 }, { 5, 204, 256 }, { 6, 205, 256 }, { 6, 206, 256 }, { 7, 207, 256 },
|
---|
3369 | { 4, 208, 256 }, { 5, 209, 256 }, { 5, 210, 256 }, { 6, 211, 256 }, { 5, 212, 256 }, { 6, 213, 256 }, { 6, 214, 256 }, { 7, 215, 256 },
|
---|
3370 | { 5, 216, 256 }, { 6, 217, 256 }, { 6, 218, 256 }, { 7, 219, 256 }, { 6, 220, 256 }, { 7, 221, 256 }, { 7, 222, 256 }, { 8, 223, 256 },
|
---|
3371 | { 4, 224, 256 }, { 5, 225, 256 }, { 5, 226, 256 }, { 6, 227, 256 }, { 5, 228, 256 }, { 6, 229, 256 }, { 6, 230, 256 }, { 7, 231, 256 },
|
---|
3372 | { 5, 232, 256 }, { 6, 233, 256 }, { 6, 234, 256 }, { 7, 235, 256 }, { 6, 236, 256 }, { 7, 237, 256 }, { 7, 238, 256 }, { 8, 239, 256 },
|
---|
3373 | { 5, 240, 256 }, { 6, 241, 256 }, { 6, 242, 256 }, { 7, 243, 256 }, { 6, 244, 256 }, { 7, 245, 256 }, { 7, 246, 256 }, { 8, 247, 256 },
|
---|
3374 | { 6, 248, 256 }, { 7, 249, 256 }, { 7, 250, 256 }, { 8, 251, 256 }, { 7, 252, 256 }, { 8, 253, 256 }, { 8, 254, 256 }, { 9, 255, 256 },
|
---|
3375 | #if FP_LUT > 9
|
---|
3376 | { 1, 0, 0 }, { 2, 1, 512 }, { 2, 2, 512 }, { 3, 3, 512 }, { 2, 4, 512 }, { 3, 5, 512 }, { 3, 6, 512 }, { 4, 7, 512 },
|
---|
3377 | { 2, 8, 512 }, { 3, 9, 512 }, { 3, 10, 512 }, { 4, 11, 512 }, { 3, 12, 512 }, { 4, 13, 512 }, { 4, 14, 512 }, { 5, 15, 512 },
|
---|
3378 | { 2, 16, 512 }, { 3, 17, 512 }, { 3, 18, 512 }, { 4, 19, 512 }, { 3, 20, 512 }, { 4, 21, 512 }, { 4, 22, 512 }, { 5, 23, 512 },
|
---|
3379 | { 3, 24, 512 }, { 4, 25, 512 }, { 4, 26, 512 }, { 5, 27, 512 }, { 4, 28, 512 }, { 5, 29, 512 }, { 5, 30, 512 }, { 6, 31, 512 },
|
---|
3380 | { 2, 32, 512 }, { 3, 33, 512 }, { 3, 34, 512 }, { 4, 35, 512 }, { 3, 36, 512 }, { 4, 37, 512 }, { 4, 38, 512 }, { 5, 39, 512 },
|
---|
3381 | { 3, 40, 512 }, { 4, 41, 512 }, { 4, 42, 512 }, { 5, 43, 512 }, { 4, 44, 512 }, { 5, 45, 512 }, { 5, 46, 512 }, { 6, 47, 512 },
|
---|
3382 | { 3, 48, 512 }, { 4, 49, 512 }, { 4, 50, 512 }, { 5, 51, 512 }, { 4, 52, 512 }, { 5, 53, 512 }, { 5, 54, 512 }, { 6, 55, 512 },
|
---|
3383 | { 4, 56, 512 }, { 5, 57, 512 }, { 5, 58, 512 }, { 6, 59, 512 }, { 5, 60, 512 }, { 6, 61, 512 }, { 6, 62, 512 }, { 7, 63, 512 },
|
---|
3384 | { 2, 64, 512 }, { 3, 65, 512 }, { 3, 66, 512 }, { 4, 67, 512 }, { 3, 68, 512 }, { 4, 69, 512 }, { 4, 70, 512 }, { 5, 71, 512 },
|
---|
3385 | { 3, 72, 512 }, { 4, 73, 512 }, { 4, 74, 512 }, { 5, 75, 512 }, { 4, 76, 512 }, { 5, 77, 512 }, { 5, 78, 512 }, { 6, 79, 512 },
|
---|
3386 | { 3, 80, 512 }, { 4, 81, 512 }, { 4, 82, 512 }, { 5, 83, 512 }, { 4, 84, 512 }, { 5, 85, 512 }, { 5, 86, 512 }, { 6, 87, 512 },
|
---|
3387 | { 4, 88, 512 }, { 5, 89, 512 }, { 5, 90, 512 }, { 6, 91, 512 }, { 5, 92, 512 }, { 6, 93, 512 }, { 6, 94, 512 }, { 7, 95, 512 },
|
---|
3388 | { 3, 96, 512 }, { 4, 97, 512 }, { 4, 98, 512 }, { 5, 99, 512 }, { 4, 100, 512 }, { 5, 101, 512 }, { 5, 102, 512 }, { 6, 103, 512 },
|
---|
3389 | { 4, 104, 512 }, { 5, 105, 512 }, { 5, 106, 512 }, { 6, 107, 512 }, { 5, 108, 512 }, { 6, 109, 512 }, { 6, 110, 512 }, { 7, 111, 512 },
|
---|
3390 | { 4, 112, 512 }, { 5, 113, 512 }, { 5, 114, 512 }, { 6, 115, 512 }, { 5, 116, 512 }, { 6, 117, 512 }, { 6, 118, 512 }, { 7, 119, 512 },
|
---|
3391 | { 5, 120, 512 }, { 6, 121, 512 }, { 6, 122, 512 }, { 7, 123, 512 }, { 6, 124, 512 }, { 7, 125, 512 }, { 7, 126, 512 }, { 8, 127, 512 },
|
---|
3392 | { 2, 128, 512 }, { 3, 129, 512 }, { 3, 130, 512 }, { 4, 131, 512 }, { 3, 132, 512 }, { 4, 133, 512 }, { 4, 134, 512 }, { 5, 135, 512 },
|
---|
3393 | { 3, 136, 512 }, { 4, 137, 512 }, { 4, 138, 512 }, { 5, 139, 512 }, { 4, 140, 512 }, { 5, 141, 512 }, { 5, 142, 512 }, { 6, 143, 512 },
|
---|
3394 | { 3, 144, 512 }, { 4, 145, 512 }, { 4, 146, 512 }, { 5, 147, 512 }, { 4, 148, 512 }, { 5, 149, 512 }, { 5, 150, 512 }, { 6, 151, 512 },
|
---|
3395 | { 4, 152, 512 }, { 5, 153, 512 }, { 5, 154, 512 }, { 6, 155, 512 }, { 5, 156, 512 }, { 6, 157, 512 }, { 6, 158, 512 }, { 7, 159, 512 },
|
---|
3396 | { 3, 160, 512 }, { 4, 161, 512 }, { 4, 162, 512 }, { 5, 163, 512 }, { 4, 164, 512 }, { 5, 165, 512 }, { 5, 166, 512 }, { 6, 167, 512 },
|
---|
3397 | { 4, 168, 512 }, { 5, 169, 512 }, { 5, 170, 512 }, { 6, 171, 512 }, { 5, 172, 512 }, { 6, 173, 512 }, { 6, 174, 512 }, { 7, 175, 512 },
|
---|
3398 | { 4, 176, 512 }, { 5, 177, 512 }, { 5, 178, 512 }, { 6, 179, 512 }, { 5, 180, 512 }, { 6, 181, 512 }, { 6, 182, 512 }, { 7, 183, 512 },
|
---|
3399 | { 5, 184, 512 }, { 6, 185, 512 }, { 6, 186, 512 }, { 7, 187, 512 }, { 6, 188, 512 }, { 7, 189, 512 }, { 7, 190, 512 }, { 8, 191, 512 },
|
---|
3400 | { 3, 192, 512 }, { 4, 193, 512 }, { 4, 194, 512 }, { 5, 195, 512 }, { 4, 196, 512 }, { 5, 197, 512 }, { 5, 198, 512 }, { 6, 199, 512 },
|
---|
3401 | { 4, 200, 512 }, { 5, 201, 512 }, { 5, 202, 512 }, { 6, 203, 512 }, { 5, 204, 512 }, { 6, 205, 512 }, { 6, 206, 512 }, { 7, 207, 512 },
|
---|
3402 | { 4, 208, 512 }, { 5, 209, 512 }, { 5, 210, 512 }, { 6, 211, 512 }, { 5, 212, 512 }, { 6, 213, 512 }, { 6, 214, 512 }, { 7, 215, 512 },
|
---|
3403 | { 5, 216, 512 }, { 6, 217, 512 }, { 6, 218, 512 }, { 7, 219, 512 }, { 6, 220, 512 }, { 7, 221, 512 }, { 7, 222, 512 }, { 8, 223, 512 },
|
---|
3404 | { 4, 224, 512 }, { 5, 225, 512 }, { 5, 226, 512 }, { 6, 227, 512 }, { 5, 228, 512 }, { 6, 229, 512 }, { 6, 230, 512 }, { 7, 231, 512 },
|
---|
3405 | { 5, 232, 512 }, { 6, 233, 512 }, { 6, 234, 512 }, { 7, 235, 512 }, { 6, 236, 512 }, { 7, 237, 512 }, { 7, 238, 512 }, { 8, 239, 512 },
|
---|
3406 | { 5, 240, 512 }, { 6, 241, 512 }, { 6, 242, 512 }, { 7, 243, 512 }, { 6, 244, 512 }, { 7, 245, 512 }, { 7, 246, 512 }, { 8, 247, 512 },
|
---|
3407 | { 6, 248, 512 }, { 7, 249, 512 }, { 7, 250, 512 }, { 8, 251, 512 }, { 7, 252, 512 }, { 8, 253, 512 }, { 8, 254, 512 }, { 9, 255, 512 },
|
---|
3408 | { 2, 256, 512 }, { 3, 257, 512 }, { 3, 258, 512 }, { 4, 259, 512 }, { 3, 260, 512 }, { 4, 261, 512 }, { 4, 262, 512 }, { 5, 263, 512 },
|
---|
3409 | { 3, 264, 512 }, { 4, 265, 512 }, { 4, 266, 512 }, { 5, 267, 512 }, { 4, 268, 512 }, { 5, 269, 512 }, { 5, 270, 512 }, { 6, 271, 512 },
|
---|
3410 | { 3, 272, 512 }, { 4, 273, 512 }, { 4, 274, 512 }, { 5, 275, 512 }, { 4, 276, 512 }, { 5, 277, 512 }, { 5, 278, 512 }, { 6, 279, 512 },
|
---|
3411 | { 4, 280, 512 }, { 5, 281, 512 }, { 5, 282, 512 }, { 6, 283, 512 }, { 5, 284, 512 }, { 6, 285, 512 }, { 6, 286, 512 }, { 7, 287, 512 },
|
---|
3412 | { 3, 288, 512 }, { 4, 289, 512 }, { 4, 290, 512 }, { 5, 291, 512 }, { 4, 292, 512 }, { 5, 293, 512 }, { 5, 294, 512 }, { 6, 295, 512 },
|
---|
3413 | { 4, 296, 512 }, { 5, 297, 512 }, { 5, 298, 512 }, { 6, 299, 512 }, { 5, 300, 512 }, { 6, 301, 512 }, { 6, 302, 512 }, { 7, 303, 512 },
|
---|
3414 | { 4, 304, 512 }, { 5, 305, 512 }, { 5, 306, 512 }, { 6, 307, 512 }, { 5, 308, 512 }, { 6, 309, 512 }, { 6, 310, 512 }, { 7, 311, 512 },
|
---|
3415 | { 5, 312, 512 }, { 6, 313, 512 }, { 6, 314, 512 }, { 7, 315, 512 }, { 6, 316, 512 }, { 7, 317, 512 }, { 7, 318, 512 }, { 8, 319, 512 },
|
---|
3416 | { 3, 320, 512 }, { 4, 321, 512 }, { 4, 322, 512 }, { 5, 323, 512 }, { 4, 324, 512 }, { 5, 325, 512 }, { 5, 326, 512 }, { 6, 327, 512 },
|
---|
3417 | { 4, 328, 512 }, { 5, 329, 512 }, { 5, 330, 512 }, { 6, 331, 512 }, { 5, 332, 512 }, { 6, 333, 512 }, { 6, 334, 512 }, { 7, 335, 512 },
|
---|
3418 | { 4, 336, 512 }, { 5, 337, 512 }, { 5, 338, 512 }, { 6, 339, 512 }, { 5, 340, 512 }, { 6, 341, 512 }, { 6, 342, 512 }, { 7, 343, 512 },
|
---|
3419 | { 5, 344, 512 }, { 6, 345, 512 }, { 6, 346, 512 }, { 7, 347, 512 }, { 6, 348, 512 }, { 7, 349, 512 }, { 7, 350, 512 }, { 8, 351, 512 },
|
---|
3420 | { 4, 352, 512 }, { 5, 353, 512 }, { 5, 354, 512 }, { 6, 355, 512 }, { 5, 356, 512 }, { 6, 357, 512 }, { 6, 358, 512 }, { 7, 359, 512 },
|
---|
3421 | { 5, 360, 512 }, { 6, 361, 512 }, { 6, 362, 512 }, { 7, 363, 512 }, { 6, 364, 512 }, { 7, 365, 512 }, { 7, 366, 512 }, { 8, 367, 512 },
|
---|
3422 | { 5, 368, 512 }, { 6, 369, 512 }, { 6, 370, 512 }, { 7, 371, 512 }, { 6, 372, 512 }, { 7, 373, 512 }, { 7, 374, 512 }, { 8, 375, 512 },
|
---|
3423 | { 6, 376, 512 }, { 7, 377, 512 }, { 7, 378, 512 }, { 8, 379, 512 }, { 7, 380, 512 }, { 8, 381, 512 }, { 8, 382, 512 }, { 9, 383, 512 },
|
---|
3424 | { 3, 384, 512 }, { 4, 385, 512 }, { 4, 386, 512 }, { 5, 387, 512 }, { 4, 388, 512 }, { 5, 389, 512 }, { 5, 390, 512 }, { 6, 391, 512 },
|
---|
3425 | { 4, 392, 512 }, { 5, 393, 512 }, { 5, 394, 512 }, { 6, 395, 512 }, { 5, 396, 512 }, { 6, 397, 512 }, { 6, 398, 512 }, { 7, 399, 512 },
|
---|
3426 | { 4, 400, 512 }, { 5, 401, 512 }, { 5, 402, 512 }, { 6, 403, 512 }, { 5, 404, 512 }, { 6, 405, 512 }, { 6, 406, 512 }, { 7, 407, 512 },
|
---|
3427 | { 5, 408, 512 }, { 6, 409, 512 }, { 6, 410, 512 }, { 7, 411, 512 }, { 6, 412, 512 }, { 7, 413, 512 }, { 7, 414, 512 }, { 8, 415, 512 },
|
---|
3428 | { 4, 416, 512 }, { 5, 417, 512 }, { 5, 418, 512 }, { 6, 419, 512 }, { 5, 420, 512 }, { 6, 421, 512 }, { 6, 422, 512 }, { 7, 423, 512 },
|
---|
3429 | { 5, 424, 512 }, { 6, 425, 512 }, { 6, 426, 512 }, { 7, 427, 512 }, { 6, 428, 512 }, { 7, 429, 512 }, { 7, 430, 512 }, { 8, 431, 512 },
|
---|
3430 | { 5, 432, 512 }, { 6, 433, 512 }, { 6, 434, 512 }, { 7, 435, 512 }, { 6, 436, 512 }, { 7, 437, 512 }, { 7, 438, 512 }, { 8, 439, 512 },
|
---|
3431 | { 6, 440, 512 }, { 7, 441, 512 }, { 7, 442, 512 }, { 8, 443, 512 }, { 7, 444, 512 }, { 8, 445, 512 }, { 8, 446, 512 }, { 9, 447, 512 },
|
---|
3432 | { 4, 448, 512 }, { 5, 449, 512 }, { 5, 450, 512 }, { 6, 451, 512 }, { 5, 452, 512 }, { 6, 453, 512 }, { 6, 454, 512 }, { 7, 455, 512 },
|
---|
3433 | { 5, 456, 512 }, { 6, 457, 512 }, { 6, 458, 512 }, { 7, 459, 512 }, { 6, 460, 512 }, { 7, 461, 512 }, { 7, 462, 512 }, { 8, 463, 512 },
|
---|
3434 | { 5, 464, 512 }, { 6, 465, 512 }, { 6, 466, 512 }, { 7, 467, 512 }, { 6, 468, 512 }, { 7, 469, 512 }, { 7, 470, 512 }, { 8, 471, 512 },
|
---|
3435 | { 6, 472, 512 }, { 7, 473, 512 }, { 7, 474, 512 }, { 8, 475, 512 }, { 7, 476, 512 }, { 8, 477, 512 }, { 8, 478, 512 }, { 9, 479, 512 },
|
---|
3436 | { 5, 480, 512 }, { 6, 481, 512 }, { 6, 482, 512 }, { 7, 483, 512 }, { 6, 484, 512 }, { 7, 485, 512 }, { 7, 486, 512 }, { 8, 487, 512 },
|
---|
3437 | { 6, 488, 512 }, { 7, 489, 512 }, { 7, 490, 512 }, { 8, 491, 512 }, { 7, 492, 512 }, { 8, 493, 512 }, { 8, 494, 512 }, { 9, 495, 512 },
|
---|
3438 | { 6, 496, 512 }, { 7, 497, 512 }, { 7, 498, 512 }, { 8, 499, 512 }, { 7, 500, 512 }, { 8, 501, 512 }, { 8, 502, 512 }, { 9, 503, 512 },
|
---|
3439 | { 7, 504, 512 }, { 8, 505, 512 }, { 8, 506, 512 }, { 9, 507, 512 }, { 8, 508, 512 }, { 9, 509, 512 }, { 9, 510, 512 }, { 10, 511, 512 },
|
---|
3440 | #if FP_LUT > 10
|
---|
3441 | { 1, 0, 0 }, { 2, 1, 1024 }, { 2, 2, 1024 }, { 3, 3, 1024 }, { 2, 4, 1024 }, { 3, 5, 1024 }, { 3, 6, 1024 }, { 4, 7, 1024 },
|
---|
3442 | { 2, 8, 1024 }, { 3, 9, 1024 }, { 3, 10, 1024 }, { 4, 11, 1024 }, { 3, 12, 1024 }, { 4, 13, 1024 }, { 4, 14, 1024 }, { 5, 15, 1024 },
|
---|
3443 | { 2, 16, 1024 }, { 3, 17, 1024 }, { 3, 18, 1024 }, { 4, 19, 1024 }, { 3, 20, 1024 }, { 4, 21, 1024 }, { 4, 22, 1024 }, { 5, 23, 1024 },
|
---|
3444 | { 3, 24, 1024 }, { 4, 25, 1024 }, { 4, 26, 1024 }, { 5, 27, 1024 }, { 4, 28, 1024 }, { 5, 29, 1024 }, { 5, 30, 1024 }, { 6, 31, 1024 },
|
---|
3445 | { 2, 32, 1024 }, { 3, 33, 1024 }, { 3, 34, 1024 }, { 4, 35, 1024 }, { 3, 36, 1024 }, { 4, 37, 1024 }, { 4, 38, 1024 }, { 5, 39, 1024 },
|
---|
3446 | { 3, 40, 1024 }, { 4, 41, 1024 }, { 4, 42, 1024 }, { 5, 43, 1024 }, { 4, 44, 1024 }, { 5, 45, 1024 }, { 5, 46, 1024 }, { 6, 47, 1024 },
|
---|
3447 | { 3, 48, 1024 }, { 4, 49, 1024 }, { 4, 50, 1024 }, { 5, 51, 1024 }, { 4, 52, 1024 }, { 5, 53, 1024 }, { 5, 54, 1024 }, { 6, 55, 1024 },
|
---|
3448 | { 4, 56, 1024 }, { 5, 57, 1024 }, { 5, 58, 1024 }, { 6, 59, 1024 }, { 5, 60, 1024 }, { 6, 61, 1024 }, { 6, 62, 1024 }, { 7, 63, 1024 },
|
---|
3449 | { 2, 64, 1024 }, { 3, 65, 1024 }, { 3, 66, 1024 }, { 4, 67, 1024 }, { 3, 68, 1024 }, { 4, 69, 1024 }, { 4, 70, 1024 }, { 5, 71, 1024 },
|
---|
3450 | { 3, 72, 1024 }, { 4, 73, 1024 }, { 4, 74, 1024 }, { 5, 75, 1024 }, { 4, 76, 1024 }, { 5, 77, 1024 }, { 5, 78, 1024 }, { 6, 79, 1024 },
|
---|
3451 | { 3, 80, 1024 }, { 4, 81, 1024 }, { 4, 82, 1024 }, { 5, 83, 1024 }, { 4, 84, 1024 }, { 5, 85, 1024 }, { 5, 86, 1024 }, { 6, 87, 1024 },
|
---|
3452 | { 4, 88, 1024 }, { 5, 89, 1024 }, { 5, 90, 1024 }, { 6, 91, 1024 }, { 5, 92, 1024 }, { 6, 93, 1024 }, { 6, 94, 1024 }, { 7, 95, 1024 },
|
---|
3453 | { 3, 96, 1024 }, { 4, 97, 1024 }, { 4, 98, 1024 }, { 5, 99, 1024 }, { 4, 100, 1024 }, { 5, 101, 1024 }, { 5, 102, 1024 }, { 6, 103, 1024 },
|
---|
3454 | { 4, 104, 1024 }, { 5, 105, 1024 }, { 5, 106, 1024 }, { 6, 107, 1024 }, { 5, 108, 1024 }, { 6, 109, 1024 }, { 6, 110, 1024 }, { 7, 111, 1024 },
|
---|
3455 | { 4, 112, 1024 }, { 5, 113, 1024 }, { 5, 114, 1024 }, { 6, 115, 1024 }, { 5, 116, 1024 }, { 6, 117, 1024 }, { 6, 118, 1024 }, { 7, 119, 1024 },
|
---|
3456 | { 5, 120, 1024 }, { 6, 121, 1024 }, { 6, 122, 1024 }, { 7, 123, 1024 }, { 6, 124, 1024 }, { 7, 125, 1024 }, { 7, 126, 1024 }, { 8, 127, 1024 },
|
---|
3457 | { 2, 128, 1024 }, { 3, 129, 1024 }, { 3, 130, 1024 }, { 4, 131, 1024 }, { 3, 132, 1024 }, { 4, 133, 1024 }, { 4, 134, 1024 }, { 5, 135, 1024 },
|
---|
3458 | { 3, 136, 1024 }, { 4, 137, 1024 }, { 4, 138, 1024 }, { 5, 139, 1024 }, { 4, 140, 1024 }, { 5, 141, 1024 }, { 5, 142, 1024 }, { 6, 143, 1024 },
|
---|
3459 | { 3, 144, 1024 }, { 4, 145, 1024 }, { 4, 146, 1024 }, { 5, 147, 1024 }, { 4, 148, 1024 }, { 5, 149, 1024 }, { 5, 150, 1024 }, { 6, 151, 1024 },
|
---|
3460 | { 4, 152, 1024 }, { 5, 153, 1024 }, { 5, 154, 1024 }, { 6, 155, 1024 }, { 5, 156, 1024 }, { 6, 157, 1024 }, { 6, 158, 1024 }, { 7, 159, 1024 },
|
---|
3461 | { 3, 160, 1024 }, { 4, 161, 1024 }, { 4, 162, 1024 }, { 5, 163, 1024 }, { 4, 164, 1024 }, { 5, 165, 1024 }, { 5, 166, 1024 }, { 6, 167, 1024 },
|
---|
3462 | { 4, 168, 1024 }, { 5, 169, 1024 }, { 5, 170, 1024 }, { 6, 171, 1024 }, { 5, 172, 1024 }, { 6, 173, 1024 }, { 6, 174, 1024 }, { 7, 175, 1024 },
|
---|
3463 | { 4, 176, 1024 }, { 5, 177, 1024 }, { 5, 178, 1024 }, { 6, 179, 1024 }, { 5, 180, 1024 }, { 6, 181, 1024 }, { 6, 182, 1024 }, { 7, 183, 1024 },
|
---|
3464 | { 5, 184, 1024 }, { 6, 185, 1024 }, { 6, 186, 1024 }, { 7, 187, 1024 }, { 6, 188, 1024 }, { 7, 189, 1024 }, { 7, 190, 1024 }, { 8, 191, 1024 },
|
---|
3465 | { 3, 192, 1024 }, { 4, 193, 1024 }, { 4, 194, 1024 }, { 5, 195, 1024 }, { 4, 196, 1024 }, { 5, 197, 1024 }, { 5, 198, 1024 }, { 6, 199, 1024 },
|
---|
3466 | { 4, 200, 1024 }, { 5, 201, 1024 }, { 5, 202, 1024 }, { 6, 203, 1024 }, { 5, 204, 1024 }, { 6, 205, 1024 }, { 6, 206, 1024 }, { 7, 207, 1024 },
|
---|
3467 | { 4, 208, 1024 }, { 5, 209, 1024 }, { 5, 210, 1024 }, { 6, 211, 1024 }, { 5, 212, 1024 }, { 6, 213, 1024 }, { 6, 214, 1024 }, { 7, 215, 1024 },
|
---|
3468 | { 5, 216, 1024 }, { 6, 217, 1024 }, { 6, 218, 1024 }, { 7, 219, 1024 }, { 6, 220, 1024 }, { 7, 221, 1024 }, { 7, 222, 1024 }, { 8, 223, 1024 },
|
---|
3469 | { 4, 224, 1024 }, { 5, 225, 1024 }, { 5, 226, 1024 }, { 6, 227, 1024 }, { 5, 228, 1024 }, { 6, 229, 1024 }, { 6, 230, 1024 }, { 7, 231, 1024 },
|
---|
3470 | { 5, 232, 1024 }, { 6, 233, 1024 }, { 6, 234, 1024 }, { 7, 235, 1024 }, { 6, 236, 1024 }, { 7, 237, 1024 }, { 7, 238, 1024 }, { 8, 239, 1024 },
|
---|
3471 | { 5, 240, 1024 }, { 6, 241, 1024 }, { 6, 242, 1024 }, { 7, 243, 1024 }, { 6, 244, 1024 }, { 7, 245, 1024 }, { 7, 246, 1024 }, { 8, 247, 1024 },
|
---|
3472 | { 6, 248, 1024 }, { 7, 249, 1024 }, { 7, 250, 1024 }, { 8, 251, 1024 }, { 7, 252, 1024 }, { 8, 253, 1024 }, { 8, 254, 1024 }, { 9, 255, 1024 },
|
---|
3473 | { 2, 256, 1024 }, { 3, 257, 1024 }, { 3, 258, 1024 }, { 4, 259, 1024 }, { 3, 260, 1024 }, { 4, 261, 1024 }, { 4, 262, 1024 }, { 5, 263, 1024 },
|
---|
3474 | { 3, 264, 1024 }, { 4, 265, 1024 }, { 4, 266, 1024 }, { 5, 267, 1024 }, { 4, 268, 1024 }, { 5, 269, 1024 }, { 5, 270, 1024 }, { 6, 271, 1024 },
|
---|
3475 | { 3, 272, 1024 }, { 4, 273, 1024 }, { 4, 274, 1024 }, { 5, 275, 1024 }, { 4, 276, 1024 }, { 5, 277, 1024 }, { 5, 278, 1024 }, { 6, 279, 1024 },
|
---|
3476 | { 4, 280, 1024 }, { 5, 281, 1024 }, { 5, 282, 1024 }, { 6, 283, 1024 }, { 5, 284, 1024 }, { 6, 285, 1024 }, { 6, 286, 1024 }, { 7, 287, 1024 },
|
---|
3477 | { 3, 288, 1024 }, { 4, 289, 1024 }, { 4, 290, 1024 }, { 5, 291, 1024 }, { 4, 292, 1024 }, { 5, 293, 1024 }, { 5, 294, 1024 }, { 6, 295, 1024 },
|
---|
3478 | { 4, 296, 1024 }, { 5, 297, 1024 }, { 5, 298, 1024 }, { 6, 299, 1024 }, { 5, 300, 1024 }, { 6, 301, 1024 }, { 6, 302, 1024 }, { 7, 303, 1024 },
|
---|
3479 | { 4, 304, 1024 }, { 5, 305, 1024 }, { 5, 306, 1024 }, { 6, 307, 1024 }, { 5, 308, 1024 }, { 6, 309, 1024 }, { 6, 310, 1024 }, { 7, 311, 1024 },
|
---|
3480 | { 5, 312, 1024 }, { 6, 313, 1024 }, { 6, 314, 1024 }, { 7, 315, 1024 }, { 6, 316, 1024 }, { 7, 317, 1024 }, { 7, 318, 1024 }, { 8, 319, 1024 },
|
---|
3481 | { 3, 320, 1024 }, { 4, 321, 1024 }, { 4, 322, 1024 }, { 5, 323, 1024 }, { 4, 324, 1024 }, { 5, 325, 1024 }, { 5, 326, 1024 }, { 6, 327, 1024 },
|
---|
3482 | { 4, 328, 1024 }, { 5, 329, 1024 }, { 5, 330, 1024 }, { 6, 331, 1024 }, { 5, 332, 1024 }, { 6, 333, 1024 }, { 6, 334, 1024 }, { 7, 335, 1024 },
|
---|
3483 | { 4, 336, 1024 }, { 5, 337, 1024 }, { 5, 338, 1024 }, { 6, 339, 1024 }, { 5, 340, 1024 }, { 6, 341, 1024 }, { 6, 342, 1024 }, { 7, 343, 1024 },
|
---|
3484 | { 5, 344, 1024 }, { 6, 345, 1024 }, { 6, 346, 1024 }, { 7, 347, 1024 }, { 6, 348, 1024 }, { 7, 349, 1024 }, { 7, 350, 1024 }, { 8, 351, 1024 },
|
---|
3485 | { 4, 352, 1024 }, { 5, 353, 1024 }, { 5, 354, 1024 }, { 6, 355, 1024 }, { 5, 356, 1024 }, { 6, 357, 1024 }, { 6, 358, 1024 }, { 7, 359, 1024 },
|
---|
3486 | { 5, 360, 1024 }, { 6, 361, 1024 }, { 6, 362, 1024 }, { 7, 363, 1024 }, { 6, 364, 1024 }, { 7, 365, 1024 }, { 7, 366, 1024 }, { 8, 367, 1024 },
|
---|
3487 | { 5, 368, 1024 }, { 6, 369, 1024 }, { 6, 370, 1024 }, { 7, 371, 1024 }, { 6, 372, 1024 }, { 7, 373, 1024 }, { 7, 374, 1024 }, { 8, 375, 1024 },
|
---|
3488 | { 6, 376, 1024 }, { 7, 377, 1024 }, { 7, 378, 1024 }, { 8, 379, 1024 }, { 7, 380, 1024 }, { 8, 381, 1024 }, { 8, 382, 1024 }, { 9, 383, 1024 },
|
---|
3489 | { 3, 384, 1024 }, { 4, 385, 1024 }, { 4, 386, 1024 }, { 5, 387, 1024 }, { 4, 388, 1024 }, { 5, 389, 1024 }, { 5, 390, 1024 }, { 6, 391, 1024 },
|
---|
3490 | { 4, 392, 1024 }, { 5, 393, 1024 }, { 5, 394, 1024 }, { 6, 395, 1024 }, { 5, 396, 1024 }, { 6, 397, 1024 }, { 6, 398, 1024 }, { 7, 399, 1024 },
|
---|
3491 | { 4, 400, 1024 }, { 5, 401, 1024 }, { 5, 402, 1024 }, { 6, 403, 1024 }, { 5, 404, 1024 }, { 6, 405, 1024 }, { 6, 406, 1024 }, { 7, 407, 1024 },
|
---|
3492 | { 5, 408, 1024 }, { 6, 409, 1024 }, { 6, 410, 1024 }, { 7, 411, 1024 }, { 6, 412, 1024 }, { 7, 413, 1024 }, { 7, 414, 1024 }, { 8, 415, 1024 },
|
---|
3493 | { 4, 416, 1024 }, { 5, 417, 1024 }, { 5, 418, 1024 }, { 6, 419, 1024 }, { 5, 420, 1024 }, { 6, 421, 1024 }, { 6, 422, 1024 }, { 7, 423, 1024 },
|
---|
3494 | { 5, 424, 1024 }, { 6, 425, 1024 }, { 6, 426, 1024 }, { 7, 427, 1024 }, { 6, 428, 1024 }, { 7, 429, 1024 }, { 7, 430, 1024 }, { 8, 431, 1024 },
|
---|
3495 | { 5, 432, 1024 }, { 6, 433, 1024 }, { 6, 434, 1024 }, { 7, 435, 1024 }, { 6, 436, 1024 }, { 7, 437, 1024 }, { 7, 438, 1024 }, { 8, 439, 1024 },
|
---|
3496 | { 6, 440, 1024 }, { 7, 441, 1024 }, { 7, 442, 1024 }, { 8, 443, 1024 }, { 7, 444, 1024 }, { 8, 445, 1024 }, { 8, 446, 1024 }, { 9, 447, 1024 },
|
---|
3497 | { 4, 448, 1024 }, { 5, 449, 1024 }, { 5, 450, 1024 }, { 6, 451, 1024 }, { 5, 452, 1024 }, { 6, 453, 1024 }, { 6, 454, 1024 }, { 7, 455, 1024 },
|
---|
3498 | { 5, 456, 1024 }, { 6, 457, 1024 }, { 6, 458, 1024 }, { 7, 459, 1024 }, { 6, 460, 1024 }, { 7, 461, 1024 }, { 7, 462, 1024 }, { 8, 463, 1024 },
|
---|
3499 | { 5, 464, 1024 }, { 6, 465, 1024 }, { 6, 466, 1024 }, { 7, 467, 1024 }, { 6, 468, 1024 }, { 7, 469, 1024 }, { 7, 470, 1024 }, { 8, 471, 1024 },
|
---|
3500 | { 6, 472, 1024 }, { 7, 473, 1024 }, { 7, 474, 1024 }, { 8, 475, 1024 }, { 7, 476, 1024 }, { 8, 477, 1024 }, { 8, 478, 1024 }, { 9, 479, 1024 },
|
---|
3501 | { 5, 480, 1024 }, { 6, 481, 1024 }, { 6, 482, 1024 }, { 7, 483, 1024 }, { 6, 484, 1024 }, { 7, 485, 1024 }, { 7, 486, 1024 }, { 8, 487, 1024 },
|
---|
3502 | { 6, 488, 1024 }, { 7, 489, 1024 }, { 7, 490, 1024 }, { 8, 491, 1024 }, { 7, 492, 1024 }, { 8, 493, 1024 }, { 8, 494, 1024 }, { 9, 495, 1024 },
|
---|
3503 | { 6, 496, 1024 }, { 7, 497, 1024 }, { 7, 498, 1024 }, { 8, 499, 1024 }, { 7, 500, 1024 }, { 8, 501, 1024 }, { 8, 502, 1024 }, { 9, 503, 1024 },
|
---|
3504 | { 7, 504, 1024 }, { 8, 505, 1024 }, { 8, 506, 1024 }, { 9, 507, 1024 }, { 8, 508, 1024 }, { 9, 509, 1024 }, { 9, 510, 1024 }, { 10, 511, 1024 },
|
---|
3505 | { 2, 512, 1024 }, { 3, 513, 1024 }, { 3, 514, 1024 }, { 4, 515, 1024 }, { 3, 516, 1024 }, { 4, 517, 1024 }, { 4, 518, 1024 }, { 5, 519, 1024 },
|
---|
3506 | { 3, 520, 1024 }, { 4, 521, 1024 }, { 4, 522, 1024 }, { 5, 523, 1024 }, { 4, 524, 1024 }, { 5, 525, 1024 }, { 5, 526, 1024 }, { 6, 527, 1024 },
|
---|
3507 | { 3, 528, 1024 }, { 4, 529, 1024 }, { 4, 530, 1024 }, { 5, 531, 1024 }, { 4, 532, 1024 }, { 5, 533, 1024 }, { 5, 534, 1024 }, { 6, 535, 1024 },
|
---|
3508 | { 4, 536, 1024 }, { 5, 537, 1024 }, { 5, 538, 1024 }, { 6, 539, 1024 }, { 5, 540, 1024 }, { 6, 541, 1024 }, { 6, 542, 1024 }, { 7, 543, 1024 },
|
---|
3509 | { 3, 544, 1024 }, { 4, 545, 1024 }, { 4, 546, 1024 }, { 5, 547, 1024 }, { 4, 548, 1024 }, { 5, 549, 1024 }, { 5, 550, 1024 }, { 6, 551, 1024 },
|
---|
3510 | { 4, 552, 1024 }, { 5, 553, 1024 }, { 5, 554, 1024 }, { 6, 555, 1024 }, { 5, 556, 1024 }, { 6, 557, 1024 }, { 6, 558, 1024 }, { 7, 559, 1024 },
|
---|
3511 | { 4, 560, 1024 }, { 5, 561, 1024 }, { 5, 562, 1024 }, { 6, 563, 1024 }, { 5, 564, 1024 }, { 6, 565, 1024 }, { 6, 566, 1024 }, { 7, 567, 1024 },
|
---|
3512 | { 5, 568, 1024 }, { 6, 569, 1024 }, { 6, 570, 1024 }, { 7, 571, 1024 }, { 6, 572, 1024 }, { 7, 573, 1024 }, { 7, 574, 1024 }, { 8, 575, 1024 },
|
---|
3513 | { 3, 576, 1024 }, { 4, 577, 1024 }, { 4, 578, 1024 }, { 5, 579, 1024 }, { 4, 580, 1024 }, { 5, 581, 1024 }, { 5, 582, 1024 }, { 6, 583, 1024 },
|
---|
3514 | { 4, 584, 1024 }, { 5, 585, 1024 }, { 5, 586, 1024 }, { 6, 587, 1024 }, { 5, 588, 1024 }, { 6, 589, 1024 }, { 6, 590, 1024 }, { 7, 591, 1024 },
|
---|
3515 | { 4, 592, 1024 }, { 5, 593, 1024 }, { 5, 594, 1024 }, { 6, 595, 1024 }, { 5, 596, 1024 }, { 6, 597, 1024 }, { 6, 598, 1024 }, { 7, 599, 1024 },
|
---|
3516 | { 5, 600, 1024 }, { 6, 601, 1024 }, { 6, 602, 1024 }, { 7, 603, 1024 }, { 6, 604, 1024 }, { 7, 605, 1024 }, { 7, 606, 1024 }, { 8, 607, 1024 },
|
---|
3517 | { 4, 608, 1024 }, { 5, 609, 1024 }, { 5, 610, 1024 }, { 6, 611, 1024 }, { 5, 612, 1024 }, { 6, 613, 1024 }, { 6, 614, 1024 }, { 7, 615, 1024 },
|
---|
3518 | { 5, 616, 1024 }, { 6, 617, 1024 }, { 6, 618, 1024 }, { 7, 619, 1024 }, { 6, 620, 1024 }, { 7, 621, 1024 }, { 7, 622, 1024 }, { 8, 623, 1024 },
|
---|
3519 | { 5, 624, 1024 }, { 6, 625, 1024 }, { 6, 626, 1024 }, { 7, 627, 1024 }, { 6, 628, 1024 }, { 7, 629, 1024 }, { 7, 630, 1024 }, { 8, 631, 1024 },
|
---|
3520 | { 6, 632, 1024 }, { 7, 633, 1024 }, { 7, 634, 1024 }, { 8, 635, 1024 }, { 7, 636, 1024 }, { 8, 637, 1024 }, { 8, 638, 1024 }, { 9, 639, 1024 },
|
---|
3521 | { 3, 640, 1024 }, { 4, 641, 1024 }, { 4, 642, 1024 }, { 5, 643, 1024 }, { 4, 644, 1024 }, { 5, 645, 1024 }, { 5, 646, 1024 }, { 6, 647, 1024 },
|
---|
3522 | { 4, 648, 1024 }, { 5, 649, 1024 }, { 5, 650, 1024 }, { 6, 651, 1024 }, { 5, 652, 1024 }, { 6, 653, 1024 }, { 6, 654, 1024 }, { 7, 655, 1024 },
|
---|
3523 | { 4, 656, 1024 }, { 5, 657, 1024 }, { 5, 658, 1024 }, { 6, 659, 1024 }, { 5, 660, 1024 }, { 6, 661, 1024 }, { 6, 662, 1024 }, { 7, 663, 1024 },
|
---|
3524 | { 5, 664, 1024 }, { 6, 665, 1024 }, { 6, 666, 1024 }, { 7, 667, 1024 }, { 6, 668, 1024 }, { 7, 669, 1024 }, { 7, 670, 1024 }, { 8, 671, 1024 },
|
---|
3525 | { 4, 672, 1024 }, { 5, 673, 1024 }, { 5, 674, 1024 }, { 6, 675, 1024 }, { 5, 676, 1024 }, { 6, 677, 1024 }, { 6, 678, 1024 }, { 7, 679, 1024 },
|
---|
3526 | { 5, 680, 1024 }, { 6, 681, 1024 }, { 6, 682, 1024 }, { 7, 683, 1024 }, { 6, 684, 1024 }, { 7, 685, 1024 }, { 7, 686, 1024 }, { 8, 687, 1024 },
|
---|
3527 | { 5, 688, 1024 }, { 6, 689, 1024 }, { 6, 690, 1024 }, { 7, 691, 1024 }, { 6, 692, 1024 }, { 7, 693, 1024 }, { 7, 694, 1024 }, { 8, 695, 1024 },
|
---|
3528 | { 6, 696, 1024 }, { 7, 697, 1024 }, { 7, 698, 1024 }, { 8, 699, 1024 }, { 7, 700, 1024 }, { 8, 701, 1024 }, { 8, 702, 1024 }, { 9, 703, 1024 },
|
---|
3529 | { 4, 704, 1024 }, { 5, 705, 1024 }, { 5, 706, 1024 }, { 6, 707, 1024 }, { 5, 708, 1024 }, { 6, 709, 1024 }, { 6, 710, 1024 }, { 7, 711, 1024 },
|
---|
3530 | { 5, 712, 1024 }, { 6, 713, 1024 }, { 6, 714, 1024 }, { 7, 715, 1024 }, { 6, 716, 1024 }, { 7, 717, 1024 }, { 7, 718, 1024 }, { 8, 719, 1024 },
|
---|
3531 | { 5, 720, 1024 }, { 6, 721, 1024 }, { 6, 722, 1024 }, { 7, 723, 1024 }, { 6, 724, 1024 }, { 7, 725, 1024 }, { 7, 726, 1024 }, { 8, 727, 1024 },
|
---|
3532 | { 6, 728, 1024 }, { 7, 729, 1024 }, { 7, 730, 1024 }, { 8, 731, 1024 }, { 7, 732, 1024 }, { 8, 733, 1024 }, { 8, 734, 1024 }, { 9, 735, 1024 },
|
---|
3533 | { 5, 736, 1024 }, { 6, 737, 1024 }, { 6, 738, 1024 }, { 7, 739, 1024 }, { 6, 740, 1024 }, { 7, 741, 1024 }, { 7, 742, 1024 }, { 8, 743, 1024 },
|
---|
3534 | { 6, 744, 1024 }, { 7, 745, 1024 }, { 7, 746, 1024 }, { 8, 747, 1024 }, { 7, 748, 1024 }, { 8, 749, 1024 }, { 8, 750, 1024 }, { 9, 751, 1024 },
|
---|
3535 | { 6, 752, 1024 }, { 7, 753, 1024 }, { 7, 754, 1024 }, { 8, 755, 1024 }, { 7, 756, 1024 }, { 8, 757, 1024 }, { 8, 758, 1024 }, { 9, 759, 1024 },
|
---|
3536 | { 7, 760, 1024 }, { 8, 761, 1024 }, { 8, 762, 1024 }, { 9, 763, 1024 }, { 8, 764, 1024 }, { 9, 765, 1024 }, { 9, 766, 1024 }, { 10, 767, 1024 },
|
---|
3537 | { 3, 768, 1024 }, { 4, 769, 1024 }, { 4, 770, 1024 }, { 5, 771, 1024 }, { 4, 772, 1024 }, { 5, 773, 1024 }, { 5, 774, 1024 }, { 6, 775, 1024 },
|
---|
3538 | { 4, 776, 1024 }, { 5, 777, 1024 }, { 5, 778, 1024 }, { 6, 779, 1024 }, { 5, 780, 1024 }, { 6, 781, 1024 }, { 6, 782, 1024 }, { 7, 783, 1024 },
|
---|
3539 | { 4, 784, 1024 }, { 5, 785, 1024 }, { 5, 786, 1024 }, { 6, 787, 1024 }, { 5, 788, 1024 }, { 6, 789, 1024 }, { 6, 790, 1024 }, { 7, 791, 1024 },
|
---|
3540 | { 5, 792, 1024 }, { 6, 793, 1024 }, { 6, 794, 1024 }, { 7, 795, 1024 }, { 6, 796, 1024 }, { 7, 797, 1024 }, { 7, 798, 1024 }, { 8, 799, 1024 },
|
---|
3541 | { 4, 800, 1024 }, { 5, 801, 1024 }, { 5, 802, 1024 }, { 6, 803, 1024 }, { 5, 804, 1024 }, { 6, 805, 1024 }, { 6, 806, 1024 }, { 7, 807, 1024 },
|
---|
3542 | { 5, 808, 1024 }, { 6, 809, 1024 }, { 6, 810, 1024 }, { 7, 811, 1024 }, { 6, 812, 1024 }, { 7, 813, 1024 }, { 7, 814, 1024 }, { 8, 815, 1024 },
|
---|
3543 | { 5, 816, 1024 }, { 6, 817, 1024 }, { 6, 818, 1024 }, { 7, 819, 1024 }, { 6, 820, 1024 }, { 7, 821, 1024 }, { 7, 822, 1024 }, { 8, 823, 1024 },
|
---|
3544 | { 6, 824, 1024 }, { 7, 825, 1024 }, { 7, 826, 1024 }, { 8, 827, 1024 }, { 7, 828, 1024 }, { 8, 829, 1024 }, { 8, 830, 1024 }, { 9, 831, 1024 },
|
---|
3545 | { 4, 832, 1024 }, { 5, 833, 1024 }, { 5, 834, 1024 }, { 6, 835, 1024 }, { 5, 836, 1024 }, { 6, 837, 1024 }, { 6, 838, 1024 }, { 7, 839, 1024 },
|
---|
3546 | { 5, 840, 1024 }, { 6, 841, 1024 }, { 6, 842, 1024 }, { 7, 843, 1024 }, { 6, 844, 1024 }, { 7, 845, 1024 }, { 7, 846, 1024 }, { 8, 847, 1024 },
|
---|
3547 | { 5, 848, 1024 }, { 6, 849, 1024 }, { 6, 850, 1024 }, { 7, 851, 1024 }, { 6, 852, 1024 }, { 7, 853, 1024 }, { 7, 854, 1024 }, { 8, 855, 1024 },
|
---|
3548 | { 6, 856, 1024 }, { 7, 857, 1024 }, { 7, 858, 1024 }, { 8, 859, 1024 }, { 7, 860, 1024 }, { 8, 861, 1024 }, { 8, 862, 1024 }, { 9, 863, 1024 },
|
---|
3549 | { 5, 864, 1024 }, { 6, 865, 1024 }, { 6, 866, 1024 }, { 7, 867, 1024 }, { 6, 868, 1024 }, { 7, 869, 1024 }, { 7, 870, 1024 }, { 8, 871, 1024 },
|
---|
3550 | { 6, 872, 1024 }, { 7, 873, 1024 }, { 7, 874, 1024 }, { 8, 875, 1024 }, { 7, 876, 1024 }, { 8, 877, 1024 }, { 8, 878, 1024 }, { 9, 879, 1024 },
|
---|
3551 | { 6, 880, 1024 }, { 7, 881, 1024 }, { 7, 882, 1024 }, { 8, 883, 1024 }, { 7, 884, 1024 }, { 8, 885, 1024 }, { 8, 886, 1024 }, { 9, 887, 1024 },
|
---|
3552 | { 7, 888, 1024 }, { 8, 889, 1024 }, { 8, 890, 1024 }, { 9, 891, 1024 }, { 8, 892, 1024 }, { 9, 893, 1024 }, { 9, 894, 1024 }, { 10, 895, 1024 },
|
---|
3553 | { 4, 896, 1024 }, { 5, 897, 1024 }, { 5, 898, 1024 }, { 6, 899, 1024 }, { 5, 900, 1024 }, { 6, 901, 1024 }, { 6, 902, 1024 }, { 7, 903, 1024 },
|
---|
3554 | { 5, 904, 1024 }, { 6, 905, 1024 }, { 6, 906, 1024 }, { 7, 907, 1024 }, { 6, 908, 1024 }, { 7, 909, 1024 }, { 7, 910, 1024 }, { 8, 911, 1024 },
|
---|
3555 | { 5, 912, 1024 }, { 6, 913, 1024 }, { 6, 914, 1024 }, { 7, 915, 1024 }, { 6, 916, 1024 }, { 7, 917, 1024 }, { 7, 918, 1024 }, { 8, 919, 1024 },
|
---|
3556 | { 6, 920, 1024 }, { 7, 921, 1024 }, { 7, 922, 1024 }, { 8, 923, 1024 }, { 7, 924, 1024 }, { 8, 925, 1024 }, { 8, 926, 1024 }, { 9, 927, 1024 },
|
---|
3557 | { 5, 928, 1024 }, { 6, 929, 1024 }, { 6, 930, 1024 }, { 7, 931, 1024 }, { 6, 932, 1024 }, { 7, 933, 1024 }, { 7, 934, 1024 }, { 8, 935, 1024 },
|
---|
3558 | { 6, 936, 1024 }, { 7, 937, 1024 }, { 7, 938, 1024 }, { 8, 939, 1024 }, { 7, 940, 1024 }, { 8, 941, 1024 }, { 8, 942, 1024 }, { 9, 943, 1024 },
|
---|
3559 | { 6, 944, 1024 }, { 7, 945, 1024 }, { 7, 946, 1024 }, { 8, 947, 1024 }, { 7, 948, 1024 }, { 8, 949, 1024 }, { 8, 950, 1024 }, { 9, 951, 1024 },
|
---|
3560 | { 7, 952, 1024 }, { 8, 953, 1024 }, { 8, 954, 1024 }, { 9, 955, 1024 }, { 8, 956, 1024 }, { 9, 957, 1024 }, { 9, 958, 1024 }, { 10, 959, 1024 },
|
---|
3561 | { 5, 960, 1024 }, { 6, 961, 1024 }, { 6, 962, 1024 }, { 7, 963, 1024 }, { 6, 964, 1024 }, { 7, 965, 1024 }, { 7, 966, 1024 }, { 8, 967, 1024 },
|
---|
3562 | { 6, 968, 1024 }, { 7, 969, 1024 }, { 7, 970, 1024 }, { 8, 971, 1024 }, { 7, 972, 1024 }, { 8, 973, 1024 }, { 8, 974, 1024 }, { 9, 975, 1024 },
|
---|
3563 | { 6, 976, 1024 }, { 7, 977, 1024 }, { 7, 978, 1024 }, { 8, 979, 1024 }, { 7, 980, 1024 }, { 8, 981, 1024 }, { 8, 982, 1024 }, { 9, 983, 1024 },
|
---|
3564 | { 7, 984, 1024 }, { 8, 985, 1024 }, { 8, 986, 1024 }, { 9, 987, 1024 }, { 8, 988, 1024 }, { 9, 989, 1024 }, { 9, 990, 1024 }, { 10, 991, 1024 },
|
---|
3565 | { 6, 992, 1024 }, { 7, 993, 1024 }, { 7, 994, 1024 }, { 8, 995, 1024 }, { 7, 996, 1024 }, { 8, 997, 1024 }, { 8, 998, 1024 }, { 9, 999, 1024 },
|
---|
3566 | { 7, 1000, 1024 }, { 8, 1001, 1024 }, { 8, 1002, 1024 }, { 9, 1003, 1024 }, { 8, 1004, 1024 }, { 9, 1005, 1024 }, { 9, 1006, 1024 }, { 10, 1007, 1024 },
|
---|
3567 | { 7, 1008, 1024 }, { 8, 1009, 1024 }, { 8, 1010, 1024 }, { 9, 1011, 1024 }, { 8, 1012, 1024 }, { 9, 1013, 1024 }, { 9, 1014, 1024 }, { 10, 1015, 1024 },
|
---|
3568 | { 8, 1016, 1024 }, { 9, 1017, 1024 }, { 9, 1018, 1024 }, { 10, 1019, 1024 }, { 9, 1020, 1024 }, { 10, 1021, 1024 }, { 10, 1022, 1024 }, { 11, 1023, 1024 },
|
---|
3569 | #if FP_LUT > 11
|
---|
3570 | { 1, 0, 0 }, { 2, 1, 2048 }, { 2, 2, 2048 }, { 3, 3, 2048 }, { 2, 4, 2048 }, { 3, 5, 2048 }, { 3, 6, 2048 }, { 4, 7, 2048 },
|
---|
3571 | { 2, 8, 2048 }, { 3, 9, 2048 }, { 3, 10, 2048 }, { 4, 11, 2048 }, { 3, 12, 2048 }, { 4, 13, 2048 }, { 4, 14, 2048 }, { 5, 15, 2048 },
|
---|
3572 | { 2, 16, 2048 }, { 3, 17, 2048 }, { 3, 18, 2048 }, { 4, 19, 2048 }, { 3, 20, 2048 }, { 4, 21, 2048 }, { 4, 22, 2048 }, { 5, 23, 2048 },
|
---|
3573 | { 3, 24, 2048 }, { 4, 25, 2048 }, { 4, 26, 2048 }, { 5, 27, 2048 }, { 4, 28, 2048 }, { 5, 29, 2048 }, { 5, 30, 2048 }, { 6, 31, 2048 },
|
---|
3574 | { 2, 32, 2048 }, { 3, 33, 2048 }, { 3, 34, 2048 }, { 4, 35, 2048 }, { 3, 36, 2048 }, { 4, 37, 2048 }, { 4, 38, 2048 }, { 5, 39, 2048 },
|
---|
3575 | { 3, 40, 2048 }, { 4, 41, 2048 }, { 4, 42, 2048 }, { 5, 43, 2048 }, { 4, 44, 2048 }, { 5, 45, 2048 }, { 5, 46, 2048 }, { 6, 47, 2048 },
|
---|
3576 | { 3, 48, 2048 }, { 4, 49, 2048 }, { 4, 50, 2048 }, { 5, 51, 2048 }, { 4, 52, 2048 }, { 5, 53, 2048 }, { 5, 54, 2048 }, { 6, 55, 2048 },
|
---|
3577 | { 4, 56, 2048 }, { 5, 57, 2048 }, { 5, 58, 2048 }, { 6, 59, 2048 }, { 5, 60, 2048 }, { 6, 61, 2048 }, { 6, 62, 2048 }, { 7, 63, 2048 },
|
---|
3578 | { 2, 64, 2048 }, { 3, 65, 2048 }, { 3, 66, 2048 }, { 4, 67, 2048 }, { 3, 68, 2048 }, { 4, 69, 2048 }, { 4, 70, 2048 }, { 5, 71, 2048 },
|
---|
3579 | { 3, 72, 2048 }, { 4, 73, 2048 }, { 4, 74, 2048 }, { 5, 75, 2048 }, { 4, 76, 2048 }, { 5, 77, 2048 }, { 5, 78, 2048 }, { 6, 79, 2048 },
|
---|
3580 | { 3, 80, 2048 }, { 4, 81, 2048 }, { 4, 82, 2048 }, { 5, 83, 2048 }, { 4, 84, 2048 }, { 5, 85, 2048 }, { 5, 86, 2048 }, { 6, 87, 2048 },
|
---|
3581 | { 4, 88, 2048 }, { 5, 89, 2048 }, { 5, 90, 2048 }, { 6, 91, 2048 }, { 5, 92, 2048 }, { 6, 93, 2048 }, { 6, 94, 2048 }, { 7, 95, 2048 },
|
---|
3582 | { 3, 96, 2048 }, { 4, 97, 2048 }, { 4, 98, 2048 }, { 5, 99, 2048 }, { 4, 100, 2048 }, { 5, 101, 2048 }, { 5, 102, 2048 }, { 6, 103, 2048 },
|
---|
3583 | { 4, 104, 2048 }, { 5, 105, 2048 }, { 5, 106, 2048 }, { 6, 107, 2048 }, { 5, 108, 2048 }, { 6, 109, 2048 }, { 6, 110, 2048 }, { 7, 111, 2048 },
|
---|
3584 | { 4, 112, 2048 }, { 5, 113, 2048 }, { 5, 114, 2048 }, { 6, 115, 2048 }, { 5, 116, 2048 }, { 6, 117, 2048 }, { 6, 118, 2048 }, { 7, 119, 2048 },
|
---|
3585 | { 5, 120, 2048 }, { 6, 121, 2048 }, { 6, 122, 2048 }, { 7, 123, 2048 }, { 6, 124, 2048 }, { 7, 125, 2048 }, { 7, 126, 2048 }, { 8, 127, 2048 },
|
---|
3586 | { 2, 128, 2048 }, { 3, 129, 2048 }, { 3, 130, 2048 }, { 4, 131, 2048 }, { 3, 132, 2048 }, { 4, 133, 2048 }, { 4, 134, 2048 }, { 5, 135, 2048 },
|
---|
3587 | { 3, 136, 2048 }, { 4, 137, 2048 }, { 4, 138, 2048 }, { 5, 139, 2048 }, { 4, 140, 2048 }, { 5, 141, 2048 }, { 5, 142, 2048 }, { 6, 143, 2048 },
|
---|
3588 | { 3, 144, 2048 }, { 4, 145, 2048 }, { 4, 146, 2048 }, { 5, 147, 2048 }, { 4, 148, 2048 }, { 5, 149, 2048 }, { 5, 150, 2048 }, { 6, 151, 2048 },
|
---|
3589 | { 4, 152, 2048 }, { 5, 153, 2048 }, { 5, 154, 2048 }, { 6, 155, 2048 }, { 5, 156, 2048 }, { 6, 157, 2048 }, { 6, 158, 2048 }, { 7, 159, 2048 },
|
---|
3590 | { 3, 160, 2048 }, { 4, 161, 2048 }, { 4, 162, 2048 }, { 5, 163, 2048 }, { 4, 164, 2048 }, { 5, 165, 2048 }, { 5, 166, 2048 }, { 6, 167, 2048 },
|
---|
3591 | { 4, 168, 2048 }, { 5, 169, 2048 }, { 5, 170, 2048 }, { 6, 171, 2048 }, { 5, 172, 2048 }, { 6, 173, 2048 }, { 6, 174, 2048 }, { 7, 175, 2048 },
|
---|
3592 | { 4, 176, 2048 }, { 5, 177, 2048 }, { 5, 178, 2048 }, { 6, 179, 2048 }, { 5, 180, 2048 }, { 6, 181, 2048 }, { 6, 182, 2048 }, { 7, 183, 2048 },
|
---|
3593 | { 5, 184, 2048 }, { 6, 185, 2048 }, { 6, 186, 2048 }, { 7, 187, 2048 }, { 6, 188, 2048 }, { 7, 189, 2048 }, { 7, 190, 2048 }, { 8, 191, 2048 },
|
---|
3594 | { 3, 192, 2048 }, { 4, 193, 2048 }, { 4, 194, 2048 }, { 5, 195, 2048 }, { 4, 196, 2048 }, { 5, 197, 2048 }, { 5, 198, 2048 }, { 6, 199, 2048 },
|
---|
3595 | { 4, 200, 2048 }, { 5, 201, 2048 }, { 5, 202, 2048 }, { 6, 203, 2048 }, { 5, 204, 2048 }, { 6, 205, 2048 }, { 6, 206, 2048 }, { 7, 207, 2048 },
|
---|
3596 | { 4, 208, 2048 }, { 5, 209, 2048 }, { 5, 210, 2048 }, { 6, 211, 2048 }, { 5, 212, 2048 }, { 6, 213, 2048 }, { 6, 214, 2048 }, { 7, 215, 2048 },
|
---|
3597 | { 5, 216, 2048 }, { 6, 217, 2048 }, { 6, 218, 2048 }, { 7, 219, 2048 }, { 6, 220, 2048 }, { 7, 221, 2048 }, { 7, 222, 2048 }, { 8, 223, 2048 },
|
---|
3598 | { 4, 224, 2048 }, { 5, 225, 2048 }, { 5, 226, 2048 }, { 6, 227, 2048 }, { 5, 228, 2048 }, { 6, 229, 2048 }, { 6, 230, 2048 }, { 7, 231, 2048 },
|
---|
3599 | { 5, 232, 2048 }, { 6, 233, 2048 }, { 6, 234, 2048 }, { 7, 235, 2048 }, { 6, 236, 2048 }, { 7, 237, 2048 }, { 7, 238, 2048 }, { 8, 239, 2048 },
|
---|
3600 | { 5, 240, 2048 }, { 6, 241, 2048 }, { 6, 242, 2048 }, { 7, 243, 2048 }, { 6, 244, 2048 }, { 7, 245, 2048 }, { 7, 246, 2048 }, { 8, 247, 2048 },
|
---|
3601 | { 6, 248, 2048 }, { 7, 249, 2048 }, { 7, 250, 2048 }, { 8, 251, 2048 }, { 7, 252, 2048 }, { 8, 253, 2048 }, { 8, 254, 2048 }, { 9, 255, 2048 },
|
---|
3602 | { 2, 256, 2048 }, { 3, 257, 2048 }, { 3, 258, 2048 }, { 4, 259, 2048 }, { 3, 260, 2048 }, { 4, 261, 2048 }, { 4, 262, 2048 }, { 5, 263, 2048 },
|
---|
3603 | { 3, 264, 2048 }, { 4, 265, 2048 }, { 4, 266, 2048 }, { 5, 267, 2048 }, { 4, 268, 2048 }, { 5, 269, 2048 }, { 5, 270, 2048 }, { 6, 271, 2048 },
|
---|
3604 | { 3, 272, 2048 }, { 4, 273, 2048 }, { 4, 274, 2048 }, { 5, 275, 2048 }, { 4, 276, 2048 }, { 5, 277, 2048 }, { 5, 278, 2048 }, { 6, 279, 2048 },
|
---|
3605 | { 4, 280, 2048 }, { 5, 281, 2048 }, { 5, 282, 2048 }, { 6, 283, 2048 }, { 5, 284, 2048 }, { 6, 285, 2048 }, { 6, 286, 2048 }, { 7, 287, 2048 },
|
---|
3606 | { 3, 288, 2048 }, { 4, 289, 2048 }, { 4, 290, 2048 }, { 5, 291, 2048 }, { 4, 292, 2048 }, { 5, 293, 2048 }, { 5, 294, 2048 }, { 6, 295, 2048 },
|
---|
3607 | { 4, 296, 2048 }, { 5, 297, 2048 }, { 5, 298, 2048 }, { 6, 299, 2048 }, { 5, 300, 2048 }, { 6, 301, 2048 }, { 6, 302, 2048 }, { 7, 303, 2048 },
|
---|
3608 | { 4, 304, 2048 }, { 5, 305, 2048 }, { 5, 306, 2048 }, { 6, 307, 2048 }, { 5, 308, 2048 }, { 6, 309, 2048 }, { 6, 310, 2048 }, { 7, 311, 2048 },
|
---|
3609 | { 5, 312, 2048 }, { 6, 313, 2048 }, { 6, 314, 2048 }, { 7, 315, 2048 }, { 6, 316, 2048 }, { 7, 317, 2048 }, { 7, 318, 2048 }, { 8, 319, 2048 },
|
---|
3610 | { 3, 320, 2048 }, { 4, 321, 2048 }, { 4, 322, 2048 }, { 5, 323, 2048 }, { 4, 324, 2048 }, { 5, 325, 2048 }, { 5, 326, 2048 }, { 6, 327, 2048 },
|
---|
3611 | { 4, 328, 2048 }, { 5, 329, 2048 }, { 5, 330, 2048 }, { 6, 331, 2048 }, { 5, 332, 2048 }, { 6, 333, 2048 }, { 6, 334, 2048 }, { 7, 335, 2048 },
|
---|
3612 | { 4, 336, 2048 }, { 5, 337, 2048 }, { 5, 338, 2048 }, { 6, 339, 2048 }, { 5, 340, 2048 }, { 6, 341, 2048 }, { 6, 342, 2048 }, { 7, 343, 2048 },
|
---|
3613 | { 5, 344, 2048 }, { 6, 345, 2048 }, { 6, 346, 2048 }, { 7, 347, 2048 }, { 6, 348, 2048 }, { 7, 349, 2048 }, { 7, 350, 2048 }, { 8, 351, 2048 },
|
---|
3614 | { 4, 352, 2048 }, { 5, 353, 2048 }, { 5, 354, 2048 }, { 6, 355, 2048 }, { 5, 356, 2048 }, { 6, 357, 2048 }, { 6, 358, 2048 }, { 7, 359, 2048 },
|
---|
3615 | { 5, 360, 2048 }, { 6, 361, 2048 }, { 6, 362, 2048 }, { 7, 363, 2048 }, { 6, 364, 2048 }, { 7, 365, 2048 }, { 7, 366, 2048 }, { 8, 367, 2048 },
|
---|
3616 | { 5, 368, 2048 }, { 6, 369, 2048 }, { 6, 370, 2048 }, { 7, 371, 2048 }, { 6, 372, 2048 }, { 7, 373, 2048 }, { 7, 374, 2048 }, { 8, 375, 2048 },
|
---|
3617 | { 6, 376, 2048 }, { 7, 377, 2048 }, { 7, 378, 2048 }, { 8, 379, 2048 }, { 7, 380, 2048 }, { 8, 381, 2048 }, { 8, 382, 2048 }, { 9, 383, 2048 },
|
---|
3618 | { 3, 384, 2048 }, { 4, 385, 2048 }, { 4, 386, 2048 }, { 5, 387, 2048 }, { 4, 388, 2048 }, { 5, 389, 2048 }, { 5, 390, 2048 }, { 6, 391, 2048 },
|
---|
3619 | { 4, 392, 2048 }, { 5, 393, 2048 }, { 5, 394, 2048 }, { 6, 395, 2048 }, { 5, 396, 2048 }, { 6, 397, 2048 }, { 6, 398, 2048 }, { 7, 399, 2048 },
|
---|
3620 | { 4, 400, 2048 }, { 5, 401, 2048 }, { 5, 402, 2048 }, { 6, 403, 2048 }, { 5, 404, 2048 }, { 6, 405, 2048 }, { 6, 406, 2048 }, { 7, 407, 2048 },
|
---|
3621 | { 5, 408, 2048 }, { 6, 409, 2048 }, { 6, 410, 2048 }, { 7, 411, 2048 }, { 6, 412, 2048 }, { 7, 413, 2048 }, { 7, 414, 2048 }, { 8, 415, 2048 },
|
---|
3622 | { 4, 416, 2048 }, { 5, 417, 2048 }, { 5, 418, 2048 }, { 6, 419, 2048 }, { 5, 420, 2048 }, { 6, 421, 2048 }, { 6, 422, 2048 }, { 7, 423, 2048 },
|
---|
3623 | { 5, 424, 2048 }, { 6, 425, 2048 }, { 6, 426, 2048 }, { 7, 427, 2048 }, { 6, 428, 2048 }, { 7, 429, 2048 }, { 7, 430, 2048 }, { 8, 431, 2048 },
|
---|
3624 | { 5, 432, 2048 }, { 6, 433, 2048 }, { 6, 434, 2048 }, { 7, 435, 2048 }, { 6, 436, 2048 }, { 7, 437, 2048 }, { 7, 438, 2048 }, { 8, 439, 2048 },
|
---|
3625 | { 6, 440, 2048 }, { 7, 441, 2048 }, { 7, 442, 2048 }, { 8, 443, 2048 }, { 7, 444, 2048 }, { 8, 445, 2048 }, { 8, 446, 2048 }, { 9, 447, 2048 },
|
---|
3626 | { 4, 448, 2048 }, { 5, 449, 2048 }, { 5, 450, 2048 }, { 6, 451, 2048 }, { 5, 452, 2048 }, { 6, 453, 2048 }, { 6, 454, 2048 }, { 7, 455, 2048 },
|
---|
3627 | { 5, 456, 2048 }, { 6, 457, 2048 }, { 6, 458, 2048 }, { 7, 459, 2048 }, { 6, 460, 2048 }, { 7, 461, 2048 }, { 7, 462, 2048 }, { 8, 463, 2048 },
|
---|
3628 | { 5, 464, 2048 }, { 6, 465, 2048 }, { 6, 466, 2048 }, { 7, 467, 2048 }, { 6, 468, 2048 }, { 7, 469, 2048 }, { 7, 470, 2048 }, { 8, 471, 2048 },
|
---|
3629 | { 6, 472, 2048 }, { 7, 473, 2048 }, { 7, 474, 2048 }, { 8, 475, 2048 }, { 7, 476, 2048 }, { 8, 477, 2048 }, { 8, 478, 2048 }, { 9, 479, 2048 },
|
---|
3630 | { 5, 480, 2048 }, { 6, 481, 2048 }, { 6, 482, 2048 }, { 7, 483, 2048 }, { 6, 484, 2048 }, { 7, 485, 2048 }, { 7, 486, 2048 }, { 8, 487, 2048 },
|
---|
3631 | { 6, 488, 2048 }, { 7, 489, 2048 }, { 7, 490, 2048 }, { 8, 491, 2048 }, { 7, 492, 2048 }, { 8, 493, 2048 }, { 8, 494, 2048 }, { 9, 495, 2048 },
|
---|
3632 | { 6, 496, 2048 }, { 7, 497, 2048 }, { 7, 498, 2048 }, { 8, 499, 2048 }, { 7, 500, 2048 }, { 8, 501, 2048 }, { 8, 502, 2048 }, { 9, 503, 2048 },
|
---|
3633 | { 7, 504, 2048 }, { 8, 505, 2048 }, { 8, 506, 2048 }, { 9, 507, 2048 }, { 8, 508, 2048 }, { 9, 509, 2048 }, { 9, 510, 2048 }, { 10, 511, 2048 },
|
---|
3634 | { 2, 512, 2048 }, { 3, 513, 2048 }, { 3, 514, 2048 }, { 4, 515, 2048 }, { 3, 516, 2048 }, { 4, 517, 2048 }, { 4, 518, 2048 }, { 5, 519, 2048 },
|
---|
3635 | { 3, 520, 2048 }, { 4, 521, 2048 }, { 4, 522, 2048 }, { 5, 523, 2048 }, { 4, 524, 2048 }, { 5, 525, 2048 }, { 5, 526, 2048 }, { 6, 527, 2048 },
|
---|
3636 | { 3, 528, 2048 }, { 4, 529, 2048 }, { 4, 530, 2048 }, { 5, 531, 2048 }, { 4, 532, 2048 }, { 5, 533, 2048 }, { 5, 534, 2048 }, { 6, 535, 2048 },
|
---|
3637 | { 4, 536, 2048 }, { 5, 537, 2048 }, { 5, 538, 2048 }, { 6, 539, 2048 }, { 5, 540, 2048 }, { 6, 541, 2048 }, { 6, 542, 2048 }, { 7, 543, 2048 },
|
---|
3638 | { 3, 544, 2048 }, { 4, 545, 2048 }, { 4, 546, 2048 }, { 5, 547, 2048 }, { 4, 548, 2048 }, { 5, 549, 2048 }, { 5, 550, 2048 }, { 6, 551, 2048 },
|
---|
3639 | { 4, 552, 2048 }, { 5, 553, 2048 }, { 5, 554, 2048 }, { 6, 555, 2048 }, { 5, 556, 2048 }, { 6, 557, 2048 }, { 6, 558, 2048 }, { 7, 559, 2048 },
|
---|
3640 | { 4, 560, 2048 }, { 5, 561, 2048 }, { 5, 562, 2048 }, { 6, 563, 2048 }, { 5, 564, 2048 }, { 6, 565, 2048 }, { 6, 566, 2048 }, { 7, 567, 2048 },
|
---|
3641 | { 5, 568, 2048 }, { 6, 569, 2048 }, { 6, 570, 2048 }, { 7, 571, 2048 }, { 6, 572, 2048 }, { 7, 573, 2048 }, { 7, 574, 2048 }, { 8, 575, 2048 },
|
---|
3642 | { 3, 576, 2048 }, { 4, 577, 2048 }, { 4, 578, 2048 }, { 5, 579, 2048 }, { 4, 580, 2048 }, { 5, 581, 2048 }, { 5, 582, 2048 }, { 6, 583, 2048 },
|
---|
3643 | { 4, 584, 2048 }, { 5, 585, 2048 }, { 5, 586, 2048 }, { 6, 587, 2048 }, { 5, 588, 2048 }, { 6, 589, 2048 }, { 6, 590, 2048 }, { 7, 591, 2048 },
|
---|
3644 | { 4, 592, 2048 }, { 5, 593, 2048 }, { 5, 594, 2048 }, { 6, 595, 2048 }, { 5, 596, 2048 }, { 6, 597, 2048 }, { 6, 598, 2048 }, { 7, 599, 2048 },
|
---|
3645 | { 5, 600, 2048 }, { 6, 601, 2048 }, { 6, 602, 2048 }, { 7, 603, 2048 }, { 6, 604, 2048 }, { 7, 605, 2048 }, { 7, 606, 2048 }, { 8, 607, 2048 },
|
---|
3646 | { 4, 608, 2048 }, { 5, 609, 2048 }, { 5, 610, 2048 }, { 6, 611, 2048 }, { 5, 612, 2048 }, { 6, 613, 2048 }, { 6, 614, 2048 }, { 7, 615, 2048 },
|
---|
3647 | { 5, 616, 2048 }, { 6, 617, 2048 }, { 6, 618, 2048 }, { 7, 619, 2048 }, { 6, 620, 2048 }, { 7, 621, 2048 }, { 7, 622, 2048 }, { 8, 623, 2048 },
|
---|
3648 | { 5, 624, 2048 }, { 6, 625, 2048 }, { 6, 626, 2048 }, { 7, 627, 2048 }, { 6, 628, 2048 }, { 7, 629, 2048 }, { 7, 630, 2048 }, { 8, 631, 2048 },
|
---|
3649 | { 6, 632, 2048 }, { 7, 633, 2048 }, { 7, 634, 2048 }, { 8, 635, 2048 }, { 7, 636, 2048 }, { 8, 637, 2048 }, { 8, 638, 2048 }, { 9, 639, 2048 },
|
---|
3650 | { 3, 640, 2048 }, { 4, 641, 2048 }, { 4, 642, 2048 }, { 5, 643, 2048 }, { 4, 644, 2048 }, { 5, 645, 2048 }, { 5, 646, 2048 }, { 6, 647, 2048 },
|
---|
3651 | { 4, 648, 2048 }, { 5, 649, 2048 }, { 5, 650, 2048 }, { 6, 651, 2048 }, { 5, 652, 2048 }, { 6, 653, 2048 }, { 6, 654, 2048 }, { 7, 655, 2048 },
|
---|
3652 | { 4, 656, 2048 }, { 5, 657, 2048 }, { 5, 658, 2048 }, { 6, 659, 2048 }, { 5, 660, 2048 }, { 6, 661, 2048 }, { 6, 662, 2048 }, { 7, 663, 2048 },
|
---|
3653 | { 5, 664, 2048 }, { 6, 665, 2048 }, { 6, 666, 2048 }, { 7, 667, 2048 }, { 6, 668, 2048 }, { 7, 669, 2048 }, { 7, 670, 2048 }, { 8, 671, 2048 },
|
---|
3654 | { 4, 672, 2048 }, { 5, 673, 2048 }, { 5, 674, 2048 }, { 6, 675, 2048 }, { 5, 676, 2048 }, { 6, 677, 2048 }, { 6, 678, 2048 }, { 7, 679, 2048 },
|
---|
3655 | { 5, 680, 2048 }, { 6, 681, 2048 }, { 6, 682, 2048 }, { 7, 683, 2048 }, { 6, 684, 2048 }, { 7, 685, 2048 }, { 7, 686, 2048 }, { 8, 687, 2048 },
|
---|
3656 | { 5, 688, 2048 }, { 6, 689, 2048 }, { 6, 690, 2048 }, { 7, 691, 2048 }, { 6, 692, 2048 }, { 7, 693, 2048 }, { 7, 694, 2048 }, { 8, 695, 2048 },
|
---|
3657 | { 6, 696, 2048 }, { 7, 697, 2048 }, { 7, 698, 2048 }, { 8, 699, 2048 }, { 7, 700, 2048 }, { 8, 701, 2048 }, { 8, 702, 2048 }, { 9, 703, 2048 },
|
---|
3658 | { 4, 704, 2048 }, { 5, 705, 2048 }, { 5, 706, 2048 }, { 6, 707, 2048 }, { 5, 708, 2048 }, { 6, 709, 2048 }, { 6, 710, 2048 }, { 7, 711, 2048 },
|
---|
3659 | { 5, 712, 2048 }, { 6, 713, 2048 }, { 6, 714, 2048 }, { 7, 715, 2048 }, { 6, 716, 2048 }, { 7, 717, 2048 }, { 7, 718, 2048 }, { 8, 719, 2048 },
|
---|
3660 | { 5, 720, 2048 }, { 6, 721, 2048 }, { 6, 722, 2048 }, { 7, 723, 2048 }, { 6, 724, 2048 }, { 7, 725, 2048 }, { 7, 726, 2048 }, { 8, 727, 2048 },
|
---|
3661 | { 6, 728, 2048 }, { 7, 729, 2048 }, { 7, 730, 2048 }, { 8, 731, 2048 }, { 7, 732, 2048 }, { 8, 733, 2048 }, { 8, 734, 2048 }, { 9, 735, 2048 },
|
---|
3662 | { 5, 736, 2048 }, { 6, 737, 2048 }, { 6, 738, 2048 }, { 7, 739, 2048 }, { 6, 740, 2048 }, { 7, 741, 2048 }, { 7, 742, 2048 }, { 8, 743, 2048 },
|
---|
3663 | { 6, 744, 2048 }, { 7, 745, 2048 }, { 7, 746, 2048 }, { 8, 747, 2048 }, { 7, 748, 2048 }, { 8, 749, 2048 }, { 8, 750, 2048 }, { 9, 751, 2048 },
|
---|
3664 | { 6, 752, 2048 }, { 7, 753, 2048 }, { 7, 754, 2048 }, { 8, 755, 2048 }, { 7, 756, 2048 }, { 8, 757, 2048 }, { 8, 758, 2048 }, { 9, 759, 2048 },
|
---|
3665 | { 7, 760, 2048 }, { 8, 761, 2048 }, { 8, 762, 2048 }, { 9, 763, 2048 }, { 8, 764, 2048 }, { 9, 765, 2048 }, { 9, 766, 2048 }, { 10, 767, 2048 },
|
---|
3666 | { 3, 768, 2048 }, { 4, 769, 2048 }, { 4, 770, 2048 }, { 5, 771, 2048 }, { 4, 772, 2048 }, { 5, 773, 2048 }, { 5, 774, 2048 }, { 6, 775, 2048 },
|
---|
3667 | { 4, 776, 2048 }, { 5, 777, 2048 }, { 5, 778, 2048 }, { 6, 779, 2048 }, { 5, 780, 2048 }, { 6, 781, 2048 }, { 6, 782, 2048 }, { 7, 783, 2048 },
|
---|
3668 | { 4, 784, 2048 }, { 5, 785, 2048 }, { 5, 786, 2048 }, { 6, 787, 2048 }, { 5, 788, 2048 }, { 6, 789, 2048 }, { 6, 790, 2048 }, { 7, 791, 2048 },
|
---|
3669 | { 5, 792, 2048 }, { 6, 793, 2048 }, { 6, 794, 2048 }, { 7, 795, 2048 }, { 6, 796, 2048 }, { 7, 797, 2048 }, { 7, 798, 2048 }, { 8, 799, 2048 },
|
---|
3670 | { 4, 800, 2048 }, { 5, 801, 2048 }, { 5, 802, 2048 }, { 6, 803, 2048 }, { 5, 804, 2048 }, { 6, 805, 2048 }, { 6, 806, 2048 }, { 7, 807, 2048 },
|
---|
3671 | { 5, 808, 2048 }, { 6, 809, 2048 }, { 6, 810, 2048 }, { 7, 811, 2048 }, { 6, 812, 2048 }, { 7, 813, 2048 }, { 7, 814, 2048 }, { 8, 815, 2048 },
|
---|
3672 | { 5, 816, 2048 }, { 6, 817, 2048 }, { 6, 818, 2048 }, { 7, 819, 2048 }, { 6, 820, 2048 }, { 7, 821, 2048 }, { 7, 822, 2048 }, { 8, 823, 2048 },
|
---|
3673 | { 6, 824, 2048 }, { 7, 825, 2048 }, { 7, 826, 2048 }, { 8, 827, 2048 }, { 7, 828, 2048 }, { 8, 829, 2048 }, { 8, 830, 2048 }, { 9, 831, 2048 },
|
---|
3674 | { 4, 832, 2048 }, { 5, 833, 2048 }, { 5, 834, 2048 }, { 6, 835, 2048 }, { 5, 836, 2048 }, { 6, 837, 2048 }, { 6, 838, 2048 }, { 7, 839, 2048 },
|
---|
3675 | { 5, 840, 2048 }, { 6, 841, 2048 }, { 6, 842, 2048 }, { 7, 843, 2048 }, { 6, 844, 2048 }, { 7, 845, 2048 }, { 7, 846, 2048 }, { 8, 847, 2048 },
|
---|
3676 | { 5, 848, 2048 }, { 6, 849, 2048 }, { 6, 850, 2048 }, { 7, 851, 2048 }, { 6, 852, 2048 }, { 7, 853, 2048 }, { 7, 854, 2048 }, { 8, 855, 2048 },
|
---|
3677 | { 6, 856, 2048 }, { 7, 857, 2048 }, { 7, 858, 2048 }, { 8, 859, 2048 }, { 7, 860, 2048 }, { 8, 861, 2048 }, { 8, 862, 2048 }, { 9, 863, 2048 },
|
---|
3678 | { 5, 864, 2048 }, { 6, 865, 2048 }, { 6, 866, 2048 }, { 7, 867, 2048 }, { 6, 868, 2048 }, { 7, 869, 2048 }, { 7, 870, 2048 }, { 8, 871, 2048 },
|
---|
3679 | { 6, 872, 2048 }, { 7, 873, 2048 }, { 7, 874, 2048 }, { 8, 875, 2048 }, { 7, 876, 2048 }, { 8, 877, 2048 }, { 8, 878, 2048 }, { 9, 879, 2048 },
|
---|
3680 | { 6, 880, 2048 }, { 7, 881, 2048 }, { 7, 882, 2048 }, { 8, 883, 2048 }, { 7, 884, 2048 }, { 8, 885, 2048 }, { 8, 886, 2048 }, { 9, 887, 2048 },
|
---|
3681 | { 7, 888, 2048 }, { 8, 889, 2048 }, { 8, 890, 2048 }, { 9, 891, 2048 }, { 8, 892, 2048 }, { 9, 893, 2048 }, { 9, 894, 2048 }, { 10, 895, 2048 },
|
---|
3682 | { 4, 896, 2048 }, { 5, 897, 2048 }, { 5, 898, 2048 }, { 6, 899, 2048 }, { 5, 900, 2048 }, { 6, 901, 2048 }, { 6, 902, 2048 }, { 7, 903, 2048 },
|
---|
3683 | { 5, 904, 2048 }, { 6, 905, 2048 }, { 6, 906, 2048 }, { 7, 907, 2048 }, { 6, 908, 2048 }, { 7, 909, 2048 }, { 7, 910, 2048 }, { 8, 911, 2048 },
|
---|
3684 | { 5, 912, 2048 }, { 6, 913, 2048 }, { 6, 914, 2048 }, { 7, 915, 2048 }, { 6, 916, 2048 }, { 7, 917, 2048 }, { 7, 918, 2048 }, { 8, 919, 2048 },
|
---|
3685 | { 6, 920, 2048 }, { 7, 921, 2048 }, { 7, 922, 2048 }, { 8, 923, 2048 }, { 7, 924, 2048 }, { 8, 925, 2048 }, { 8, 926, 2048 }, { 9, 927, 2048 },
|
---|
3686 | { 5, 928, 2048 }, { 6, 929, 2048 }, { 6, 930, 2048 }, { 7, 931, 2048 }, { 6, 932, 2048 }, { 7, 933, 2048 }, { 7, 934, 2048 }, { 8, 935, 2048 },
|
---|
3687 | { 6, 936, 2048 }, { 7, 937, 2048 }, { 7, 938, 2048 }, { 8, 939, 2048 }, { 7, 940, 2048 }, { 8, 941, 2048 }, { 8, 942, 2048 }, { 9, 943, 2048 },
|
---|
3688 | { 6, 944, 2048 }, { 7, 945, 2048 }, { 7, 946, 2048 }, { 8, 947, 2048 }, { 7, 948, 2048 }, { 8, 949, 2048 }, { 8, 950, 2048 }, { 9, 951, 2048 },
|
---|
3689 | { 7, 952, 2048 }, { 8, 953, 2048 }, { 8, 954, 2048 }, { 9, 955, 2048 }, { 8, 956, 2048 }, { 9, 957, 2048 }, { 9, 958, 2048 }, { 10, 959, 2048 },
|
---|
3690 | { 5, 960, 2048 }, { 6, 961, 2048 }, { 6, 962, 2048 }, { 7, 963, 2048 }, { 6, 964, 2048 }, { 7, 965, 2048 }, { 7, 966, 2048 }, { 8, 967, 2048 },
|
---|
3691 | { 6, 968, 2048 }, { 7, 969, 2048 }, { 7, 970, 2048 }, { 8, 971, 2048 }, { 7, 972, 2048 }, { 8, 973, 2048 }, { 8, 974, 2048 }, { 9, 975, 2048 },
|
---|
3692 | { 6, 976, 2048 }, { 7, 977, 2048 }, { 7, 978, 2048 }, { 8, 979, 2048 }, { 7, 980, 2048 }, { 8, 981, 2048 }, { 8, 982, 2048 }, { 9, 983, 2048 },
|
---|
3693 | { 7, 984, 2048 }, { 8, 985, 2048 }, { 8, 986, 2048 }, { 9, 987, 2048 }, { 8, 988, 2048 }, { 9, 989, 2048 }, { 9, 990, 2048 }, { 10, 991, 2048 },
|
---|
3694 | { 6, 992, 2048 }, { 7, 993, 2048 }, { 7, 994, 2048 }, { 8, 995, 2048 }, { 7, 996, 2048 }, { 8, 997, 2048 }, { 8, 998, 2048 }, { 9, 999, 2048 },
|
---|
3695 | { 7, 1000, 2048 }, { 8, 1001, 2048 }, { 8, 1002, 2048 }, { 9, 1003, 2048 }, { 8, 1004, 2048 }, { 9, 1005, 2048 }, { 9, 1006, 2048 }, { 10, 1007, 2048 },
|
---|
3696 | { 7, 1008, 2048 }, { 8, 1009, 2048 }, { 8, 1010, 2048 }, { 9, 1011, 2048 }, { 8, 1012, 2048 }, { 9, 1013, 2048 }, { 9, 1014, 2048 }, { 10, 1015, 2048 },
|
---|
3697 | { 8, 1016, 2048 }, { 9, 1017, 2048 }, { 9, 1018, 2048 }, { 10, 1019, 2048 }, { 9, 1020, 2048 }, { 10, 1021, 2048 }, { 10, 1022, 2048 }, { 11, 1023, 2048 },
|
---|
3698 | { 2, 1024, 2048 }, { 3, 1025, 2048 }, { 3, 1026, 2048 }, { 4, 1027, 2048 }, { 3, 1028, 2048 }, { 4, 1029, 2048 }, { 4, 1030, 2048 }, { 5, 1031, 2048 },
|
---|
3699 | { 3, 1032, 2048 }, { 4, 1033, 2048 }, { 4, 1034, 2048 }, { 5, 1035, 2048 }, { 4, 1036, 2048 }, { 5, 1037, 2048 }, { 5, 1038, 2048 }, { 6, 1039, 2048 },
|
---|
3700 | { 3, 1040, 2048 }, { 4, 1041, 2048 }, { 4, 1042, 2048 }, { 5, 1043, 2048 }, { 4, 1044, 2048 }, { 5, 1045, 2048 }, { 5, 1046, 2048 }, { 6, 1047, 2048 },
|
---|
3701 | { 4, 1048, 2048 }, { 5, 1049, 2048 }, { 5, 1050, 2048 }, { 6, 1051, 2048 }, { 5, 1052, 2048 }, { 6, 1053, 2048 }, { 6, 1054, 2048 }, { 7, 1055, 2048 },
|
---|
3702 | { 3, 1056, 2048 }, { 4, 1057, 2048 }, { 4, 1058, 2048 }, { 5, 1059, 2048 }, { 4, 1060, 2048 }, { 5, 1061, 2048 }, { 5, 1062, 2048 }, { 6, 1063, 2048 },
|
---|
3703 | { 4, 1064, 2048 }, { 5, 1065, 2048 }, { 5, 1066, 2048 }, { 6, 1067, 2048 }, { 5, 1068, 2048 }, { 6, 1069, 2048 }, { 6, 1070, 2048 }, { 7, 1071, 2048 },
|
---|
3704 | { 4, 1072, 2048 }, { 5, 1073, 2048 }, { 5, 1074, 2048 }, { 6, 1075, 2048 }, { 5, 1076, 2048 }, { 6, 1077, 2048 }, { 6, 1078, 2048 }, { 7, 1079, 2048 },
|
---|
3705 | { 5, 1080, 2048 }, { 6, 1081, 2048 }, { 6, 1082, 2048 }, { 7, 1083, 2048 }, { 6, 1084, 2048 }, { 7, 1085, 2048 }, { 7, 1086, 2048 }, { 8, 1087, 2048 },
|
---|
3706 | { 3, 1088, 2048 }, { 4, 1089, 2048 }, { 4, 1090, 2048 }, { 5, 1091, 2048 }, { 4, 1092, 2048 }, { 5, 1093, 2048 }, { 5, 1094, 2048 }, { 6, 1095, 2048 },
|
---|
3707 | { 4, 1096, 2048 }, { 5, 1097, 2048 }, { 5, 1098, 2048 }, { 6, 1099, 2048 }, { 5, 1100, 2048 }, { 6, 1101, 2048 }, { 6, 1102, 2048 }, { 7, 1103, 2048 },
|
---|
3708 | { 4, 1104, 2048 }, { 5, 1105, 2048 }, { 5, 1106, 2048 }, { 6, 1107, 2048 }, { 5, 1108, 2048 }, { 6, 1109, 2048 }, { 6, 1110, 2048 }, { 7, 1111, 2048 },
|
---|
3709 | { 5, 1112, 2048 }, { 6, 1113, 2048 }, { 6, 1114, 2048 }, { 7, 1115, 2048 }, { 6, 1116, 2048 }, { 7, 1117, 2048 }, { 7, 1118, 2048 }, { 8, 1119, 2048 },
|
---|
3710 | { 4, 1120, 2048 }, { 5, 1121, 2048 }, { 5, 1122, 2048 }, { 6, 1123, 2048 }, { 5, 1124, 2048 }, { 6, 1125, 2048 }, { 6, 1126, 2048 }, { 7, 1127, 2048 },
|
---|
3711 | { 5, 1128, 2048 }, { 6, 1129, 2048 }, { 6, 1130, 2048 }, { 7, 1131, 2048 }, { 6, 1132, 2048 }, { 7, 1133, 2048 }, { 7, 1134, 2048 }, { 8, 1135, 2048 },
|
---|
3712 | { 5, 1136, 2048 }, { 6, 1137, 2048 }, { 6, 1138, 2048 }, { 7, 1139, 2048 }, { 6, 1140, 2048 }, { 7, 1141, 2048 }, { 7, 1142, 2048 }, { 8, 1143, 2048 },
|
---|
3713 | { 6, 1144, 2048 }, { 7, 1145, 2048 }, { 7, 1146, 2048 }, { 8, 1147, 2048 }, { 7, 1148, 2048 }, { 8, 1149, 2048 }, { 8, 1150, 2048 }, { 9, 1151, 2048 },
|
---|
3714 | { 3, 1152, 2048 }, { 4, 1153, 2048 }, { 4, 1154, 2048 }, { 5, 1155, 2048 }, { 4, 1156, 2048 }, { 5, 1157, 2048 }, { 5, 1158, 2048 }, { 6, 1159, 2048 },
|
---|
3715 | { 4, 1160, 2048 }, { 5, 1161, 2048 }, { 5, 1162, 2048 }, { 6, 1163, 2048 }, { 5, 1164, 2048 }, { 6, 1165, 2048 }, { 6, 1166, 2048 }, { 7, 1167, 2048 },
|
---|
3716 | { 4, 1168, 2048 }, { 5, 1169, 2048 }, { 5, 1170, 2048 }, { 6, 1171, 2048 }, { 5, 1172, 2048 }, { 6, 1173, 2048 }, { 6, 1174, 2048 }, { 7, 1175, 2048 },
|
---|
3717 | { 5, 1176, 2048 }, { 6, 1177, 2048 }, { 6, 1178, 2048 }, { 7, 1179, 2048 }, { 6, 1180, 2048 }, { 7, 1181, 2048 }, { 7, 1182, 2048 }, { 8, 1183, 2048 },
|
---|
3718 | { 4, 1184, 2048 }, { 5, 1185, 2048 }, { 5, 1186, 2048 }, { 6, 1187, 2048 }, { 5, 1188, 2048 }, { 6, 1189, 2048 }, { 6, 1190, 2048 }, { 7, 1191, 2048 },
|
---|
3719 | { 5, 1192, 2048 }, { 6, 1193, 2048 }, { 6, 1194, 2048 }, { 7, 1195, 2048 }, { 6, 1196, 2048 }, { 7, 1197, 2048 }, { 7, 1198, 2048 }, { 8, 1199, 2048 },
|
---|
3720 | { 5, 1200, 2048 }, { 6, 1201, 2048 }, { 6, 1202, 2048 }, { 7, 1203, 2048 }, { 6, 1204, 2048 }, { 7, 1205, 2048 }, { 7, 1206, 2048 }, { 8, 1207, 2048 },
|
---|
3721 | { 6, 1208, 2048 }, { 7, 1209, 2048 }, { 7, 1210, 2048 }, { 8, 1211, 2048 }, { 7, 1212, 2048 }, { 8, 1213, 2048 }, { 8, 1214, 2048 }, { 9, 1215, 2048 },
|
---|
3722 | { 4, 1216, 2048 }, { 5, 1217, 2048 }, { 5, 1218, 2048 }, { 6, 1219, 2048 }, { 5, 1220, 2048 }, { 6, 1221, 2048 }, { 6, 1222, 2048 }, { 7, 1223, 2048 },
|
---|
3723 | { 5, 1224, 2048 }, { 6, 1225, 2048 }, { 6, 1226, 2048 }, { 7, 1227, 2048 }, { 6, 1228, 2048 }, { 7, 1229, 2048 }, { 7, 1230, 2048 }, { 8, 1231, 2048 },
|
---|
3724 | { 5, 1232, 2048 }, { 6, 1233, 2048 }, { 6, 1234, 2048 }, { 7, 1235, 2048 }, { 6, 1236, 2048 }, { 7, 1237, 2048 }, { 7, 1238, 2048 }, { 8, 1239, 2048 },
|
---|
3725 | { 6, 1240, 2048 }, { 7, 1241, 2048 }, { 7, 1242, 2048 }, { 8, 1243, 2048 }, { 7, 1244, 2048 }, { 8, 1245, 2048 }, { 8, 1246, 2048 }, { 9, 1247, 2048 },
|
---|
3726 | { 5, 1248, 2048 }, { 6, 1249, 2048 }, { 6, 1250, 2048 }, { 7, 1251, 2048 }, { 6, 1252, 2048 }, { 7, 1253, 2048 }, { 7, 1254, 2048 }, { 8, 1255, 2048 },
|
---|
3727 | { 6, 1256, 2048 }, { 7, 1257, 2048 }, { 7, 1258, 2048 }, { 8, 1259, 2048 }, { 7, 1260, 2048 }, { 8, 1261, 2048 }, { 8, 1262, 2048 }, { 9, 1263, 2048 },
|
---|
3728 | { 6, 1264, 2048 }, { 7, 1265, 2048 }, { 7, 1266, 2048 }, { 8, 1267, 2048 }, { 7, 1268, 2048 }, { 8, 1269, 2048 }, { 8, 1270, 2048 }, { 9, 1271, 2048 },
|
---|
3729 | { 7, 1272, 2048 }, { 8, 1273, 2048 }, { 8, 1274, 2048 }, { 9, 1275, 2048 }, { 8, 1276, 2048 }, { 9, 1277, 2048 }, { 9, 1278, 2048 }, { 10, 1279, 2048 },
|
---|
3730 | { 3, 1280, 2048 }, { 4, 1281, 2048 }, { 4, 1282, 2048 }, { 5, 1283, 2048 }, { 4, 1284, 2048 }, { 5, 1285, 2048 }, { 5, 1286, 2048 }, { 6, 1287, 2048 },
|
---|
3731 | { 4, 1288, 2048 }, { 5, 1289, 2048 }, { 5, 1290, 2048 }, { 6, 1291, 2048 }, { 5, 1292, 2048 }, { 6, 1293, 2048 }, { 6, 1294, 2048 }, { 7, 1295, 2048 },
|
---|
3732 | { 4, 1296, 2048 }, { 5, 1297, 2048 }, { 5, 1298, 2048 }, { 6, 1299, 2048 }, { 5, 1300, 2048 }, { 6, 1301, 2048 }, { 6, 1302, 2048 }, { 7, 1303, 2048 },
|
---|
3733 | { 5, 1304, 2048 }, { 6, 1305, 2048 }, { 6, 1306, 2048 }, { 7, 1307, 2048 }, { 6, 1308, 2048 }, { 7, 1309, 2048 }, { 7, 1310, 2048 }, { 8, 1311, 2048 },
|
---|
3734 | { 4, 1312, 2048 }, { 5, 1313, 2048 }, { 5, 1314, 2048 }, { 6, 1315, 2048 }, { 5, 1316, 2048 }, { 6, 1317, 2048 }, { 6, 1318, 2048 }, { 7, 1319, 2048 },
|
---|
3735 | { 5, 1320, 2048 }, { 6, 1321, 2048 }, { 6, 1322, 2048 }, { 7, 1323, 2048 }, { 6, 1324, 2048 }, { 7, 1325, 2048 }, { 7, 1326, 2048 }, { 8, 1327, 2048 },
|
---|
3736 | { 5, 1328, 2048 }, { 6, 1329, 2048 }, { 6, 1330, 2048 }, { 7, 1331, 2048 }, { 6, 1332, 2048 }, { 7, 1333, 2048 }, { 7, 1334, 2048 }, { 8, 1335, 2048 },
|
---|
3737 | { 6, 1336, 2048 }, { 7, 1337, 2048 }, { 7, 1338, 2048 }, { 8, 1339, 2048 }, { 7, 1340, 2048 }, { 8, 1341, 2048 }, { 8, 1342, 2048 }, { 9, 1343, 2048 },
|
---|
3738 | { 4, 1344, 2048 }, { 5, 1345, 2048 }, { 5, 1346, 2048 }, { 6, 1347, 2048 }, { 5, 1348, 2048 }, { 6, 1349, 2048 }, { 6, 1350, 2048 }, { 7, 1351, 2048 },
|
---|
3739 | { 5, 1352, 2048 }, { 6, 1353, 2048 }, { 6, 1354, 2048 }, { 7, 1355, 2048 }, { 6, 1356, 2048 }, { 7, 1357, 2048 }, { 7, 1358, 2048 }, { 8, 1359, 2048 },
|
---|
3740 | { 5, 1360, 2048 }, { 6, 1361, 2048 }, { 6, 1362, 2048 }, { 7, 1363, 2048 }, { 6, 1364, 2048 }, { 7, 1365, 2048 }, { 7, 1366, 2048 }, { 8, 1367, 2048 },
|
---|
3741 | { 6, 1368, 2048 }, { 7, 1369, 2048 }, { 7, 1370, 2048 }, { 8, 1371, 2048 }, { 7, 1372, 2048 }, { 8, 1373, 2048 }, { 8, 1374, 2048 }, { 9, 1375, 2048 },
|
---|
3742 | { 5, 1376, 2048 }, { 6, 1377, 2048 }, { 6, 1378, 2048 }, { 7, 1379, 2048 }, { 6, 1380, 2048 }, { 7, 1381, 2048 }, { 7, 1382, 2048 }, { 8, 1383, 2048 },
|
---|
3743 | { 6, 1384, 2048 }, { 7, 1385, 2048 }, { 7, 1386, 2048 }, { 8, 1387, 2048 }, { 7, 1388, 2048 }, { 8, 1389, 2048 }, { 8, 1390, 2048 }, { 9, 1391, 2048 },
|
---|
3744 | { 6, 1392, 2048 }, { 7, 1393, 2048 }, { 7, 1394, 2048 }, { 8, 1395, 2048 }, { 7, 1396, 2048 }, { 8, 1397, 2048 }, { 8, 1398, 2048 }, { 9, 1399, 2048 },
|
---|
3745 | { 7, 1400, 2048 }, { 8, 1401, 2048 }, { 8, 1402, 2048 }, { 9, 1403, 2048 }, { 8, 1404, 2048 }, { 9, 1405, 2048 }, { 9, 1406, 2048 }, { 10, 1407, 2048 },
|
---|
3746 | { 4, 1408, 2048 }, { 5, 1409, 2048 }, { 5, 1410, 2048 }, { 6, 1411, 2048 }, { 5, 1412, 2048 }, { 6, 1413, 2048 }, { 6, 1414, 2048 }, { 7, 1415, 2048 },
|
---|
3747 | { 5, 1416, 2048 }, { 6, 1417, 2048 }, { 6, 1418, 2048 }, { 7, 1419, 2048 }, { 6, 1420, 2048 }, { 7, 1421, 2048 }, { 7, 1422, 2048 }, { 8, 1423, 2048 },
|
---|
3748 | { 5, 1424, 2048 }, { 6, 1425, 2048 }, { 6, 1426, 2048 }, { 7, 1427, 2048 }, { 6, 1428, 2048 }, { 7, 1429, 2048 }, { 7, 1430, 2048 }, { 8, 1431, 2048 },
|
---|
3749 | { 6, 1432, 2048 }, { 7, 1433, 2048 }, { 7, 1434, 2048 }, { 8, 1435, 2048 }, { 7, 1436, 2048 }, { 8, 1437, 2048 }, { 8, 1438, 2048 }, { 9, 1439, 2048 },
|
---|
3750 | { 5, 1440, 2048 }, { 6, 1441, 2048 }, { 6, 1442, 2048 }, { 7, 1443, 2048 }, { 6, 1444, 2048 }, { 7, 1445, 2048 }, { 7, 1446, 2048 }, { 8, 1447, 2048 },
|
---|
3751 | { 6, 1448, 2048 }, { 7, 1449, 2048 }, { 7, 1450, 2048 }, { 8, 1451, 2048 }, { 7, 1452, 2048 }, { 8, 1453, 2048 }, { 8, 1454, 2048 }, { 9, 1455, 2048 },
|
---|
3752 | { 6, 1456, 2048 }, { 7, 1457, 2048 }, { 7, 1458, 2048 }, { 8, 1459, 2048 }, { 7, 1460, 2048 }, { 8, 1461, 2048 }, { 8, 1462, 2048 }, { 9, 1463, 2048 },
|
---|
3753 | { 7, 1464, 2048 }, { 8, 1465, 2048 }, { 8, 1466, 2048 }, { 9, 1467, 2048 }, { 8, 1468, 2048 }, { 9, 1469, 2048 }, { 9, 1470, 2048 }, { 10, 1471, 2048 },
|
---|
3754 | { 5, 1472, 2048 }, { 6, 1473, 2048 }, { 6, 1474, 2048 }, { 7, 1475, 2048 }, { 6, 1476, 2048 }, { 7, 1477, 2048 }, { 7, 1478, 2048 }, { 8, 1479, 2048 },
|
---|
3755 | { 6, 1480, 2048 }, { 7, 1481, 2048 }, { 7, 1482, 2048 }, { 8, 1483, 2048 }, { 7, 1484, 2048 }, { 8, 1485, 2048 }, { 8, 1486, 2048 }, { 9, 1487, 2048 },
|
---|
3756 | { 6, 1488, 2048 }, { 7, 1489, 2048 }, { 7, 1490, 2048 }, { 8, 1491, 2048 }, { 7, 1492, 2048 }, { 8, 1493, 2048 }, { 8, 1494, 2048 }, { 9, 1495, 2048 },
|
---|
3757 | { 7, 1496, 2048 }, { 8, 1497, 2048 }, { 8, 1498, 2048 }, { 9, 1499, 2048 }, { 8, 1500, 2048 }, { 9, 1501, 2048 }, { 9, 1502, 2048 }, { 10, 1503, 2048 },
|
---|
3758 | { 6, 1504, 2048 }, { 7, 1505, 2048 }, { 7, 1506, 2048 }, { 8, 1507, 2048 }, { 7, 1508, 2048 }, { 8, 1509, 2048 }, { 8, 1510, 2048 }, { 9, 1511, 2048 },
|
---|
3759 | { 7, 1512, 2048 }, { 8, 1513, 2048 }, { 8, 1514, 2048 }, { 9, 1515, 2048 }, { 8, 1516, 2048 }, { 9, 1517, 2048 }, { 9, 1518, 2048 }, { 10, 1519, 2048 },
|
---|
3760 | { 7, 1520, 2048 }, { 8, 1521, 2048 }, { 8, 1522, 2048 }, { 9, 1523, 2048 }, { 8, 1524, 2048 }, { 9, 1525, 2048 }, { 9, 1526, 2048 }, { 10, 1527, 2048 },
|
---|
3761 | { 8, 1528, 2048 }, { 9, 1529, 2048 }, { 9, 1530, 2048 }, { 10, 1531, 2048 }, { 9, 1532, 2048 }, { 10, 1533, 2048 }, { 10, 1534, 2048 }, { 11, 1535, 2048 },
|
---|
3762 | { 3, 1536, 2048 }, { 4, 1537, 2048 }, { 4, 1538, 2048 }, { 5, 1539, 2048 }, { 4, 1540, 2048 }, { 5, 1541, 2048 }, { 5, 1542, 2048 }, { 6, 1543, 2048 },
|
---|
3763 | { 4, 1544, 2048 }, { 5, 1545, 2048 }, { 5, 1546, 2048 }, { 6, 1547, 2048 }, { 5, 1548, 2048 }, { 6, 1549, 2048 }, { 6, 1550, 2048 }, { 7, 1551, 2048 },
|
---|
3764 | { 4, 1552, 2048 }, { 5, 1553, 2048 }, { 5, 1554, 2048 }, { 6, 1555, 2048 }, { 5, 1556, 2048 }, { 6, 1557, 2048 }, { 6, 1558, 2048 }, { 7, 1559, 2048 },
|
---|
3765 | { 5, 1560, 2048 }, { 6, 1561, 2048 }, { 6, 1562, 2048 }, { 7, 1563, 2048 }, { 6, 1564, 2048 }, { 7, 1565, 2048 }, { 7, 1566, 2048 }, { 8, 1567, 2048 },
|
---|
3766 | { 4, 1568, 2048 }, { 5, 1569, 2048 }, { 5, 1570, 2048 }, { 6, 1571, 2048 }, { 5, 1572, 2048 }, { 6, 1573, 2048 }, { 6, 1574, 2048 }, { 7, 1575, 2048 },
|
---|
3767 | { 5, 1576, 2048 }, { 6, 1577, 2048 }, { 6, 1578, 2048 }, { 7, 1579, 2048 }, { 6, 1580, 2048 }, { 7, 1581, 2048 }, { 7, 1582, 2048 }, { 8, 1583, 2048 },
|
---|
3768 | { 5, 1584, 2048 }, { 6, 1585, 2048 }, { 6, 1586, 2048 }, { 7, 1587, 2048 }, { 6, 1588, 2048 }, { 7, 1589, 2048 }, { 7, 1590, 2048 }, { 8, 1591, 2048 },
|
---|
3769 | { 6, 1592, 2048 }, { 7, 1593, 2048 }, { 7, 1594, 2048 }, { 8, 1595, 2048 }, { 7, 1596, 2048 }, { 8, 1597, 2048 }, { 8, 1598, 2048 }, { 9, 1599, 2048 },
|
---|
3770 | { 4, 1600, 2048 }, { 5, 1601, 2048 }, { 5, 1602, 2048 }, { 6, 1603, 2048 }, { 5, 1604, 2048 }, { 6, 1605, 2048 }, { 6, 1606, 2048 }, { 7, 1607, 2048 },
|
---|
3771 | { 5, 1608, 2048 }, { 6, 1609, 2048 }, { 6, 1610, 2048 }, { 7, 1611, 2048 }, { 6, 1612, 2048 }, { 7, 1613, 2048 }, { 7, 1614, 2048 }, { 8, 1615, 2048 },
|
---|
3772 | { 5, 1616, 2048 }, { 6, 1617, 2048 }, { 6, 1618, 2048 }, { 7, 1619, 2048 }, { 6, 1620, 2048 }, { 7, 1621, 2048 }, { 7, 1622, 2048 }, { 8, 1623, 2048 },
|
---|
3773 | { 6, 1624, 2048 }, { 7, 1625, 2048 }, { 7, 1626, 2048 }, { 8, 1627, 2048 }, { 7, 1628, 2048 }, { 8, 1629, 2048 }, { 8, 1630, 2048 }, { 9, 1631, 2048 },
|
---|
3774 | { 5, 1632, 2048 }, { 6, 1633, 2048 }, { 6, 1634, 2048 }, { 7, 1635, 2048 }, { 6, 1636, 2048 }, { 7, 1637, 2048 }, { 7, 1638, 2048 }, { 8, 1639, 2048 },
|
---|
3775 | { 6, 1640, 2048 }, { 7, 1641, 2048 }, { 7, 1642, 2048 }, { 8, 1643, 2048 }, { 7, 1644, 2048 }, { 8, 1645, 2048 }, { 8, 1646, 2048 }, { 9, 1647, 2048 },
|
---|
3776 | { 6, 1648, 2048 }, { 7, 1649, 2048 }, { 7, 1650, 2048 }, { 8, 1651, 2048 }, { 7, 1652, 2048 }, { 8, 1653, 2048 }, { 8, 1654, 2048 }, { 9, 1655, 2048 },
|
---|
3777 | { 7, 1656, 2048 }, { 8, 1657, 2048 }, { 8, 1658, 2048 }, { 9, 1659, 2048 }, { 8, 1660, 2048 }, { 9, 1661, 2048 }, { 9, 1662, 2048 }, { 10, 1663, 2048 },
|
---|
3778 | { 4, 1664, 2048 }, { 5, 1665, 2048 }, { 5, 1666, 2048 }, { 6, 1667, 2048 }, { 5, 1668, 2048 }, { 6, 1669, 2048 }, { 6, 1670, 2048 }, { 7, 1671, 2048 },
|
---|
3779 | { 5, 1672, 2048 }, { 6, 1673, 2048 }, { 6, 1674, 2048 }, { 7, 1675, 2048 }, { 6, 1676, 2048 }, { 7, 1677, 2048 }, { 7, 1678, 2048 }, { 8, 1679, 2048 },
|
---|
3780 | { 5, 1680, 2048 }, { 6, 1681, 2048 }, { 6, 1682, 2048 }, { 7, 1683, 2048 }, { 6, 1684, 2048 }, { 7, 1685, 2048 }, { 7, 1686, 2048 }, { 8, 1687, 2048 },
|
---|
3781 | { 6, 1688, 2048 }, { 7, 1689, 2048 }, { 7, 1690, 2048 }, { 8, 1691, 2048 }, { 7, 1692, 2048 }, { 8, 1693, 2048 }, { 8, 1694, 2048 }, { 9, 1695, 2048 },
|
---|
3782 | { 5, 1696, 2048 }, { 6, 1697, 2048 }, { 6, 1698, 2048 }, { 7, 1699, 2048 }, { 6, 1700, 2048 }, { 7, 1701, 2048 }, { 7, 1702, 2048 }, { 8, 1703, 2048 },
|
---|
3783 | { 6, 1704, 2048 }, { 7, 1705, 2048 }, { 7, 1706, 2048 }, { 8, 1707, 2048 }, { 7, 1708, 2048 }, { 8, 1709, 2048 }, { 8, 1710, 2048 }, { 9, 1711, 2048 },
|
---|
3784 | { 6, 1712, 2048 }, { 7, 1713, 2048 }, { 7, 1714, 2048 }, { 8, 1715, 2048 }, { 7, 1716, 2048 }, { 8, 1717, 2048 }, { 8, 1718, 2048 }, { 9, 1719, 2048 },
|
---|
3785 | { 7, 1720, 2048 }, { 8, 1721, 2048 }, { 8, 1722, 2048 }, { 9, 1723, 2048 }, { 8, 1724, 2048 }, { 9, 1725, 2048 }, { 9, 1726, 2048 }, { 10, 1727, 2048 },
|
---|
3786 | { 5, 1728, 2048 }, { 6, 1729, 2048 }, { 6, 1730, 2048 }, { 7, 1731, 2048 }, { 6, 1732, 2048 }, { 7, 1733, 2048 }, { 7, 1734, 2048 }, { 8, 1735, 2048 },
|
---|
3787 | { 6, 1736, 2048 }, { 7, 1737, 2048 }, { 7, 1738, 2048 }, { 8, 1739, 2048 }, { 7, 1740, 2048 }, { 8, 1741, 2048 }, { 8, 1742, 2048 }, { 9, 1743, 2048 },
|
---|
3788 | { 6, 1744, 2048 }, { 7, 1745, 2048 }, { 7, 1746, 2048 }, { 8, 1747, 2048 }, { 7, 1748, 2048 }, { 8, 1749, 2048 }, { 8, 1750, 2048 }, { 9, 1751, 2048 },
|
---|
3789 | { 7, 1752, 2048 }, { 8, 1753, 2048 }, { 8, 1754, 2048 }, { 9, 1755, 2048 }, { 8, 1756, 2048 }, { 9, 1757, 2048 }, { 9, 1758, 2048 }, { 10, 1759, 2048 },
|
---|
3790 | { 6, 1760, 2048 }, { 7, 1761, 2048 }, { 7, 1762, 2048 }, { 8, 1763, 2048 }, { 7, 1764, 2048 }, { 8, 1765, 2048 }, { 8, 1766, 2048 }, { 9, 1767, 2048 },
|
---|
3791 | { 7, 1768, 2048 }, { 8, 1769, 2048 }, { 8, 1770, 2048 }, { 9, 1771, 2048 }, { 8, 1772, 2048 }, { 9, 1773, 2048 }, { 9, 1774, 2048 }, { 10, 1775, 2048 },
|
---|
3792 | { 7, 1776, 2048 }, { 8, 1777, 2048 }, { 8, 1778, 2048 }, { 9, 1779, 2048 }, { 8, 1780, 2048 }, { 9, 1781, 2048 }, { 9, 1782, 2048 }, { 10, 1783, 2048 },
|
---|
3793 | { 8, 1784, 2048 }, { 9, 1785, 2048 }, { 9, 1786, 2048 }, { 10, 1787, 2048 }, { 9, 1788, 2048 }, { 10, 1789, 2048 }, { 10, 1790, 2048 }, { 11, 1791, 2048 },
|
---|
3794 | { 4, 1792, 2048 }, { 5, 1793, 2048 }, { 5, 1794, 2048 }, { 6, 1795, 2048 }, { 5, 1796, 2048 }, { 6, 1797, 2048 }, { 6, 1798, 2048 }, { 7, 1799, 2048 },
|
---|
3795 | { 5, 1800, 2048 }, { 6, 1801, 2048 }, { 6, 1802, 2048 }, { 7, 1803, 2048 }, { 6, 1804, 2048 }, { 7, 1805, 2048 }, { 7, 1806, 2048 }, { 8, 1807, 2048 },
|
---|
3796 | { 5, 1808, 2048 }, { 6, 1809, 2048 }, { 6, 1810, 2048 }, { 7, 1811, 2048 }, { 6, 1812, 2048 }, { 7, 1813, 2048 }, { 7, 1814, 2048 }, { 8, 1815, 2048 },
|
---|
3797 | { 6, 1816, 2048 }, { 7, 1817, 2048 }, { 7, 1818, 2048 }, { 8, 1819, 2048 }, { 7, 1820, 2048 }, { 8, 1821, 2048 }, { 8, 1822, 2048 }, { 9, 1823, 2048 },
|
---|
3798 | { 5, 1824, 2048 }, { 6, 1825, 2048 }, { 6, 1826, 2048 }, { 7, 1827, 2048 }, { 6, 1828, 2048 }, { 7, 1829, 2048 }, { 7, 1830, 2048 }, { 8, 1831, 2048 },
|
---|
3799 | { 6, 1832, 2048 }, { 7, 1833, 2048 }, { 7, 1834, 2048 }, { 8, 1835, 2048 }, { 7, 1836, 2048 }, { 8, 1837, 2048 }, { 8, 1838, 2048 }, { 9, 1839, 2048 },
|
---|
3800 | { 6, 1840, 2048 }, { 7, 1841, 2048 }, { 7, 1842, 2048 }, { 8, 1843, 2048 }, { 7, 1844, 2048 }, { 8, 1845, 2048 }, { 8, 1846, 2048 }, { 9, 1847, 2048 },
|
---|
3801 | { 7, 1848, 2048 }, { 8, 1849, 2048 }, { 8, 1850, 2048 }, { 9, 1851, 2048 }, { 8, 1852, 2048 }, { 9, 1853, 2048 }, { 9, 1854, 2048 }, { 10, 1855, 2048 },
|
---|
3802 | { 5, 1856, 2048 }, { 6, 1857, 2048 }, { 6, 1858, 2048 }, { 7, 1859, 2048 }, { 6, 1860, 2048 }, { 7, 1861, 2048 }, { 7, 1862, 2048 }, { 8, 1863, 2048 },
|
---|
3803 | { 6, 1864, 2048 }, { 7, 1865, 2048 }, { 7, 1866, 2048 }, { 8, 1867, 2048 }, { 7, 1868, 2048 }, { 8, 1869, 2048 }, { 8, 1870, 2048 }, { 9, 1871, 2048 },
|
---|
3804 | { 6, 1872, 2048 }, { 7, 1873, 2048 }, { 7, 1874, 2048 }, { 8, 1875, 2048 }, { 7, 1876, 2048 }, { 8, 1877, 2048 }, { 8, 1878, 2048 }, { 9, 1879, 2048 },
|
---|
3805 | { 7, 1880, 2048 }, { 8, 1881, 2048 }, { 8, 1882, 2048 }, { 9, 1883, 2048 }, { 8, 1884, 2048 }, { 9, 1885, 2048 }, { 9, 1886, 2048 }, { 10, 1887, 2048 },
|
---|
3806 | { 6, 1888, 2048 }, { 7, 1889, 2048 }, { 7, 1890, 2048 }, { 8, 1891, 2048 }, { 7, 1892, 2048 }, { 8, 1893, 2048 }, { 8, 1894, 2048 }, { 9, 1895, 2048 },
|
---|
3807 | { 7, 1896, 2048 }, { 8, 1897, 2048 }, { 8, 1898, 2048 }, { 9, 1899, 2048 }, { 8, 1900, 2048 }, { 9, 1901, 2048 }, { 9, 1902, 2048 }, { 10, 1903, 2048 },
|
---|
3808 | { 7, 1904, 2048 }, { 8, 1905, 2048 }, { 8, 1906, 2048 }, { 9, 1907, 2048 }, { 8, 1908, 2048 }, { 9, 1909, 2048 }, { 9, 1910, 2048 }, { 10, 1911, 2048 },
|
---|
3809 | { 8, 1912, 2048 }, { 9, 1913, 2048 }, { 9, 1914, 2048 }, { 10, 1915, 2048 }, { 9, 1916, 2048 }, { 10, 1917, 2048 }, { 10, 1918, 2048 }, { 11, 1919, 2048 },
|
---|
3810 | { 5, 1920, 2048 }, { 6, 1921, 2048 }, { 6, 1922, 2048 }, { 7, 1923, 2048 }, { 6, 1924, 2048 }, { 7, 1925, 2048 }, { 7, 1926, 2048 }, { 8, 1927, 2048 },
|
---|
3811 | { 6, 1928, 2048 }, { 7, 1929, 2048 }, { 7, 1930, 2048 }, { 8, 1931, 2048 }, { 7, 1932, 2048 }, { 8, 1933, 2048 }, { 8, 1934, 2048 }, { 9, 1935, 2048 },
|
---|
3812 | { 6, 1936, 2048 }, { 7, 1937, 2048 }, { 7, 1938, 2048 }, { 8, 1939, 2048 }, { 7, 1940, 2048 }, { 8, 1941, 2048 }, { 8, 1942, 2048 }, { 9, 1943, 2048 },
|
---|
3813 | { 7, 1944, 2048 }, { 8, 1945, 2048 }, { 8, 1946, 2048 }, { 9, 1947, 2048 }, { 8, 1948, 2048 }, { 9, 1949, 2048 }, { 9, 1950, 2048 }, { 10, 1951, 2048 },
|
---|
3814 | { 6, 1952, 2048 }, { 7, 1953, 2048 }, { 7, 1954, 2048 }, { 8, 1955, 2048 }, { 7, 1956, 2048 }, { 8, 1957, 2048 }, { 8, 1958, 2048 }, { 9, 1959, 2048 },
|
---|
3815 | { 7, 1960, 2048 }, { 8, 1961, 2048 }, { 8, 1962, 2048 }, { 9, 1963, 2048 }, { 8, 1964, 2048 }, { 9, 1965, 2048 }, { 9, 1966, 2048 }, { 10, 1967, 2048 },
|
---|
3816 | { 7, 1968, 2048 }, { 8, 1969, 2048 }, { 8, 1970, 2048 }, { 9, 1971, 2048 }, { 8, 1972, 2048 }, { 9, 1973, 2048 }, { 9, 1974, 2048 }, { 10, 1975, 2048 },
|
---|
3817 | { 8, 1976, 2048 }, { 9, 1977, 2048 }, { 9, 1978, 2048 }, { 10, 1979, 2048 }, { 9, 1980, 2048 }, { 10, 1981, 2048 }, { 10, 1982, 2048 }, { 11, 1983, 2048 },
|
---|
3818 | { 6, 1984, 2048 }, { 7, 1985, 2048 }, { 7, 1986, 2048 }, { 8, 1987, 2048 }, { 7, 1988, 2048 }, { 8, 1989, 2048 }, { 8, 1990, 2048 }, { 9, 1991, 2048 },
|
---|
3819 | { 7, 1992, 2048 }, { 8, 1993, 2048 }, { 8, 1994, 2048 }, { 9, 1995, 2048 }, { 8, 1996, 2048 }, { 9, 1997, 2048 }, { 9, 1998, 2048 }, { 10, 1999, 2048 },
|
---|
3820 | { 7, 2000, 2048 }, { 8, 2001, 2048 }, { 8, 2002, 2048 }, { 9, 2003, 2048 }, { 8, 2004, 2048 }, { 9, 2005, 2048 }, { 9, 2006, 2048 }, { 10, 2007, 2048 },
|
---|
3821 | { 8, 2008, 2048 }, { 9, 2009, 2048 }, { 9, 2010, 2048 }, { 10, 2011, 2048 }, { 9, 2012, 2048 }, { 10, 2013, 2048 }, { 10, 2014, 2048 }, { 11, 2015, 2048 },
|
---|
3822 | { 7, 2016, 2048 }, { 8, 2017, 2048 }, { 8, 2018, 2048 }, { 9, 2019, 2048 }, { 8, 2020, 2048 }, { 9, 2021, 2048 }, { 9, 2022, 2048 }, { 10, 2023, 2048 },
|
---|
3823 | { 8, 2024, 2048 }, { 9, 2025, 2048 }, { 9, 2026, 2048 }, { 10, 2027, 2048 }, { 9, 2028, 2048 }, { 10, 2029, 2048 }, { 10, 2030, 2048 }, { 11, 2031, 2048 },
|
---|
3824 | { 8, 2032, 2048 }, { 9, 2033, 2048 }, { 9, 2034, 2048 }, { 10, 2035, 2048 }, { 9, 2036, 2048 }, { 10, 2037, 2048 }, { 10, 2038, 2048 }, { 11, 2039, 2048 },
|
---|
3825 | { 9, 2040, 2048 }, { 10, 2041, 2048 }, { 10, 2042, 2048 }, { 11, 2043, 2048 }, { 10, 2044, 2048 }, { 11, 2045, 2048 }, { 11, 2046, 2048 }, { 12, 2047, 2048 },
|
---|
3826 | #endif
|
---|
3827 | #endif
|
---|
3828 | #endif
|
---|
3829 | #endif
|
---|
3830 | #endif
|
---|
3831 | #endif
|
---|
3832 | };
|
---|
3833 |
|
---|
3834 | /* find a hole and free as required, return -1 if no hole found */
|
---|
3835 | static int find_hole(void)
|
---|
3836 | {
|
---|
3837 | unsigned x;
|
---|
3838 | int y, z;
|
---|
3839 | for (z = -1, y = INT_MAX, x = 0; x < FP_ENTRIES; x++) {
|
---|
3840 | if (fp_cache[x].lru_count < y && fp_cache[x].lock == 0) {
|
---|
3841 | z = x;
|
---|
3842 | y = fp_cache[x].lru_count;
|
---|
3843 | }
|
---|
3844 | }
|
---|
3845 |
|
---|
3846 | /* decrease all */
|
---|
3847 | for (x = 0; x < FP_ENTRIES; x++) {
|
---|
3848 | if (fp_cache[x].lru_count > 3) {
|
---|
3849 | --(fp_cache[x].lru_count);
|
---|
3850 | }
|
---|
3851 | }
|
---|
3852 |
|
---|
3853 | /* free entry z */
|
---|
3854 | if (z >= 0 && fp_cache[z].g) {
|
---|
3855 | mp_clear(&fp_cache[z].mu);
|
---|
3856 | wc_ecc_del_point(fp_cache[z].g);
|
---|
3857 | fp_cache[z].g = NULL;
|
---|
3858 | for (x = 0; x < (1U<<FP_LUT); x++) {
|
---|
3859 | wc_ecc_del_point(fp_cache[z].LUT[x]);
|
---|
3860 | fp_cache[z].LUT[x] = NULL;
|
---|
3861 | }
|
---|
3862 | fp_cache[z].lru_count = 0;
|
---|
3863 | }
|
---|
3864 | return z;
|
---|
3865 | }
|
---|
3866 |
|
---|
3867 | /* determine if a base is already in the cache and if so, where */
|
---|
3868 | static int find_base(ecc_point* g)
|
---|
3869 | {
|
---|
3870 | int x;
|
---|
3871 | for (x = 0; x < FP_ENTRIES; x++) {
|
---|
3872 | if (fp_cache[x].g != NULL &&
|
---|
3873 | mp_cmp(fp_cache[x].g->x, g->x) == MP_EQ &&
|
---|
3874 | mp_cmp(fp_cache[x].g->y, g->y) == MP_EQ &&
|
---|
3875 | mp_cmp(fp_cache[x].g->z, g->z) == MP_EQ) {
|
---|
3876 | break;
|
---|
3877 | }
|
---|
3878 | }
|
---|
3879 | if (x == FP_ENTRIES) {
|
---|
3880 | x = -1;
|
---|
3881 | }
|
---|
3882 | return x;
|
---|
3883 | }
|
---|
3884 |
|
---|
3885 | /* add a new base to the cache */
|
---|
3886 | static int add_entry(int idx, ecc_point *g)
|
---|
3887 | {
|
---|
3888 | unsigned x, y;
|
---|
3889 |
|
---|
3890 | /* allocate base and LUT */
|
---|
3891 | fp_cache[idx].g = wc_ecc_new_point();
|
---|
3892 | if (fp_cache[idx].g == NULL) {
|
---|
3893 | return GEN_MEM_ERR;
|
---|
3894 | }
|
---|
3895 |
|
---|
3896 | /* copy x and y */
|
---|
3897 | if ((mp_copy(g->x, fp_cache[idx].g->x) != MP_OKAY) ||
|
---|
3898 | (mp_copy(g->y, fp_cache[idx].g->y) != MP_OKAY) ||
|
---|
3899 | (mp_copy(g->z, fp_cache[idx].g->z) != MP_OKAY)) {
|
---|
3900 | wc_ecc_del_point(fp_cache[idx].g);
|
---|
3901 | fp_cache[idx].g = NULL;
|
---|
3902 | return GEN_MEM_ERR;
|
---|
3903 | }
|
---|
3904 |
|
---|
3905 | for (x = 0; x < (1U<<FP_LUT); x++) {
|
---|
3906 | fp_cache[idx].LUT[x] = wc_ecc_new_point();
|
---|
3907 | if (fp_cache[idx].LUT[x] == NULL) {
|
---|
3908 | for (y = 0; y < x; y++) {
|
---|
3909 | wc_ecc_del_point(fp_cache[idx].LUT[y]);
|
---|
3910 | fp_cache[idx].LUT[y] = NULL;
|
---|
3911 | }
|
---|
3912 | wc_ecc_del_point(fp_cache[idx].g);
|
---|
3913 | fp_cache[idx].g = NULL;
|
---|
3914 | fp_cache[idx].lru_count = 0;
|
---|
3915 | return GEN_MEM_ERR;
|
---|
3916 | }
|
---|
3917 | }
|
---|
3918 |
|
---|
3919 | fp_cache[idx].lru_count = 0;
|
---|
3920 |
|
---|
3921 | return MP_OKAY;
|
---|
3922 | }
|
---|
3923 |
|
---|
3924 | /* build the LUT by spacing the bits of the input by #modulus/FP_LUT bits apart
|
---|
3925 | *
|
---|
3926 | * The algorithm builds patterns in increasing bit order by first making all
|
---|
3927 | * single bit input patterns, then all two bit input patterns and so on
|
---|
3928 | */
|
---|
3929 | static int build_lut(int idx, mp_int* modulus, mp_digit* mp, mp_int* mu)
|
---|
3930 | {
|
---|
3931 | unsigned x, y, err, bitlen, lut_gap;
|
---|
3932 | mp_int tmp;
|
---|
3933 |
|
---|
3934 | if (mp_init(&tmp) != MP_OKAY)
|
---|
3935 | return GEN_MEM_ERR;
|
---|
3936 |
|
---|
3937 | /* sanity check to make sure lut_order table is of correct size,
|
---|
3938 | should compile out to a NOP if true */
|
---|
3939 | if ((sizeof(lut_orders) / sizeof(lut_orders[0])) < (1U<<FP_LUT)) {
|
---|
3940 | err = BAD_FUNC_ARG;
|
---|
3941 | }
|
---|
3942 | else {
|
---|
3943 | /* get bitlen and round up to next multiple of FP_LUT */
|
---|
3944 | bitlen = mp_unsigned_bin_size(modulus) << 3;
|
---|
3945 | x = bitlen % FP_LUT;
|
---|
3946 | if (x) {
|
---|
3947 | bitlen += FP_LUT - x;
|
---|
3948 | }
|
---|
3949 | lut_gap = bitlen / FP_LUT;
|
---|
3950 |
|
---|
3951 | /* init the mu */
|
---|
3952 | err = mp_init_copy(&fp_cache[idx].mu, mu);
|
---|
3953 | }
|
---|
3954 |
|
---|
3955 | /* copy base */
|
---|
3956 | if (err == MP_OKAY) {
|
---|
3957 | if ((mp_mulmod(fp_cache[idx].g->x, mu, modulus,
|
---|
3958 | fp_cache[idx].LUT[1]->x) != MP_OKAY) ||
|
---|
3959 | (mp_mulmod(fp_cache[idx].g->y, mu, modulus,
|
---|
3960 | fp_cache[idx].LUT[1]->y) != MP_OKAY) ||
|
---|
3961 | (mp_mulmod(fp_cache[idx].g->z, mu, modulus,
|
---|
3962 | fp_cache[idx].LUT[1]->z) != MP_OKAY)) {
|
---|
3963 | err = MP_MULMOD_E;
|
---|
3964 | }
|
---|
3965 | }
|
---|
3966 |
|
---|
3967 | /* make all single bit entries */
|
---|
3968 | for (x = 1; x < FP_LUT; x++) {
|
---|
3969 | if (err != MP_OKAY)
|
---|
3970 | break;
|
---|
3971 | if ((mp_copy(fp_cache[idx].LUT[1<<(x-1)]->x,
|
---|
3972 | fp_cache[idx].LUT[1<<x]->x) != MP_OKAY) ||
|
---|
3973 | (mp_copy(fp_cache[idx].LUT[1<<(x-1)]->y,
|
---|
3974 | fp_cache[idx].LUT[1<<x]->y) != MP_OKAY) ||
|
---|
3975 | (mp_copy(fp_cache[idx].LUT[1<<(x-1)]->z,
|
---|
3976 | fp_cache[idx].LUT[1<<x]->z) != MP_OKAY)){
|
---|
3977 | err = MP_INIT_E;
|
---|
3978 | break;
|
---|
3979 | } else {
|
---|
3980 |
|
---|
3981 | /* now double it bitlen/FP_LUT times */
|
---|
3982 | for (y = 0; y < lut_gap; y++) {
|
---|
3983 | if ((err = ecc_projective_dbl_point(fp_cache[idx].LUT[1<<x],
|
---|
3984 | fp_cache[idx].LUT[1<<x], modulus, mp)) != MP_OKAY) {
|
---|
3985 | break;
|
---|
3986 | }
|
---|
3987 | }
|
---|
3988 | }
|
---|
3989 | }
|
---|
3990 |
|
---|
3991 | /* now make all entries in increase order of hamming weight */
|
---|
3992 | for (x = 2; x <= FP_LUT; x++) {
|
---|
3993 | if (err != MP_OKAY)
|
---|
3994 | break;
|
---|
3995 | for (y = 0; y < (1UL<<FP_LUT); y++) {
|
---|
3996 | if (err != MP_OKAY)
|
---|
3997 | break;
|
---|
3998 | if (lut_orders[y].ham != (int)x) continue;
|
---|
3999 |
|
---|
4000 | /* perform the add */
|
---|
4001 | if ((err = ecc_projective_add_point(
|
---|
4002 | fp_cache[idx].LUT[lut_orders[y].terma],
|
---|
4003 | fp_cache[idx].LUT[lut_orders[y].termb],
|
---|
4004 | fp_cache[idx].LUT[y], modulus, mp)) != MP_OKAY) {
|
---|
4005 | break;
|
---|
4006 | }
|
---|
4007 | }
|
---|
4008 | }
|
---|
4009 |
|
---|
4010 | /* now map all entries back to affine space to make point addition faster */
|
---|
4011 | for (x = 1; x < (1UL<<FP_LUT); x++) {
|
---|
4012 | if (err != MP_OKAY)
|
---|
4013 | break;
|
---|
4014 |
|
---|
4015 | /* convert z to normal from montgomery */
|
---|
4016 | err = mp_montgomery_reduce(fp_cache[idx].LUT[x]->z, modulus, *mp);
|
---|
4017 |
|
---|
4018 | /* invert it */
|
---|
4019 | if (err == MP_OKAY)
|
---|
4020 | err = mp_invmod(fp_cache[idx].LUT[x]->z, modulus,
|
---|
4021 | fp_cache[idx].LUT[x]->z);
|
---|
4022 |
|
---|
4023 | if (err == MP_OKAY)
|
---|
4024 | /* now square it */
|
---|
4025 | err = mp_sqrmod(fp_cache[idx].LUT[x]->z, modulus, &tmp);
|
---|
4026 |
|
---|
4027 | if (err == MP_OKAY)
|
---|
4028 | /* fix x */
|
---|
4029 | err = mp_mulmod(fp_cache[idx].LUT[x]->x, &tmp, modulus,
|
---|
4030 | fp_cache[idx].LUT[x]->x);
|
---|
4031 |
|
---|
4032 | if (err == MP_OKAY)
|
---|
4033 | /* get 1/z^3 */
|
---|
4034 | err = mp_mulmod(&tmp, fp_cache[idx].LUT[x]->z, modulus, &tmp);
|
---|
4035 |
|
---|
4036 | if (err == MP_OKAY)
|
---|
4037 | /* fix y */
|
---|
4038 | err = mp_mulmod(fp_cache[idx].LUT[x]->y, &tmp, modulus,
|
---|
4039 | fp_cache[idx].LUT[x]->y);
|
---|
4040 |
|
---|
4041 | if (err == MP_OKAY)
|
---|
4042 | /* free z */
|
---|
4043 | mp_clear(fp_cache[idx].LUT[x]->z);
|
---|
4044 | }
|
---|
4045 | mp_clear(&tmp);
|
---|
4046 |
|
---|
4047 | if (err == MP_OKAY)
|
---|
4048 | return MP_OKAY;
|
---|
4049 |
|
---|
4050 | /* err cleanup */
|
---|
4051 | for (y = 0; y < (1U<<FP_LUT); y++) {
|
---|
4052 | wc_ecc_del_point(fp_cache[idx].LUT[y]);
|
---|
4053 | fp_cache[idx].LUT[y] = NULL;
|
---|
4054 | }
|
---|
4055 | wc_ecc_del_point(fp_cache[idx].g);
|
---|
4056 | fp_cache[idx].g = NULL;
|
---|
4057 | fp_cache[idx].lru_count = 0;
|
---|
4058 | mp_clear(&fp_cache[idx].mu);
|
---|
4059 | mp_clear(&tmp);
|
---|
4060 |
|
---|
4061 | return err;
|
---|
4062 | }
|
---|
4063 |
|
---|
4064 | /* perform a fixed point ECC mulmod */
|
---|
4065 | static int accel_fp_mul(int idx, mp_int* k, ecc_point *R, mp_int* modulus,
|
---|
4066 | mp_digit* mp, int map)
|
---|
4067 | {
|
---|
4068 | #define KB_SIZE 128
|
---|
4069 |
|
---|
4070 | #ifdef WOLFSSL_SMALL_STACK
|
---|
4071 | unsigned char* kb;
|
---|
4072 | #else
|
---|
4073 | unsigned char kb[128];
|
---|
4074 | #endif
|
---|
4075 | int x;
|
---|
4076 | unsigned y, z, err, bitlen, bitpos, lut_gap, first;
|
---|
4077 | mp_int tk;
|
---|
4078 |
|
---|
4079 | if (mp_init(&tk) != MP_OKAY)
|
---|
4080 | return MP_INIT_E;
|
---|
4081 |
|
---|
4082 | /* if it's smaller than modulus we fine */
|
---|
4083 | if (mp_unsigned_bin_size(k) > mp_unsigned_bin_size(modulus)) {
|
---|
4084 | mp_int order;
|
---|
4085 | if (mp_init(&order) != MP_OKAY) {
|
---|
4086 | mp_clear(&tk);
|
---|
4087 | return MP_INIT_E;
|
---|
4088 | }
|
---|
4089 |
|
---|
4090 | /* find order */
|
---|
4091 | y = mp_unsigned_bin_size(modulus);
|
---|
4092 | for (x = 0; ecc_sets[x].size; x++) {
|
---|
4093 | if (y <= (unsigned)ecc_sets[x].size) break;
|
---|
4094 | }
|
---|
4095 |
|
---|
4096 | /* back off if we are on the 521 bit curve */
|
---|
4097 | if (y == 66) --x;
|
---|
4098 |
|
---|
4099 | if ((err = mp_read_radix(&order, ecc_sets[x].order, 16)) != MP_OKAY) {
|
---|
4100 | mp_clear(&order);
|
---|
4101 | mp_clear(&tk);
|
---|
4102 | return err;
|
---|
4103 | }
|
---|
4104 |
|
---|
4105 | /* k must be less than modulus */
|
---|
4106 | if (mp_cmp(k, &order) != MP_LT) {
|
---|
4107 | if ((err = mp_mod(k, &order, &tk)) != MP_OKAY) {
|
---|
4108 | mp_clear(&tk);
|
---|
4109 | mp_clear(&order);
|
---|
4110 | return err;
|
---|
4111 | }
|
---|
4112 | } else {
|
---|
4113 | mp_copy(k, &tk);
|
---|
4114 | }
|
---|
4115 | mp_clear(&order);
|
---|
4116 | } else {
|
---|
4117 | mp_copy(k, &tk);
|
---|
4118 | }
|
---|
4119 |
|
---|
4120 | /* get bitlen and round up to next multiple of FP_LUT */
|
---|
4121 | bitlen = mp_unsigned_bin_size(modulus) << 3;
|
---|
4122 | x = bitlen % FP_LUT;
|
---|
4123 | if (x) {
|
---|
4124 | bitlen += FP_LUT - x;
|
---|
4125 | }
|
---|
4126 | lut_gap = bitlen / FP_LUT;
|
---|
4127 |
|
---|
4128 | /* get the k value */
|
---|
4129 | if (mp_unsigned_bin_size(&tk) > (int)(KB_SIZE - 2)) {
|
---|
4130 | mp_clear(&tk);
|
---|
4131 | return BUFFER_E;
|
---|
4132 | }
|
---|
4133 |
|
---|
4134 | /* store k */
|
---|
4135 | #ifdef WOLFSSL_SMALL_STACK
|
---|
4136 | kb = (unsigned char*)XMALLOC(KB_SIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
4137 | if (kb == NULL)
|
---|
4138 | return MEMORY_E;
|
---|
4139 | #endif
|
---|
4140 |
|
---|
4141 | XMEMSET(kb, 0, KB_SIZE);
|
---|
4142 | if ((err = mp_to_unsigned_bin(&tk, kb)) != MP_OKAY) {
|
---|
4143 | mp_clear(&tk);
|
---|
4144 | }
|
---|
4145 | else {
|
---|
4146 | /* let's reverse kb so it's little endian */
|
---|
4147 | x = 0;
|
---|
4148 | y = mp_unsigned_bin_size(&tk) - 1;
|
---|
4149 | mp_clear(&tk);
|
---|
4150 |
|
---|
4151 | while ((unsigned)x < y) {
|
---|
4152 | z = kb[x]; kb[x] = kb[y]; kb[y] = z;
|
---|
4153 | ++x; --y;
|
---|
4154 | }
|
---|
4155 |
|
---|
4156 | /* at this point we can start, yipee */
|
---|
4157 | first = 1;
|
---|
4158 | for (x = lut_gap-1; x >= 0; x--) {
|
---|
4159 | /* extract FP_LUT bits from kb spread out by lut_gap bits and offset
|
---|
4160 | by x bits from the start */
|
---|
4161 | bitpos = x;
|
---|
4162 | for (y = z = 0; y < FP_LUT; y++) {
|
---|
4163 | z |= ((kb[bitpos>>3] >> (bitpos&7)) & 1) << y;
|
---|
4164 | bitpos += lut_gap; /* it's y*lut_gap + x, but here we can avoid
|
---|
4165 | the mult in each loop */
|
---|
4166 | }
|
---|
4167 |
|
---|
4168 | /* double if not first */
|
---|
4169 | if (!first) {
|
---|
4170 | if ((err = ecc_projective_dbl_point(R, R, modulus,
|
---|
4171 | mp)) != MP_OKAY) {
|
---|
4172 | break;
|
---|
4173 | }
|
---|
4174 | }
|
---|
4175 |
|
---|
4176 | /* add if not first, otherwise copy */
|
---|
4177 | if (!first && z) {
|
---|
4178 | if ((err = ecc_projective_add_point(R, fp_cache[idx].LUT[z], R,
|
---|
4179 | modulus, mp)) != MP_OKAY) {
|
---|
4180 | break;
|
---|
4181 | }
|
---|
4182 | } else if (z) {
|
---|
4183 | if ((mp_copy(fp_cache[idx].LUT[z]->x, R->x) != MP_OKAY) ||
|
---|
4184 | (mp_copy(fp_cache[idx].LUT[z]->y, R->y) != MP_OKAY) ||
|
---|
4185 | (mp_copy(&fp_cache[idx].mu, R->z) != MP_OKAY)) {
|
---|
4186 | err = GEN_MEM_ERR;
|
---|
4187 | break;
|
---|
4188 | }
|
---|
4189 | first = 0;
|
---|
4190 | }
|
---|
4191 | }
|
---|
4192 | }
|
---|
4193 |
|
---|
4194 | if (err == MP_OKAY) {
|
---|
4195 | z = 0;
|
---|
4196 | ForceZero(kb, KB_SIZE);
|
---|
4197 | /* map R back from projective space */
|
---|
4198 | if (map) {
|
---|
4199 | err = ecc_map(R, modulus, mp);
|
---|
4200 | } else {
|
---|
4201 | err = MP_OKAY;
|
---|
4202 | }
|
---|
4203 | }
|
---|
4204 |
|
---|
4205 | #ifdef WOLFSSL_SMALL_STACK
|
---|
4206 | XFREE(kb, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
4207 | #endif
|
---|
4208 |
|
---|
4209 | #undef KB_SIZE
|
---|
4210 |
|
---|
4211 | return err;
|
---|
4212 | }
|
---|
4213 |
|
---|
4214 | #ifdef ECC_SHAMIR
|
---|
4215 | /* perform a fixed point ECC mulmod */
|
---|
4216 | static int accel_fp_mul2add(int idx1, int idx2,
|
---|
4217 | mp_int* kA, mp_int* kB,
|
---|
4218 | ecc_point *R, mp_int* modulus, mp_digit* mp)
|
---|
4219 | {
|
---|
4220 | #define KB_SIZE 128
|
---|
4221 |
|
---|
4222 | #ifdef WOLFSSL_SMALL_STACK
|
---|
4223 | unsigned char* kb[2];
|
---|
4224 | #else
|
---|
4225 | unsigned char kb[2][128];
|
---|
4226 | #endif
|
---|
4227 | int x;
|
---|
4228 | unsigned y, z, err, bitlen, bitpos, lut_gap, first, zA, zB;
|
---|
4229 | mp_int tka;
|
---|
4230 | mp_int tkb;
|
---|
4231 | mp_int order;
|
---|
4232 |
|
---|
4233 | if (mp_init_multi(&tka, &tkb, 0, 0, 0, 0) != MP_OKAY)
|
---|
4234 | return MP_INIT_E;
|
---|
4235 |
|
---|
4236 | /* if it's smaller than modulus we fine */
|
---|
4237 | if (mp_unsigned_bin_size(kA) > mp_unsigned_bin_size(modulus)) {
|
---|
4238 | /* find order */
|
---|
4239 | y = mp_unsigned_bin_size(modulus);
|
---|
4240 | for (x = 0; ecc_sets[x].size; x++) {
|
---|
4241 | if (y <= (unsigned)ecc_sets[x].size) break;
|
---|
4242 | }
|
---|
4243 |
|
---|
4244 | /* back off if we are on the 521 bit curve */
|
---|
4245 | if (y == 66) --x;
|
---|
4246 |
|
---|
4247 | if ((err = mp_init(&order)) != MP_OKAY) {
|
---|
4248 | mp_clear(&tkb);
|
---|
4249 | mp_clear(&tka);
|
---|
4250 | return err;
|
---|
4251 | }
|
---|
4252 | if ((err = mp_read_radix(&order, ecc_sets[x].order, 16)) != MP_OKAY) {
|
---|
4253 | mp_clear(&tkb);
|
---|
4254 | mp_clear(&tka);
|
---|
4255 | mp_clear(&order);
|
---|
4256 | return err;
|
---|
4257 | }
|
---|
4258 |
|
---|
4259 | /* kA must be less than modulus */
|
---|
4260 | if (mp_cmp(kA, &order) != MP_LT) {
|
---|
4261 | if ((err = mp_mod(kA, &order, &tka)) != MP_OKAY) {
|
---|
4262 | mp_clear(&tkb);
|
---|
4263 | mp_clear(&tka);
|
---|
4264 | mp_clear(&order);
|
---|
4265 | return err;
|
---|
4266 | }
|
---|
4267 | } else {
|
---|
4268 | mp_copy(kA, &tka);
|
---|
4269 | }
|
---|
4270 | mp_clear(&order);
|
---|
4271 | } else {
|
---|
4272 | mp_copy(kA, &tka);
|
---|
4273 | }
|
---|
4274 |
|
---|
4275 | /* if it's smaller than modulus we fine */
|
---|
4276 | if (mp_unsigned_bin_size(kB) > mp_unsigned_bin_size(modulus)) {
|
---|
4277 | /* find order */
|
---|
4278 | y = mp_unsigned_bin_size(modulus);
|
---|
4279 | for (x = 0; ecc_sets[x].size; x++) {
|
---|
4280 | if (y <= (unsigned)ecc_sets[x].size) break;
|
---|
4281 | }
|
---|
4282 |
|
---|
4283 | /* back off if we are on the 521 bit curve */
|
---|
4284 | if (y == 66) --x;
|
---|
4285 |
|
---|
4286 | if ((err = mp_init(&order)) != MP_OKAY) {
|
---|
4287 | mp_clear(&tkb);
|
---|
4288 | mp_clear(&tka);
|
---|
4289 | return err;
|
---|
4290 | }
|
---|
4291 | if ((err = mp_read_radix(&order, ecc_sets[x].order, 16)) != MP_OKAY) {
|
---|
4292 | mp_clear(&tkb);
|
---|
4293 | mp_clear(&tka);
|
---|
4294 | mp_clear(&order);
|
---|
4295 | return err;
|
---|
4296 | }
|
---|
4297 |
|
---|
4298 | /* kB must be less than modulus */
|
---|
4299 | if (mp_cmp(kB, &order) != MP_LT) {
|
---|
4300 | if ((err = mp_mod(kB, &order, &tkb)) != MP_OKAY) {
|
---|
4301 | mp_clear(&tkb);
|
---|
4302 | mp_clear(&tka);
|
---|
4303 | mp_clear(&order);
|
---|
4304 | return err;
|
---|
4305 | }
|
---|
4306 | } else {
|
---|
4307 | mp_copy(kB, &tkb);
|
---|
4308 | }
|
---|
4309 | mp_clear(&order);
|
---|
4310 | } else {
|
---|
4311 | mp_copy(kB, &tkb);
|
---|
4312 | }
|
---|
4313 |
|
---|
4314 | /* get bitlen and round up to next multiple of FP_LUT */
|
---|
4315 | bitlen = mp_unsigned_bin_size(modulus) << 3;
|
---|
4316 | x = bitlen % FP_LUT;
|
---|
4317 | if (x) {
|
---|
4318 | bitlen += FP_LUT - x;
|
---|
4319 | }
|
---|
4320 | lut_gap = bitlen / FP_LUT;
|
---|
4321 |
|
---|
4322 | /* get the k value */
|
---|
4323 | if ((mp_unsigned_bin_size(&tka) > (int)(KB_SIZE - 2)) ||
|
---|
4324 | (mp_unsigned_bin_size(&tkb) > (int)(KB_SIZE - 2)) ) {
|
---|
4325 | mp_clear(&tka);
|
---|
4326 | mp_clear(&tkb);
|
---|
4327 | return BUFFER_E;
|
---|
4328 | }
|
---|
4329 |
|
---|
4330 | /* store k */
|
---|
4331 | #ifdef WOLFSSL_SMALL_STACK
|
---|
4332 | kb[0] = (unsigned char*)XMALLOC(KB_SIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
4333 | if (kb[0] == NULL)
|
---|
4334 | return MEMORY_E;
|
---|
4335 | #endif
|
---|
4336 |
|
---|
4337 | XMEMSET(kb[0], 0, KB_SIZE);
|
---|
4338 | if ((err = mp_to_unsigned_bin(&tka, kb[0])) != MP_OKAY) {
|
---|
4339 | mp_clear(&tka);
|
---|
4340 | mp_clear(&tkb);
|
---|
4341 | #ifdef WOLFSSL_SMALL_STACK
|
---|
4342 | XFREE(kb[0], NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
4343 | #endif
|
---|
4344 | return err;
|
---|
4345 | }
|
---|
4346 |
|
---|
4347 | /* let's reverse kb so it's little endian */
|
---|
4348 | x = 0;
|
---|
4349 | y = mp_unsigned_bin_size(&tka) - 1;
|
---|
4350 | mp_clear(&tka);
|
---|
4351 | while ((unsigned)x < y) {
|
---|
4352 | z = kb[0][x]; kb[0][x] = kb[0][y]; kb[0][y] = z;
|
---|
4353 | ++x; --y;
|
---|
4354 | }
|
---|
4355 |
|
---|
4356 | /* store b */
|
---|
4357 | #ifdef WOLFSSL_SMALL_STACK
|
---|
4358 | kb[1] = (unsigned char*)XMALLOC(KB_SIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
4359 | if (kb[1] == NULL) {
|
---|
4360 | XFREE(kb[0], NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
4361 | return MEMORY_E;
|
---|
4362 | }
|
---|
4363 | #endif
|
---|
4364 |
|
---|
4365 | XMEMSET(kb[1], 0, KB_SIZE);
|
---|
4366 | if ((err = mp_to_unsigned_bin(&tkb, kb[1])) != MP_OKAY) {
|
---|
4367 | mp_clear(&tkb);
|
---|
4368 | }
|
---|
4369 | else {
|
---|
4370 | x = 0;
|
---|
4371 | y = mp_unsigned_bin_size(&tkb) - 1;
|
---|
4372 | mp_clear(&tkb);
|
---|
4373 | while ((unsigned)x < y) {
|
---|
4374 | z = kb[1][x]; kb[1][x] = kb[1][y]; kb[1][y] = z;
|
---|
4375 | ++x; --y;
|
---|
4376 | }
|
---|
4377 |
|
---|
4378 | /* at this point we can start, yipee */
|
---|
4379 | first = 1;
|
---|
4380 | for (x = lut_gap-1; x >= 0; x--) {
|
---|
4381 | /* extract FP_LUT bits from kb spread out by lut_gap bits and
|
---|
4382 | offset by x bits from the start */
|
---|
4383 | bitpos = x;
|
---|
4384 | for (y = zA = zB = 0; y < FP_LUT; y++) {
|
---|
4385 | zA |= ((kb[0][bitpos>>3] >> (bitpos&7)) & 1) << y;
|
---|
4386 | zB |= ((kb[1][bitpos>>3] >> (bitpos&7)) & 1) << y;
|
---|
4387 | bitpos += lut_gap; /* it's y*lut_gap + x, but here we can avoid
|
---|
4388 | the mult in each loop */
|
---|
4389 | }
|
---|
4390 |
|
---|
4391 | /* double if not first */
|
---|
4392 | if (!first) {
|
---|
4393 | if ((err = ecc_projective_dbl_point(R, R, modulus,
|
---|
4394 | mp)) != MP_OKAY) {
|
---|
4395 | break;
|
---|
4396 | }
|
---|
4397 | }
|
---|
4398 |
|
---|
4399 | /* add if not first, otherwise copy */
|
---|
4400 | if (!first) {
|
---|
4401 | if (zA) {
|
---|
4402 | if ((err = ecc_projective_add_point(R, fp_cache[idx1].LUT[zA],
|
---|
4403 | R, modulus, mp)) != MP_OKAY) {
|
---|
4404 | break;
|
---|
4405 | }
|
---|
4406 | }
|
---|
4407 | if (zB) {
|
---|
4408 | if ((err = ecc_projective_add_point(R, fp_cache[idx2].LUT[zB],
|
---|
4409 | R, modulus, mp)) != MP_OKAY) {
|
---|
4410 | break;
|
---|
4411 | }
|
---|
4412 | }
|
---|
4413 | } else {
|
---|
4414 | if (zA) {
|
---|
4415 | if ((mp_copy(fp_cache[idx1].LUT[zA]->x, R->x) != MP_OKAY) ||
|
---|
4416 | (mp_copy(fp_cache[idx1].LUT[zA]->y, R->y) != MP_OKAY) ||
|
---|
4417 | (mp_copy(&fp_cache[idx1].mu, R->z) != MP_OKAY)) {
|
---|
4418 | err = GEN_MEM_ERR;
|
---|
4419 | break;
|
---|
4420 | }
|
---|
4421 | first = 0;
|
---|
4422 | }
|
---|
4423 | if (zB && first == 0) {
|
---|
4424 | if (zB) {
|
---|
4425 | if ((err = ecc_projective_add_point(R,
|
---|
4426 | fp_cache[idx2].LUT[zB], R, modulus, mp)) != MP_OKAY){
|
---|
4427 | break;
|
---|
4428 | }
|
---|
4429 | }
|
---|
4430 | } else if (zB && first == 1) {
|
---|
4431 | if ((mp_copy(fp_cache[idx2].LUT[zB]->x, R->x) != MP_OKAY) ||
|
---|
4432 | (mp_copy(fp_cache[idx2].LUT[zB]->y, R->y) != MP_OKAY) ||
|
---|
4433 | (mp_copy(&fp_cache[idx2].mu, R->z) != MP_OKAY)) {
|
---|
4434 | err = GEN_MEM_ERR;
|
---|
4435 | break;
|
---|
4436 | }
|
---|
4437 | first = 0;
|
---|
4438 | }
|
---|
4439 | }
|
---|
4440 | }
|
---|
4441 | }
|
---|
4442 |
|
---|
4443 | ForceZero(kb[0], KB_SIZE);
|
---|
4444 | ForceZero(kb[1], KB_SIZE);
|
---|
4445 |
|
---|
4446 | #ifdef WOLFSSL_SMALL_STACK
|
---|
4447 | XFREE(kb[0], NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
4448 | XFREE(kb[1], NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
4449 | #endif
|
---|
4450 |
|
---|
4451 | #undef KB_SIZE
|
---|
4452 |
|
---|
4453 | return ecc_map(R, modulus, mp);
|
---|
4454 | }
|
---|
4455 |
|
---|
4456 | /** ECC Fixed Point mulmod global
|
---|
4457 | Computes kA*A + kB*B = C using Shamir's Trick
|
---|
4458 | A First point to multiply
|
---|
4459 | kA What to multiple A by
|
---|
4460 | B Second point to multiply
|
---|
4461 | kB What to multiple B by
|
---|
4462 | C [out] Destination point (can overlap with A or B)
|
---|
4463 | modulus Modulus for curve
|
---|
4464 | return MP_OKAY on success
|
---|
4465 | */
|
---|
4466 | int ecc_mul2add(ecc_point* A, mp_int* kA,
|
---|
4467 | ecc_point* B, mp_int* kB,
|
---|
4468 | ecc_point* C, mp_int* modulus)
|
---|
4469 | {
|
---|
4470 | int idx1 = -1, idx2 = -1, err = MP_OKAY, mpInit = 0;
|
---|
4471 | mp_digit mp;
|
---|
4472 | mp_int mu;
|
---|
4473 |
|
---|
4474 | err = mp_init(&mu);
|
---|
4475 | if (err != MP_OKAY)
|
---|
4476 | return err;
|
---|
4477 |
|
---|
4478 | #ifndef HAVE_THREAD_LS
|
---|
4479 | if (initMutex == 0) {
|
---|
4480 | InitMutex(&ecc_fp_lock);
|
---|
4481 | initMutex = 1;
|
---|
4482 | }
|
---|
4483 | if (LockMutex(&ecc_fp_lock) != 0)
|
---|
4484 | return BAD_MUTEX_E;
|
---|
4485 | #endif /* HAVE_THREAD_LS */
|
---|
4486 |
|
---|
4487 | /* find point */
|
---|
4488 | idx1 = find_base(A);
|
---|
4489 |
|
---|
4490 | /* no entry? */
|
---|
4491 | if (idx1 == -1) {
|
---|
4492 | /* find hole and add it */
|
---|
4493 | if ((idx1 = find_hole()) >= 0) {
|
---|
4494 | err = add_entry(idx1, A);
|
---|
4495 | }
|
---|
4496 | }
|
---|
4497 | if (err == MP_OKAY && idx1 != -1) {
|
---|
4498 | /* increment LRU */
|
---|
4499 | ++(fp_cache[idx1].lru_count);
|
---|
4500 | }
|
---|
4501 |
|
---|
4502 | if (err == MP_OKAY)
|
---|
4503 | /* find point */
|
---|
4504 | idx2 = find_base(B);
|
---|
4505 |
|
---|
4506 | if (err == MP_OKAY) {
|
---|
4507 | /* no entry? */
|
---|
4508 | if (idx2 == -1) {
|
---|
4509 | /* find hole and add it */
|
---|
4510 | if ((idx2 = find_hole()) >= 0)
|
---|
4511 | err = add_entry(idx2, B);
|
---|
4512 | }
|
---|
4513 | }
|
---|
4514 |
|
---|
4515 | if (err == MP_OKAY && idx2 != -1) {
|
---|
4516 | /* increment LRU */
|
---|
4517 | ++(fp_cache[idx2].lru_count);
|
---|
4518 | }
|
---|
4519 |
|
---|
4520 | if (err == MP_OKAY) {
|
---|
4521 | /* if it's 2 build the LUT, if it's higher just use the LUT */
|
---|
4522 | if (idx1 >= 0 && fp_cache[idx1].lru_count == 2) {
|
---|
4523 | /* compute mp */
|
---|
4524 | err = mp_montgomery_setup(modulus, &mp);
|
---|
4525 |
|
---|
4526 | if (err == MP_OKAY) {
|
---|
4527 | mpInit = 1;
|
---|
4528 | err = mp_montgomery_calc_normalization(&mu, modulus);
|
---|
4529 | }
|
---|
4530 |
|
---|
4531 | if (err == MP_OKAY)
|
---|
4532 | /* build the LUT */
|
---|
4533 | err = build_lut(idx1, modulus, &mp, &mu);
|
---|
4534 | }
|
---|
4535 | }
|
---|
4536 |
|
---|
4537 | if (err == MP_OKAY) {
|
---|
4538 | /* if it's 2 build the LUT, if it's higher just use the LUT */
|
---|
4539 | if (idx2 >= 0 && fp_cache[idx2].lru_count == 2) {
|
---|
4540 | if (mpInit == 0) {
|
---|
4541 | /* compute mp */
|
---|
4542 | err = mp_montgomery_setup(modulus, &mp);
|
---|
4543 | if (err == MP_OKAY) {
|
---|
4544 | mpInit = 1;
|
---|
4545 | err = mp_montgomery_calc_normalization(&mu, modulus);
|
---|
4546 | }
|
---|
4547 | }
|
---|
4548 |
|
---|
4549 | if (err == MP_OKAY)
|
---|
4550 | /* build the LUT */
|
---|
4551 | err = build_lut(idx2, modulus, &mp, &mu);
|
---|
4552 | }
|
---|
4553 | }
|
---|
4554 |
|
---|
4555 |
|
---|
4556 | if (err == MP_OKAY) {
|
---|
4557 | if (idx1 >=0 && idx2 >= 0 && fp_cache[idx1].lru_count >= 2 &&
|
---|
4558 | fp_cache[idx2].lru_count >= 2) {
|
---|
4559 | if (mpInit == 0) {
|
---|
4560 | /* compute mp */
|
---|
4561 | err = mp_montgomery_setup(modulus, &mp);
|
---|
4562 | }
|
---|
4563 | if (err == MP_OKAY)
|
---|
4564 | err = accel_fp_mul2add(idx1, idx2, kA, kB, C, modulus, &mp);
|
---|
4565 | } else {
|
---|
4566 | err = normal_ecc_mul2add(A, kA, B, kB, C, modulus);
|
---|
4567 | }
|
---|
4568 | }
|
---|
4569 |
|
---|
4570 | #ifndef HAVE_THREAD_LS
|
---|
4571 | UnLockMutex(&ecc_fp_lock);
|
---|
4572 | #endif /* HAVE_THREAD_LS */
|
---|
4573 | mp_clear(&mu);
|
---|
4574 |
|
---|
4575 | return err;
|
---|
4576 | }
|
---|
4577 | #endif /* ECC_SHAMIR */
|
---|
4578 |
|
---|
4579 | /** ECC Fixed Point mulmod global
|
---|
4580 | k The multiplicand
|
---|
4581 | G Base point to multiply
|
---|
4582 | R [out] Destination of product
|
---|
4583 | modulus The modulus for the curve
|
---|
4584 | map [boolean] If non-zero maps the point back to affine co-ordinates,
|
---|
4585 | otherwise it's left in jacobian-montgomery form
|
---|
4586 | return MP_OKAY if successful
|
---|
4587 | */
|
---|
4588 | int wc_ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R, mp_int* modulus,
|
---|
4589 | int map)
|
---|
4590 | {
|
---|
4591 | int idx, err = MP_OKAY;
|
---|
4592 | mp_digit mp;
|
---|
4593 | mp_int mu;
|
---|
4594 | int mpSetup = 0;
|
---|
4595 |
|
---|
4596 | if (mp_init(&mu) != MP_OKAY)
|
---|
4597 | return MP_INIT_E;
|
---|
4598 |
|
---|
4599 | #ifndef HAVE_THREAD_LS
|
---|
4600 | if (initMutex == 0) {
|
---|
4601 | InitMutex(&ecc_fp_lock);
|
---|
4602 | initMutex = 1;
|
---|
4603 | }
|
---|
4604 |
|
---|
4605 | if (LockMutex(&ecc_fp_lock) != 0)
|
---|
4606 | return BAD_MUTEX_E;
|
---|
4607 | #endif /* HAVE_THREAD_LS */
|
---|
4608 |
|
---|
4609 | /* find point */
|
---|
4610 | idx = find_base(G);
|
---|
4611 |
|
---|
4612 | /* no entry? */
|
---|
4613 | if (idx == -1) {
|
---|
4614 | /* find hole and add it */
|
---|
4615 | idx = find_hole();
|
---|
4616 |
|
---|
4617 | if (idx >= 0)
|
---|
4618 | err = add_entry(idx, G);
|
---|
4619 | }
|
---|
4620 | if (err == MP_OKAY && idx >= 0) {
|
---|
4621 | /* increment LRU */
|
---|
4622 | ++(fp_cache[idx].lru_count);
|
---|
4623 | }
|
---|
4624 |
|
---|
4625 |
|
---|
4626 | if (err == MP_OKAY) {
|
---|
4627 | /* if it's 2 build the LUT, if it's higher just use the LUT */
|
---|
4628 | if (idx >= 0 && fp_cache[idx].lru_count == 2) {
|
---|
4629 | /* compute mp */
|
---|
4630 | err = mp_montgomery_setup(modulus, &mp);
|
---|
4631 |
|
---|
4632 | if (err == MP_OKAY) {
|
---|
4633 | /* compute mu */
|
---|
4634 | mpSetup = 1;
|
---|
4635 | err = mp_montgomery_calc_normalization(&mu, modulus);
|
---|
4636 | }
|
---|
4637 |
|
---|
4638 | if (err == MP_OKAY)
|
---|
4639 | /* build the LUT */
|
---|
4640 | err = build_lut(idx, modulus, &mp, &mu);
|
---|
4641 | }
|
---|
4642 | }
|
---|
4643 |
|
---|
4644 | if (err == MP_OKAY) {
|
---|
4645 | if (idx >= 0 && fp_cache[idx].lru_count >= 2) {
|
---|
4646 | if (mpSetup == 0) {
|
---|
4647 | /* compute mp */
|
---|
4648 | err = mp_montgomery_setup(modulus, &mp);
|
---|
4649 | }
|
---|
4650 | if (err == MP_OKAY)
|
---|
4651 | err = accel_fp_mul(idx, k, R, modulus, &mp, map);
|
---|
4652 | } else {
|
---|
4653 | err = normal_ecc_mulmod(k, G, R, modulus, map);
|
---|
4654 | }
|
---|
4655 | }
|
---|
4656 |
|
---|
4657 | #ifndef HAVE_THREAD_LS
|
---|
4658 | UnLockMutex(&ecc_fp_lock);
|
---|
4659 | #endif /* HAVE_THREAD_LS */
|
---|
4660 | mp_clear(&mu);
|
---|
4661 |
|
---|
4662 | return err;
|
---|
4663 | }
|
---|
4664 |
|
---|
4665 | /* helper function for freeing the cache ...
|
---|
4666 | must be called with the cache mutex locked */
|
---|
4667 | static void wc_ecc_fp_free_cache(void)
|
---|
4668 | {
|
---|
4669 | unsigned x, y;
|
---|
4670 | for (x = 0; x < FP_ENTRIES; x++) {
|
---|
4671 | if (fp_cache[x].g != NULL) {
|
---|
4672 | for (y = 0; y < (1U<<FP_LUT); y++) {
|
---|
4673 | wc_ecc_del_point(fp_cache[x].LUT[y]);
|
---|
4674 | fp_cache[x].LUT[y] = NULL;
|
---|
4675 | }
|
---|
4676 | wc_ecc_del_point(fp_cache[x].g);
|
---|
4677 | fp_cache[x].g = NULL;
|
---|
4678 | mp_clear(&fp_cache[x].mu);
|
---|
4679 | fp_cache[x].lru_count = 0;
|
---|
4680 | fp_cache[x].lock = 0;
|
---|
4681 | }
|
---|
4682 | }
|
---|
4683 | }
|
---|
4684 |
|
---|
4685 | /** Free the Fixed Point cache */
|
---|
4686 | void wc_ecc_fp_free(void)
|
---|
4687 | {
|
---|
4688 | #ifndef HAVE_THREAD_LS
|
---|
4689 | if (initMutex == 0) {
|
---|
4690 | InitMutex(&ecc_fp_lock);
|
---|
4691 | initMutex = 1;
|
---|
4692 | }
|
---|
4693 |
|
---|
4694 | if (LockMutex(&ecc_fp_lock) == 0) {
|
---|
4695 | #endif /* HAVE_THREAD_LS */
|
---|
4696 |
|
---|
4697 | wc_ecc_fp_free_cache();
|
---|
4698 |
|
---|
4699 | #ifndef HAVE_THREAD_LS
|
---|
4700 | UnLockMutex(&ecc_fp_lock);
|
---|
4701 | FreeMutex(&ecc_fp_lock);
|
---|
4702 | initMutex = 0;
|
---|
4703 | }
|
---|
4704 | #endif /* HAVE_THREAD_LS */
|
---|
4705 | }
|
---|
4706 |
|
---|
4707 |
|
---|
4708 | #endif /* FP_ECC */
|
---|
4709 |
|
---|
4710 | #ifdef HAVE_ECC_ENCRYPT
|
---|
4711 |
|
---|
4712 |
|
---|
4713 | enum ecCliState {
|
---|
4714 | ecCLI_INIT = 1,
|
---|
4715 | ecCLI_SALT_GET = 2,
|
---|
4716 | ecCLI_SALT_SET = 3,
|
---|
4717 | ecCLI_SENT_REQ = 4,
|
---|
4718 | ecCLI_RECV_RESP = 5,
|
---|
4719 | ecCLI_BAD_STATE = 99
|
---|
4720 | };
|
---|
4721 |
|
---|
4722 | enum ecSrvState {
|
---|
4723 | ecSRV_INIT = 1,
|
---|
4724 | ecSRV_SALT_GET = 2,
|
---|
4725 | ecSRV_SALT_SET = 3,
|
---|
4726 | ecSRV_RECV_REQ = 4,
|
---|
4727 | ecSRV_SENT_RESP = 5,
|
---|
4728 | ecSRV_BAD_STATE = 99
|
---|
4729 | };
|
---|
4730 |
|
---|
4731 |
|
---|
4732 | struct ecEncCtx {
|
---|
4733 | const byte* kdfSalt; /* optional salt for kdf */
|
---|
4734 | const byte* kdfInfo; /* optional info for kdf */
|
---|
4735 | const byte* macSalt; /* optional salt for mac */
|
---|
4736 | word32 kdfSaltSz; /* size of kdfSalt */
|
---|
4737 | word32 kdfInfoSz; /* size of kdfInfo */
|
---|
4738 | word32 macSaltSz; /* size of macSalt */
|
---|
4739 | byte clientSalt[EXCHANGE_SALT_SZ]; /* for msg exchange */
|
---|
4740 | byte serverSalt[EXCHANGE_SALT_SZ]; /* for msg exchange */
|
---|
4741 | byte encAlgo; /* which encryption type */
|
---|
4742 | byte kdfAlgo; /* which key derivation function type */
|
---|
4743 | byte macAlgo; /* which mac function type */
|
---|
4744 | byte protocol; /* are we REQ_RESP client or server ? */
|
---|
4745 | byte cliSt; /* protocol state, for sanity checks */
|
---|
4746 | byte srvSt; /* protocol state, for sanity checks */
|
---|
4747 | };
|
---|
4748 |
|
---|
4749 |
|
---|
4750 | const byte* wc_ecc_ctx_get_own_salt(ecEncCtx* ctx)
|
---|
4751 | {
|
---|
4752 | if (ctx == NULL || ctx->protocol == 0)
|
---|
4753 | return NULL;
|
---|
4754 |
|
---|
4755 | if (ctx->protocol == REQ_RESP_CLIENT) {
|
---|
4756 | if (ctx->cliSt == ecCLI_INIT) {
|
---|
4757 | ctx->cliSt = ecCLI_SALT_GET;
|
---|
4758 | return ctx->clientSalt;
|
---|
4759 | }
|
---|
4760 | else {
|
---|
4761 | ctx->cliSt = ecCLI_BAD_STATE;
|
---|
4762 | return NULL;
|
---|
4763 | }
|
---|
4764 | }
|
---|
4765 | else if (ctx->protocol == REQ_RESP_SERVER) {
|
---|
4766 | if (ctx->srvSt == ecSRV_INIT) {
|
---|
4767 | ctx->srvSt = ecSRV_SALT_GET;
|
---|
4768 | return ctx->serverSalt;
|
---|
4769 | }
|
---|
4770 | else {
|
---|
4771 | ctx->srvSt = ecSRV_BAD_STATE;
|
---|
4772 | return NULL;
|
---|
4773 | }
|
---|
4774 | }
|
---|
4775 |
|
---|
4776 | return NULL;
|
---|
4777 | }
|
---|
4778 |
|
---|
4779 |
|
---|
4780 | /* optional set info, can be called before or after set_peer_salt */
|
---|
4781 | int wc_ecc_ctx_set_info(ecEncCtx* ctx, const byte* info, int sz)
|
---|
4782 | {
|
---|
4783 | if (ctx == NULL || info == 0 || sz < 0)
|
---|
4784 | return BAD_FUNC_ARG;
|
---|
4785 |
|
---|
4786 | ctx->kdfInfo = info;
|
---|
4787 | ctx->kdfInfoSz = sz;
|
---|
4788 |
|
---|
4789 | return 0;
|
---|
4790 | }
|
---|
4791 |
|
---|
4792 |
|
---|
4793 | static const char* exchange_info = "Secure Message Exchange";
|
---|
4794 |
|
---|
4795 | int wc_ecc_ctx_set_peer_salt(ecEncCtx* ctx, const byte* salt)
|
---|
4796 | {
|
---|
4797 | byte tmp[EXCHANGE_SALT_SZ/2];
|
---|
4798 | int halfSz = EXCHANGE_SALT_SZ/2;
|
---|
4799 |
|
---|
4800 | if (ctx == NULL || ctx->protocol == 0 || salt == NULL)
|
---|
4801 | return BAD_FUNC_ARG;
|
---|
4802 |
|
---|
4803 | if (ctx->protocol == REQ_RESP_CLIENT) {
|
---|
4804 | XMEMCPY(ctx->serverSalt, salt, EXCHANGE_SALT_SZ);
|
---|
4805 | if (ctx->cliSt == ecCLI_SALT_GET)
|
---|
4806 | ctx->cliSt = ecCLI_SALT_SET;
|
---|
4807 | else {
|
---|
4808 | ctx->cliSt = ecCLI_BAD_STATE;
|
---|
4809 | return BAD_ENC_STATE_E;
|
---|
4810 | }
|
---|
4811 | }
|
---|
4812 | else {
|
---|
4813 | XMEMCPY(ctx->clientSalt, salt, EXCHANGE_SALT_SZ);
|
---|
4814 | if (ctx->srvSt == ecSRV_SALT_GET)
|
---|
4815 | ctx->srvSt = ecSRV_SALT_SET;
|
---|
4816 | else {
|
---|
4817 | ctx->srvSt = ecSRV_BAD_STATE;
|
---|
4818 | return BAD_ENC_STATE_E;
|
---|
4819 | }
|
---|
4820 | }
|
---|
4821 |
|
---|
4822 | /* mix half and half */
|
---|
4823 | /* tmp stores 2nd half of client before overwrite */
|
---|
4824 | XMEMCPY(tmp, ctx->clientSalt + halfSz, halfSz);
|
---|
4825 | XMEMCPY(ctx->clientSalt + halfSz, ctx->serverSalt, halfSz);
|
---|
4826 | XMEMCPY(ctx->serverSalt, tmp, halfSz);
|
---|
4827 |
|
---|
4828 | ctx->kdfSalt = ctx->clientSalt;
|
---|
4829 | ctx->kdfSaltSz = EXCHANGE_SALT_SZ;
|
---|
4830 |
|
---|
4831 | ctx->macSalt = ctx->serverSalt;
|
---|
4832 | ctx->macSaltSz = EXCHANGE_SALT_SZ;
|
---|
4833 |
|
---|
4834 | if (ctx->kdfInfo == NULL) {
|
---|
4835 | /* default info */
|
---|
4836 | ctx->kdfInfo = (const byte*)exchange_info;
|
---|
4837 | ctx->kdfInfoSz = EXCHANGE_INFO_SZ;
|
---|
4838 | }
|
---|
4839 |
|
---|
4840 | return 0;
|
---|
4841 | }
|
---|
4842 |
|
---|
4843 |
|
---|
4844 | static int ecc_ctx_set_salt(ecEncCtx* ctx, int flags, WC_RNG* rng)
|
---|
4845 | {
|
---|
4846 | byte* saltBuffer = NULL;
|
---|
4847 |
|
---|
4848 | if (ctx == NULL || rng == NULL || flags == 0)
|
---|
4849 | return BAD_FUNC_ARG;
|
---|
4850 |
|
---|
4851 | saltBuffer = (flags == REQ_RESP_CLIENT) ? ctx->clientSalt : ctx->serverSalt;
|
---|
4852 |
|
---|
4853 | return wc_RNG_GenerateBlock(rng, saltBuffer, EXCHANGE_SALT_SZ);
|
---|
4854 | }
|
---|
4855 |
|
---|
4856 |
|
---|
4857 | static void ecc_ctx_init(ecEncCtx* ctx, int flags)
|
---|
4858 | {
|
---|
4859 | if (ctx) {
|
---|
4860 | XMEMSET(ctx, 0, sizeof(ecEncCtx));
|
---|
4861 |
|
---|
4862 | ctx->encAlgo = ecAES_128_CBC;
|
---|
4863 | ctx->kdfAlgo = ecHKDF_SHA256;
|
---|
4864 | ctx->macAlgo = ecHMAC_SHA256;
|
---|
4865 | ctx->protocol = (byte)flags;
|
---|
4866 |
|
---|
4867 | if (flags == REQ_RESP_CLIENT)
|
---|
4868 | ctx->cliSt = ecCLI_INIT;
|
---|
4869 | if (flags == REQ_RESP_SERVER)
|
---|
4870 | ctx->srvSt = ecSRV_INIT;
|
---|
4871 | }
|
---|
4872 | }
|
---|
4873 |
|
---|
4874 |
|
---|
4875 | /* allow ecc context reset so user doesn't have to init/free for resue */
|
---|
4876 | int wc_ecc_ctx_reset(ecEncCtx* ctx, WC_RNG* rng)
|
---|
4877 | {
|
---|
4878 | if (ctx == NULL || rng == NULL)
|
---|
4879 | return BAD_FUNC_ARG;
|
---|
4880 |
|
---|
4881 | ecc_ctx_init(ctx, ctx->protocol);
|
---|
4882 | return ecc_ctx_set_salt(ctx, ctx->protocol, rng);
|
---|
4883 | }
|
---|
4884 |
|
---|
4885 |
|
---|
4886 | /* alloc/init and set defaults, return new Context */
|
---|
4887 | ecEncCtx* wc_ecc_ctx_new(int flags, WC_RNG* rng)
|
---|
4888 | {
|
---|
4889 | int ret = 0;
|
---|
4890 | ecEncCtx* ctx = (ecEncCtx*)XMALLOC(sizeof(ecEncCtx), 0, DYNAMIC_TYPE_ECC);
|
---|
4891 |
|
---|
4892 | if (ctx)
|
---|
4893 | ctx->protocol = (byte)flags;
|
---|
4894 |
|
---|
4895 | ret = wc_ecc_ctx_reset(ctx, rng);
|
---|
4896 | if (ret != 0) {
|
---|
4897 | wc_ecc_ctx_free(ctx);
|
---|
4898 | ctx = NULL;
|
---|
4899 | }
|
---|
4900 |
|
---|
4901 | return ctx;
|
---|
4902 | }
|
---|
4903 |
|
---|
4904 |
|
---|
4905 | /* free any resources, clear any keys */
|
---|
4906 | void wc_ecc_ctx_free(ecEncCtx* ctx)
|
---|
4907 | {
|
---|
4908 | if (ctx) {
|
---|
4909 | ForceZero(ctx, sizeof(ecEncCtx));
|
---|
4910 | XFREE(ctx, 0, DYNAMIC_TYPE_ECC);
|
---|
4911 | }
|
---|
4912 | }
|
---|
4913 |
|
---|
4914 |
|
---|
4915 | static int ecc_get_key_sizes(ecEncCtx* ctx, int* encKeySz, int* ivSz,
|
---|
4916 | int* keysLen, word32* digestSz, word32* blockSz)
|
---|
4917 | {
|
---|
4918 | if (ctx) {
|
---|
4919 | switch (ctx->encAlgo) {
|
---|
4920 | case ecAES_128_CBC:
|
---|
4921 | *encKeySz = KEY_SIZE_128;
|
---|
4922 | *ivSz = IV_SIZE_128;
|
---|
4923 | *blockSz = AES_BLOCK_SIZE;
|
---|
4924 | break;
|
---|
4925 | default:
|
---|
4926 | return BAD_FUNC_ARG;
|
---|
4927 | }
|
---|
4928 |
|
---|
4929 | switch (ctx->macAlgo) {
|
---|
4930 | case ecHMAC_SHA256:
|
---|
4931 | *digestSz = SHA256_DIGEST_SIZE;
|
---|
4932 | break;
|
---|
4933 | default:
|
---|
4934 | return BAD_FUNC_ARG;
|
---|
4935 | }
|
---|
4936 | } else
|
---|
4937 | return BAD_FUNC_ARG;
|
---|
4938 |
|
---|
4939 | *keysLen = *encKeySz + *ivSz + *digestSz;
|
---|
4940 |
|
---|
4941 | return 0;
|
---|
4942 | }
|
---|
4943 |
|
---|
4944 |
|
---|
4945 | /* ecc encrypt with shared secret run through kdf
|
---|
4946 | ctx holds non default algos and inputs
|
---|
4947 | msgSz should be the right size for encAlgo, i.e., already padded
|
---|
4948 | return 0 on success */
|
---|
4949 | int wc_ecc_encrypt(ecc_key* privKey, ecc_key* pubKey, const byte* msg,
|
---|
4950 | word32 msgSz, byte* out, word32* outSz, ecEncCtx* ctx)
|
---|
4951 | {
|
---|
4952 | int ret;
|
---|
4953 | word32 blockSz;
|
---|
4954 | word32 digestSz;
|
---|
4955 | ecEncCtx localCtx;
|
---|
4956 | #ifdef WOLFSSL_SMALL_STACK
|
---|
4957 | byte* sharedSecret;
|
---|
4958 | byte* keys;
|
---|
4959 | #else
|
---|
4960 | byte sharedSecret[ECC_MAXSIZE]; /* 521 max size */
|
---|
4961 | byte keys[ECC_BUFSIZE]; /* max size */
|
---|
4962 | #endif
|
---|
4963 | word32 sharedSz = ECC_MAXSIZE;
|
---|
4964 | int keysLen;
|
---|
4965 | int encKeySz;
|
---|
4966 | int ivSz;
|
---|
4967 | int offset = 0; /* keys offset if doing msg exchange */
|
---|
4968 | byte* encKey;
|
---|
4969 | byte* encIv;
|
---|
4970 | byte* macKey;
|
---|
4971 |
|
---|
4972 | if (privKey == NULL || pubKey == NULL || msg == NULL || out == NULL ||
|
---|
4973 | outSz == NULL)
|
---|
4974 | return BAD_FUNC_ARG;
|
---|
4975 |
|
---|
4976 | if (ctx == NULL) { /* use defaults */
|
---|
4977 | ecc_ctx_init(&localCtx, 0);
|
---|
4978 | ctx = &localCtx;
|
---|
4979 | }
|
---|
4980 |
|
---|
4981 | ret = ecc_get_key_sizes(ctx, &encKeySz, &ivSz, &keysLen, &digestSz,
|
---|
4982 | &blockSz);
|
---|
4983 | if (ret != 0)
|
---|
4984 | return ret;
|
---|
4985 |
|
---|
4986 | if (ctx->protocol == REQ_RESP_SERVER) {
|
---|
4987 | offset = keysLen;
|
---|
4988 | keysLen *= 2;
|
---|
4989 |
|
---|
4990 | if (ctx->srvSt != ecSRV_RECV_REQ)
|
---|
4991 | return BAD_ENC_STATE_E;
|
---|
4992 |
|
---|
4993 | ctx->srvSt = ecSRV_BAD_STATE; /* we're done no more ops allowed */
|
---|
4994 | }
|
---|
4995 | else if (ctx->protocol == REQ_RESP_CLIENT) {
|
---|
4996 | if (ctx->cliSt != ecCLI_SALT_SET)
|
---|
4997 | return BAD_ENC_STATE_E;
|
---|
4998 |
|
---|
4999 | ctx->cliSt = ecCLI_SENT_REQ; /* only do this once */
|
---|
5000 | }
|
---|
5001 |
|
---|
5002 | if (keysLen > ECC_BUFSIZE) /* keys size */
|
---|
5003 | return BUFFER_E;
|
---|
5004 |
|
---|
5005 | if ( (msgSz%blockSz) != 0)
|
---|
5006 | return BAD_PADDING_E;
|
---|
5007 |
|
---|
5008 | if (*outSz < (msgSz + digestSz))
|
---|
5009 | return BUFFER_E;
|
---|
5010 |
|
---|
5011 | #ifdef WOLFSSL_SMALL_STACK
|
---|
5012 | sharedSecret = (byte*)XMALLOC(ECC_MAXSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
5013 | if (sharedSecret == NULL)
|
---|
5014 | return MEMORY_E;
|
---|
5015 |
|
---|
5016 | keys = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
5017 | if (keys == NULL) {
|
---|
5018 | XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
5019 | return MEMORY_E;
|
---|
5020 | }
|
---|
5021 | #endif
|
---|
5022 |
|
---|
5023 | ret = wc_ecc_shared_secret(privKey, pubKey, sharedSecret, &sharedSz);
|
---|
5024 |
|
---|
5025 | if (ret == 0) {
|
---|
5026 | switch (ctx->kdfAlgo) {
|
---|
5027 | case ecHKDF_SHA256 :
|
---|
5028 | ret = wc_HKDF(SHA256, sharedSecret, sharedSz, ctx->kdfSalt,
|
---|
5029 | ctx->kdfSaltSz, ctx->kdfInfo, ctx->kdfInfoSz,
|
---|
5030 | keys, keysLen);
|
---|
5031 | break;
|
---|
5032 |
|
---|
5033 | default:
|
---|
5034 | ret = BAD_FUNC_ARG;
|
---|
5035 | break;
|
---|
5036 | }
|
---|
5037 | }
|
---|
5038 |
|
---|
5039 | if (ret == 0) {
|
---|
5040 | encKey = keys + offset;
|
---|
5041 | encIv = encKey + encKeySz;
|
---|
5042 | macKey = encKey + encKeySz + ivSz;
|
---|
5043 |
|
---|
5044 | switch (ctx->encAlgo) {
|
---|
5045 | case ecAES_128_CBC:
|
---|
5046 | {
|
---|
5047 | Aes aes;
|
---|
5048 | ret = wc_AesSetKey(&aes, encKey, KEY_SIZE_128, encIv,
|
---|
5049 | AES_ENCRYPTION);
|
---|
5050 | if (ret != 0)
|
---|
5051 | break;
|
---|
5052 | ret = wc_AesCbcEncrypt(&aes, out, msg, msgSz);
|
---|
5053 | }
|
---|
5054 | break;
|
---|
5055 |
|
---|
5056 | default:
|
---|
5057 | ret = BAD_FUNC_ARG;
|
---|
5058 | break;
|
---|
5059 | }
|
---|
5060 | }
|
---|
5061 |
|
---|
5062 | if (ret == 0) {
|
---|
5063 | switch (ctx->macAlgo) {
|
---|
5064 | case ecHMAC_SHA256:
|
---|
5065 | {
|
---|
5066 | Hmac hmac;
|
---|
5067 | ret = wc_HmacSetKey(&hmac, SHA256, macKey, SHA256_DIGEST_SIZE);
|
---|
5068 | if (ret != 0)
|
---|
5069 | break;
|
---|
5070 | ret = wc_HmacUpdate(&hmac, out, msgSz);
|
---|
5071 | if (ret != 0)
|
---|
5072 | break;
|
---|
5073 | ret = wc_HmacUpdate(&hmac, ctx->macSalt, ctx->macSaltSz);
|
---|
5074 | if (ret != 0)
|
---|
5075 | break;
|
---|
5076 | ret = wc_HmacFinal(&hmac, out+msgSz);
|
---|
5077 | }
|
---|
5078 | break;
|
---|
5079 |
|
---|
5080 | default:
|
---|
5081 | ret = BAD_FUNC_ARG;
|
---|
5082 | break;
|
---|
5083 | }
|
---|
5084 | }
|
---|
5085 |
|
---|
5086 | if (ret == 0)
|
---|
5087 | *outSz = msgSz + digestSz;
|
---|
5088 |
|
---|
5089 | #ifdef WOLFSSL_SMALL_STACK
|
---|
5090 | XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
5091 | XFREE(keys, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
5092 | #endif
|
---|
5093 |
|
---|
5094 | return ret;
|
---|
5095 | }
|
---|
5096 |
|
---|
5097 |
|
---|
5098 | /* ecc decrypt with shared secret run through kdf
|
---|
5099 | ctx holds non default algos and inputs
|
---|
5100 | return 0 on success */
|
---|
5101 | int wc_ecc_decrypt(ecc_key* privKey, ecc_key* pubKey, const byte* msg,
|
---|
5102 | word32 msgSz, byte* out, word32* outSz, ecEncCtx* ctx)
|
---|
5103 | {
|
---|
5104 | int ret;
|
---|
5105 | word32 blockSz;
|
---|
5106 | word32 digestSz;
|
---|
5107 | ecEncCtx localCtx;
|
---|
5108 | #ifdef WOLFSSL_SMALL_STACK
|
---|
5109 | byte* sharedSecret;
|
---|
5110 | byte* keys;
|
---|
5111 | #else
|
---|
5112 | byte sharedSecret[ECC_MAXSIZE]; /* 521 max size */
|
---|
5113 | byte keys[ECC_BUFSIZE]; /* max size */
|
---|
5114 | #endif
|
---|
5115 | word32 sharedSz = ECC_MAXSIZE;
|
---|
5116 | int keysLen;
|
---|
5117 | int encKeySz;
|
---|
5118 | int ivSz;
|
---|
5119 | int offset = 0; /* in case using msg exchange */
|
---|
5120 | byte* encKey;
|
---|
5121 | byte* encIv;
|
---|
5122 | byte* macKey;
|
---|
5123 |
|
---|
5124 | if (privKey == NULL || pubKey == NULL || msg == NULL || out == NULL ||
|
---|
5125 | outSz == NULL)
|
---|
5126 | return BAD_FUNC_ARG;
|
---|
5127 |
|
---|
5128 | if (ctx == NULL) { /* use defaults */
|
---|
5129 | ecc_ctx_init(&localCtx, 0);
|
---|
5130 | ctx = &localCtx;
|
---|
5131 | }
|
---|
5132 |
|
---|
5133 | ret = ecc_get_key_sizes(ctx, &encKeySz, &ivSz, &keysLen, &digestSz,
|
---|
5134 | &blockSz);
|
---|
5135 | if (ret != 0)
|
---|
5136 | return ret;
|
---|
5137 |
|
---|
5138 | if (ctx->protocol == REQ_RESP_CLIENT) {
|
---|
5139 | offset = keysLen;
|
---|
5140 | keysLen *= 2;
|
---|
5141 |
|
---|
5142 | if (ctx->cliSt != ecCLI_SENT_REQ)
|
---|
5143 | return BAD_ENC_STATE_E;
|
---|
5144 |
|
---|
5145 | ctx->cliSt = ecSRV_BAD_STATE; /* we're done no more ops allowed */
|
---|
5146 | }
|
---|
5147 | else if (ctx->protocol == REQ_RESP_SERVER) {
|
---|
5148 | if (ctx->srvSt != ecSRV_SALT_SET)
|
---|
5149 | return BAD_ENC_STATE_E;
|
---|
5150 |
|
---|
5151 | ctx->srvSt = ecSRV_RECV_REQ; /* only do this once */
|
---|
5152 | }
|
---|
5153 |
|
---|
5154 | if (keysLen > ECC_BUFSIZE) /* keys size */
|
---|
5155 | return BUFFER_E;
|
---|
5156 |
|
---|
5157 | if ( ((msgSz-digestSz) % blockSz) != 0)
|
---|
5158 | return BAD_PADDING_E;
|
---|
5159 |
|
---|
5160 | if (*outSz < (msgSz - digestSz))
|
---|
5161 | return BUFFER_E;
|
---|
5162 |
|
---|
5163 | #ifdef WOLFSSL_SMALL_STACK
|
---|
5164 | sharedSecret = (byte*)XMALLOC(ECC_MAXSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
5165 | if (sharedSecret == NULL)
|
---|
5166 | return MEMORY_E;
|
---|
5167 |
|
---|
5168 | keys = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
5169 | if (keys == NULL) {
|
---|
5170 | XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
5171 | return MEMORY_E;
|
---|
5172 | }
|
---|
5173 | #endif
|
---|
5174 |
|
---|
5175 | ret = wc_ecc_shared_secret(privKey, pubKey, sharedSecret, &sharedSz);
|
---|
5176 |
|
---|
5177 | if (ret == 0) {
|
---|
5178 | switch (ctx->kdfAlgo) {
|
---|
5179 | case ecHKDF_SHA256 :
|
---|
5180 | ret = wc_HKDF(SHA256, sharedSecret, sharedSz, ctx->kdfSalt,
|
---|
5181 | ctx->kdfSaltSz, ctx->kdfInfo, ctx->kdfInfoSz,
|
---|
5182 | keys, keysLen);
|
---|
5183 | break;
|
---|
5184 |
|
---|
5185 | default:
|
---|
5186 | ret = BAD_FUNC_ARG;
|
---|
5187 | break;
|
---|
5188 | }
|
---|
5189 | }
|
---|
5190 |
|
---|
5191 | if (ret == 0) {
|
---|
5192 | encKey = keys + offset;
|
---|
5193 | encIv = encKey + encKeySz;
|
---|
5194 | macKey = encKey + encKeySz + ivSz;
|
---|
5195 |
|
---|
5196 | switch (ctx->macAlgo) {
|
---|
5197 | case ecHMAC_SHA256:
|
---|
5198 | {
|
---|
5199 | byte verify[SHA256_DIGEST_SIZE];
|
---|
5200 | Hmac hmac;
|
---|
5201 | ret = wc_HmacSetKey(&hmac, SHA256, macKey, SHA256_DIGEST_SIZE);
|
---|
5202 | if (ret != 0)
|
---|
5203 | break;
|
---|
5204 | ret = wc_HmacUpdate(&hmac, msg, msgSz-digestSz);
|
---|
5205 | if (ret != 0)
|
---|
5206 | break;
|
---|
5207 | ret = wc_HmacUpdate(&hmac, ctx->macSalt, ctx->macSaltSz);
|
---|
5208 | if (ret != 0)
|
---|
5209 | break;
|
---|
5210 | ret = wc_HmacFinal(&hmac, verify);
|
---|
5211 | if (ret != 0)
|
---|
5212 | break;
|
---|
5213 | if (memcmp(verify, msg + msgSz - digestSz, digestSz) != 0)
|
---|
5214 | ret = -1;
|
---|
5215 | }
|
---|
5216 | break;
|
---|
5217 |
|
---|
5218 | default:
|
---|
5219 | ret = BAD_FUNC_ARG;
|
---|
5220 | break;
|
---|
5221 | }
|
---|
5222 | }
|
---|
5223 |
|
---|
5224 | if (ret == 0) {
|
---|
5225 | switch (ctx->encAlgo) {
|
---|
5226 | case ecAES_128_CBC:
|
---|
5227 | {
|
---|
5228 | Aes aes;
|
---|
5229 | ret = wc_AesSetKey(&aes, encKey, KEY_SIZE_128, encIv,
|
---|
5230 | AES_DECRYPTION);
|
---|
5231 | if (ret != 0)
|
---|
5232 | break;
|
---|
5233 | ret = wc_AesCbcDecrypt(&aes, out, msg, msgSz-digestSz);
|
---|
5234 | }
|
---|
5235 | break;
|
---|
5236 |
|
---|
5237 | default:
|
---|
5238 | ret = BAD_FUNC_ARG;
|
---|
5239 | break;
|
---|
5240 | }
|
---|
5241 | }
|
---|
5242 |
|
---|
5243 | if (ret == 0)
|
---|
5244 | *outSz = msgSz - digestSz;
|
---|
5245 |
|
---|
5246 | #ifdef WOLFSSL_SMALL_STACK
|
---|
5247 | XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
5248 | XFREE(keys, NULL, DYNAMIC_TYPE_TMP_BUFFER);
|
---|
5249 | #endif
|
---|
5250 |
|
---|
5251 | return ret;
|
---|
5252 | }
|
---|
5253 |
|
---|
5254 |
|
---|
5255 | #endif /* HAVE_ECC_ENCRYPT */
|
---|
5256 |
|
---|
5257 |
|
---|
5258 | #ifdef HAVE_COMP_KEY
|
---|
5259 |
|
---|
5260 | /* computes the jacobi c = (a | n) (or Legendre if n is prime)
|
---|
5261 | * HAC pp. 73 Algorithm 2.149
|
---|
5262 | */
|
---|
5263 | int mp_jacobi(mp_int* a, mp_int* p, int* c)
|
---|
5264 | {
|
---|
5265 | mp_int a1, p1;
|
---|
5266 | int k, s, r, res;
|
---|
5267 | mp_digit residue;
|
---|
5268 |
|
---|
5269 | /* if p <= 0 return MP_VAL */
|
---|
5270 | if (mp_cmp_d(p, 0) != MP_GT) {
|
---|
5271 | return MP_VAL;
|
---|
5272 | }
|
---|
5273 |
|
---|
5274 | /* step 1. if a == 0, return 0 */
|
---|
5275 | if (mp_iszero (a) == 1) {
|
---|
5276 | *c = 0;
|
---|
5277 | return MP_OKAY;
|
---|
5278 | }
|
---|
5279 |
|
---|
5280 | /* step 2. if a == 1, return 1 */
|
---|
5281 | if (mp_cmp_d (a, 1) == MP_EQ) {
|
---|
5282 | *c = 1;
|
---|
5283 | return MP_OKAY;
|
---|
5284 | }
|
---|
5285 |
|
---|
5286 | /* default */
|
---|
5287 | s = 0;
|
---|
5288 |
|
---|
5289 | /* step 3. write a = a1 * 2**k */
|
---|
5290 | if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
|
---|
5291 | return res;
|
---|
5292 | }
|
---|
5293 |
|
---|
5294 | if ((res = mp_init (&p1)) != MP_OKAY) {
|
---|
5295 | mp_clear(&a1);
|
---|
5296 | return res;
|
---|
5297 | }
|
---|
5298 |
|
---|
5299 | /* divide out larger power of two */
|
---|
5300 | k = mp_cnt_lsb(&a1);
|
---|
5301 | res = mp_div_2d(&a1, k, &a1, NULL);
|
---|
5302 |
|
---|
5303 | if (res == MP_OKAY) {
|
---|
5304 | /* step 4. if e is even set s=1 */
|
---|
5305 | if ((k & 1) == 0) {
|
---|
5306 | s = 1;
|
---|
5307 | } else {
|
---|
5308 | /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
|
---|
5309 | residue = p->dp[0] & 7;
|
---|
5310 |
|
---|
5311 | if (residue == 1 || residue == 7) {
|
---|
5312 | s = 1;
|
---|
5313 | } else if (residue == 3 || residue == 5) {
|
---|
5314 | s = -1;
|
---|
5315 | }
|
---|
5316 | }
|
---|
5317 |
|
---|
5318 | /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
|
---|
5319 | if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
|
---|
5320 | s = -s;
|
---|
5321 | }
|
---|
5322 | }
|
---|
5323 |
|
---|
5324 | if (res == MP_OKAY) {
|
---|
5325 | /* if a1 == 1 we're done */
|
---|
5326 | if (mp_cmp_d (&a1, 1) == MP_EQ) {
|
---|
5327 | *c = s;
|
---|
5328 | } else {
|
---|
5329 | /* n1 = n mod a1 */
|
---|
5330 | res = mp_mod (p, &a1, &p1);
|
---|
5331 | if (res == MP_OKAY)
|
---|
5332 | res = mp_jacobi (&p1, &a1, &r);
|
---|
5333 |
|
---|
5334 | if (res == MP_OKAY)
|
---|
5335 | *c = s * r;
|
---|
5336 | }
|
---|
5337 | }
|
---|
5338 |
|
---|
5339 | /* done */
|
---|
5340 | mp_clear (&p1);
|
---|
5341 | mp_clear (&a1);
|
---|
5342 |
|
---|
5343 | return res;
|
---|
5344 | }
|
---|
5345 |
|
---|
5346 |
|
---|
5347 | int mp_sqrtmod_prime(mp_int* n, mp_int* prime, mp_int* ret)
|
---|
5348 | {
|
---|
5349 | int res, legendre, done = 0;
|
---|
5350 | mp_int t1, C, Q, S, Z, M, T, R, two;
|
---|
5351 | mp_digit i;
|
---|
5352 |
|
---|
5353 | /* first handle the simple cases */
|
---|
5354 | if (mp_cmp_d(n, 0) == MP_EQ) {
|
---|
5355 | mp_zero(ret);
|
---|
5356 | return MP_OKAY;
|
---|
5357 | }
|
---|
5358 | if (mp_cmp_d(prime, 2) == MP_EQ) return MP_VAL; /* prime must be odd */
|
---|
5359 | /* TAO removed
|
---|
5360 | if ((res = mp_jacobi(n, prime, &legendre)) != MP_OKAY) return res;
|
---|
5361 | if (legendre == -1) return MP_VAL; */ /* quadratic non-residue mod prime */
|
---|
5362 |
|
---|
5363 | if ((res = mp_init_multi(&t1, &C, &Q, &S, &Z, &M)) != MP_OKAY)
|
---|
5364 | return res;
|
---|
5365 |
|
---|
5366 | if ((res = mp_init_multi(&T, &R, &two, NULL, NULL, NULL))
|
---|
5367 | != MP_OKAY) {
|
---|
5368 | mp_clear(&t1); mp_clear(&C); mp_clear(&Q); mp_clear(&S); mp_clear(&Z);
|
---|
5369 | mp_clear(&M);
|
---|
5370 | return res;
|
---|
5371 | }
|
---|
5372 |
|
---|
5373 | /* SPECIAL CASE: if prime mod 4 == 3
|
---|
5374 | * compute directly: res = n^(prime+1)/4 mod prime
|
---|
5375 | * Handbook of Applied Cryptography algorithm 3.36
|
---|
5376 | */
|
---|
5377 | res = mp_mod_d(prime, 4, &i);
|
---|
5378 | if (res == MP_OKAY && i == 3) {
|
---|
5379 | res = mp_add_d(prime, 1, &t1);
|
---|
5380 |
|
---|
5381 | if (res == MP_OKAY)
|
---|
5382 | res = mp_div_2(&t1, &t1);
|
---|
5383 | if (res == MP_OKAY)
|
---|
5384 | res = mp_div_2(&t1, &t1);
|
---|
5385 | if (res == MP_OKAY)
|
---|
5386 | res = mp_exptmod(n, &t1, prime, ret);
|
---|
5387 |
|
---|
5388 | done = 1;
|
---|
5389 | }
|
---|
5390 |
|
---|
5391 | /* NOW: TonelliShanks algorithm */
|
---|
5392 |
|
---|
5393 | if (res == MP_OKAY && done == 0) {
|
---|
5394 |
|
---|
5395 | /* factor out powers of 2 from prime-1, defining Q and S
|
---|
5396 | * as: prime-1 = Q*2^S */
|
---|
5397 | res = mp_copy(prime, &Q);
|
---|
5398 | if (res == MP_OKAY)
|
---|
5399 | res = mp_sub_d(&Q, 1, &Q);
|
---|
5400 | /* Q = prime - 1 */
|
---|
5401 | if (res == MP_OKAY)
|
---|
5402 | mp_zero(&S);
|
---|
5403 | /* S = 0 */
|
---|
5404 | while (res == MP_OKAY && mp_iseven(&Q)) {
|
---|
5405 | res = mp_div_2(&Q, &Q);
|
---|
5406 | /* Q = Q / 2 */
|
---|
5407 | if (res == MP_OKAY)
|
---|
5408 | res = mp_add_d(&S, 1, &S);
|
---|
5409 | /* S = S + 1 */
|
---|
5410 | }
|
---|
5411 |
|
---|
5412 | /* find a Z such that the Legendre symbol (Z|prime) == -1 */
|
---|
5413 | if (res == MP_OKAY)
|
---|
5414 | res = mp_set_int(&Z, 2);
|
---|
5415 | /* Z = 2 */
|
---|
5416 | while (res == MP_OKAY) {
|
---|
5417 | res = mp_jacobi(&Z, prime, &legendre);
|
---|
5418 | if (res == MP_OKAY && legendre == -1)
|
---|
5419 | break;
|
---|
5420 | if (res == MP_OKAY)
|
---|
5421 | res = mp_add_d(&Z, 1, &Z);
|
---|
5422 | /* Z = Z + 1 */
|
---|
5423 | }
|
---|
5424 |
|
---|
5425 | if (res == MP_OKAY)
|
---|
5426 | res = mp_exptmod(&Z, &Q, prime, &C);
|
---|
5427 | /* C = Z ^ Q mod prime */
|
---|
5428 | if (res == MP_OKAY)
|
---|
5429 | res = mp_add_d(&Q, 1, &t1);
|
---|
5430 | if (res == MP_OKAY)
|
---|
5431 | res = mp_div_2(&t1, &t1);
|
---|
5432 | /* t1 = (Q + 1) / 2 */
|
---|
5433 | if (res == MP_OKAY)
|
---|
5434 | res = mp_exptmod(n, &t1, prime, &R);
|
---|
5435 | /* R = n ^ ((Q + 1) / 2) mod prime */
|
---|
5436 | if (res == MP_OKAY)
|
---|
5437 | res = mp_exptmod(n, &Q, prime, &T);
|
---|
5438 | /* T = n ^ Q mod prime */
|
---|
5439 | if (res == MP_OKAY)
|
---|
5440 | res = mp_copy(&S, &M);
|
---|
5441 | /* M = S */
|
---|
5442 | if (res == MP_OKAY)
|
---|
5443 | res = mp_set_int(&two, 2);
|
---|
5444 |
|
---|
5445 | while (res == MP_OKAY && done == 0) {
|
---|
5446 | res = mp_copy(&T, &t1);
|
---|
5447 | i = 0;
|
---|
5448 | while (res == MP_OKAY) {
|
---|
5449 | if (mp_cmp_d(&t1, 1) == MP_EQ)
|
---|
5450 | break;
|
---|
5451 | res = mp_exptmod(&t1, &two, prime, &t1);
|
---|
5452 | if (res == MP_OKAY)
|
---|
5453 | i++;
|
---|
5454 | }
|
---|
5455 | if (res == MP_OKAY && i == 0) {
|
---|
5456 | mp_copy(&R, ret);
|
---|
5457 | res = MP_OKAY;
|
---|
5458 | done = 1;
|
---|
5459 | }
|
---|
5460 |
|
---|
5461 | if (done == 0) {
|
---|
5462 | if (res == MP_OKAY)
|
---|
5463 | res = mp_sub_d(&M, i, &t1);
|
---|
5464 | if (res == MP_OKAY)
|
---|
5465 | res = mp_sub_d(&t1, 1, &t1);
|
---|
5466 | if (res == MP_OKAY)
|
---|
5467 | res = mp_exptmod(&two, &t1, prime, &t1);
|
---|
5468 | /* t1 = 2 ^ (M - i - 1) */
|
---|
5469 | if (res == MP_OKAY)
|
---|
5470 | res = mp_exptmod(&C, &t1, prime, &t1);
|
---|
5471 | /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
|
---|
5472 | if (res == MP_OKAY)
|
---|
5473 | res = mp_sqrmod(&t1, prime, &C);
|
---|
5474 | /* C = (t1 * t1) mod prime */
|
---|
5475 | if (res == MP_OKAY)
|
---|
5476 | res = mp_mulmod(&R, &t1, prime, &R);
|
---|
5477 | /* R = (R * t1) mod prime */
|
---|
5478 | if (res == MP_OKAY)
|
---|
5479 | res = mp_mulmod(&T, &C, prime, &T);
|
---|
5480 | /* T = (T * C) mod prime */
|
---|
5481 | if (res == MP_OKAY)
|
---|
5482 | mp_set(&M, i);
|
---|
5483 | /* M = i */
|
---|
5484 | }
|
---|
5485 | }
|
---|
5486 | }
|
---|
5487 |
|
---|
5488 | /* done */
|
---|
5489 | mp_clear(&t1);
|
---|
5490 | mp_clear(&C);
|
---|
5491 | mp_clear(&Q);
|
---|
5492 | mp_clear(&S);
|
---|
5493 | mp_clear(&Z);
|
---|
5494 | mp_clear(&M);
|
---|
5495 | mp_clear(&T);
|
---|
5496 | mp_clear(&R);
|
---|
5497 | mp_clear(&two);
|
---|
5498 |
|
---|
5499 | return res;
|
---|
5500 | }
|
---|
5501 |
|
---|
5502 |
|
---|
5503 | /* export public ECC key in ANSI X9.63 format compressed */
|
---|
5504 | int wc_ecc_export_x963_compressed(ecc_key* key, byte* out, word32* outLen)
|
---|
5505 | {
|
---|
5506 | word32 numlen;
|
---|
5507 | int ret = MP_OKAY;
|
---|
5508 |
|
---|
5509 | if (key == NULL || out == NULL || outLen == NULL)
|
---|
5510 | return ECC_BAD_ARG_E;
|
---|
5511 |
|
---|
5512 | if (wc_ecc_is_valid_idx(key->idx) == 0) {
|
---|
5513 | return ECC_BAD_ARG_E;
|
---|
5514 | }
|
---|
5515 | numlen = key->dp->size;
|
---|
5516 |
|
---|
5517 | if (*outLen < (1 + numlen)) {
|
---|
5518 | *outLen = 1 + numlen;
|
---|
5519 | return BUFFER_E;
|
---|
5520 | }
|
---|
5521 |
|
---|
5522 | /* store first byte */
|
---|
5523 | out[0] = mp_isodd(key->pubkey.y) ? 0x03 : 0x02;
|
---|
5524 |
|
---|
5525 | /* pad and store x */
|
---|
5526 | XMEMSET(out+1, 0, numlen);
|
---|
5527 | ret = mp_to_unsigned_bin(key->pubkey.x,
|
---|
5528 | out+1 + (numlen - mp_unsigned_bin_size(key->pubkey.x)));
|
---|
5529 | *outLen = 1 + numlen;
|
---|
5530 | return ret;
|
---|
5531 | }
|
---|
5532 |
|
---|
5533 |
|
---|
5534 | /* d = a - b (mod c) */
|
---|
5535 | int mp_submod(mp_int* a, mp_int* b, mp_int* c, mp_int* d)
|
---|
5536 | {
|
---|
5537 | int res;
|
---|
5538 | mp_int t;
|
---|
5539 |
|
---|
5540 | if ((res = mp_init (&t)) != MP_OKAY) {
|
---|
5541 | return res;
|
---|
5542 | }
|
---|
5543 |
|
---|
5544 | if ((res = mp_sub (a, b, &t)) != MP_OKAY) {
|
---|
5545 | mp_clear (&t);
|
---|
5546 | return res;
|
---|
5547 | }
|
---|
5548 | res = mp_mod (&t, c, d);
|
---|
5549 | mp_clear (&t);
|
---|
5550 |
|
---|
5551 | return res;
|
---|
5552 | }
|
---|
5553 |
|
---|
5554 |
|
---|
5555 | #endif /* HAVE_COMP_KEY */
|
---|
5556 |
|
---|
5557 | #endif /* HAVE_ECC */
|
---|