[331] | 1 | /*
|
---|
| 2 | * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
|
---|
| 3 | *
|
---|
| 4 | * Licensed under the OpenSSL license (the "License"). You may not use
|
---|
| 5 | * this file except in compliance with the License. You can obtain a copy
|
---|
| 6 | * in the file LICENSE in the source distribution or at
|
---|
| 7 | * https://www.openssl.org/source/license.html
|
---|
| 8 | */
|
---|
| 9 |
|
---|
| 10 | #include <openssl/bn.h>
|
---|
| 11 | #include "internal/cryptlib.h"
|
---|
| 12 | #include "bn_lcl.h"
|
---|
| 13 |
|
---|
| 14 | /* The old slow way */
|
---|
| 15 | #if 0
|
---|
| 16 | int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
|
---|
| 17 | BN_CTX *ctx)
|
---|
| 18 | {
|
---|
| 19 | int i, nm, nd;
|
---|
| 20 | int ret = 0;
|
---|
| 21 | BIGNUM *D;
|
---|
| 22 |
|
---|
| 23 | bn_check_top(m);
|
---|
| 24 | bn_check_top(d);
|
---|
| 25 | if (BN_is_zero(d)) {
|
---|
| 26 | BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
|
---|
| 27 | return (0);
|
---|
| 28 | }
|
---|
| 29 |
|
---|
| 30 | if (BN_ucmp(m, d) < 0) {
|
---|
| 31 | if (rem != NULL) {
|
---|
| 32 | if (BN_copy(rem, m) == NULL)
|
---|
| 33 | return (0);
|
---|
| 34 | }
|
---|
| 35 | if (dv != NULL)
|
---|
| 36 | BN_zero(dv);
|
---|
| 37 | return (1);
|
---|
| 38 | }
|
---|
| 39 |
|
---|
| 40 | BN_CTX_start(ctx);
|
---|
| 41 | D = BN_CTX_get(ctx);
|
---|
| 42 | if (dv == NULL)
|
---|
| 43 | dv = BN_CTX_get(ctx);
|
---|
| 44 | if (rem == NULL)
|
---|
| 45 | rem = BN_CTX_get(ctx);
|
---|
| 46 | if (D == NULL || dv == NULL || rem == NULL)
|
---|
| 47 | goto end;
|
---|
| 48 |
|
---|
| 49 | nd = BN_num_bits(d);
|
---|
| 50 | nm = BN_num_bits(m);
|
---|
| 51 | if (BN_copy(D, d) == NULL)
|
---|
| 52 | goto end;
|
---|
| 53 | if (BN_copy(rem, m) == NULL)
|
---|
| 54 | goto end;
|
---|
| 55 |
|
---|
| 56 | /*
|
---|
| 57 | * The next 2 are needed so we can do a dv->d[0]|=1 later since
|
---|
| 58 | * BN_lshift1 will only work once there is a value :-)
|
---|
| 59 | */
|
---|
| 60 | BN_zero(dv);
|
---|
| 61 | if (bn_wexpand(dv, 1) == NULL)
|
---|
| 62 | goto end;
|
---|
| 63 | dv->top = 1;
|
---|
| 64 |
|
---|
| 65 | if (!BN_lshift(D, D, nm - nd))
|
---|
| 66 | goto end;
|
---|
| 67 | for (i = nm - nd; i >= 0; i--) {
|
---|
| 68 | if (!BN_lshift1(dv, dv))
|
---|
| 69 | goto end;
|
---|
| 70 | if (BN_ucmp(rem, D) >= 0) {
|
---|
| 71 | dv->d[0] |= 1;
|
---|
| 72 | if (!BN_usub(rem, rem, D))
|
---|
| 73 | goto end;
|
---|
| 74 | }
|
---|
| 75 | /* CAN IMPROVE (and have now :=) */
|
---|
| 76 | if (!BN_rshift1(D, D))
|
---|
| 77 | goto end;
|
---|
| 78 | }
|
---|
| 79 | rem->neg = BN_is_zero(rem) ? 0 : m->neg;
|
---|
| 80 | dv->neg = m->neg ^ d->neg;
|
---|
| 81 | ret = 1;
|
---|
| 82 | end:
|
---|
| 83 | BN_CTX_end(ctx);
|
---|
| 84 | return (ret);
|
---|
| 85 | }
|
---|
| 86 |
|
---|
| 87 | #else
|
---|
| 88 |
|
---|
| 89 | # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
|
---|
| 90 | && !defined(PEDANTIC) && !defined(BN_DIV3W)
|
---|
| 91 | # if defined(__GNUC__) && __GNUC__>=2
|
---|
| 92 | # if defined(__i386) || defined (__i386__)
|
---|
| 93 | /*-
|
---|
| 94 | * There were two reasons for implementing this template:
|
---|
| 95 | * - GNU C generates a call to a function (__udivdi3 to be exact)
|
---|
| 96 | * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
|
---|
| 97 | * understand why...);
|
---|
| 98 | * - divl doesn't only calculate quotient, but also leaves
|
---|
| 99 | * remainder in %edx which we can definitely use here:-)
|
---|
| 100 | *
|
---|
| 101 | * <appro@fy.chalmers.se>
|
---|
| 102 | */
|
---|
| 103 | # undef bn_div_words
|
---|
| 104 | # define bn_div_words(n0,n1,d0) \
|
---|
| 105 | ({ asm volatile ( \
|
---|
| 106 | "divl %4" \
|
---|
| 107 | : "=a"(q), "=d"(rem) \
|
---|
| 108 | : "a"(n1), "d"(n0), "r"(d0) \
|
---|
| 109 | : "cc"); \
|
---|
| 110 | q; \
|
---|
| 111 | })
|
---|
| 112 | # define REMAINDER_IS_ALREADY_CALCULATED
|
---|
| 113 | # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
|
---|
| 114 | /*
|
---|
| 115 | * Same story here, but it's 128-bit by 64-bit division. Wow!
|
---|
| 116 | * <appro@fy.chalmers.se>
|
---|
| 117 | */
|
---|
| 118 | # undef bn_div_words
|
---|
| 119 | # define bn_div_words(n0,n1,d0) \
|
---|
| 120 | ({ asm volatile ( \
|
---|
| 121 | "divq %4" \
|
---|
| 122 | : "=a"(q), "=d"(rem) \
|
---|
| 123 | : "a"(n1), "d"(n0), "r"(d0) \
|
---|
| 124 | : "cc"); \
|
---|
| 125 | q; \
|
---|
| 126 | })
|
---|
| 127 | # define REMAINDER_IS_ALREADY_CALCULATED
|
---|
| 128 | # endif /* __<cpu> */
|
---|
| 129 | # endif /* __GNUC__ */
|
---|
| 130 | # endif /* OPENSSL_NO_ASM */
|
---|
| 131 |
|
---|
| 132 | /*-
|
---|
| 133 | * BN_div computes dv := num / divisor, rounding towards
|
---|
| 134 | * zero, and sets up rm such that dv*divisor + rm = num holds.
|
---|
| 135 | * Thus:
|
---|
| 136 | * dv->neg == num->neg ^ divisor->neg (unless the result is zero)
|
---|
| 137 | * rm->neg == num->neg (unless the remainder is zero)
|
---|
| 138 | * If 'dv' or 'rm' is NULL, the respective value is not returned.
|
---|
| 139 | */
|
---|
| 140 | int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
|
---|
| 141 | BN_CTX *ctx)
|
---|
| 142 | {
|
---|
| 143 | int norm_shift, i, loop;
|
---|
| 144 | BIGNUM *tmp, wnum, *snum, *sdiv, *res;
|
---|
| 145 | BN_ULONG *resp, *wnump;
|
---|
| 146 | BN_ULONG d0, d1;
|
---|
| 147 | int num_n, div_n;
|
---|
| 148 | int no_branch = 0;
|
---|
| 149 |
|
---|
| 150 | /*
|
---|
| 151 | * Invalid zero-padding would have particularly bad consequences so don't
|
---|
| 152 | * just rely on bn_check_top() here (bn_check_top() works only for
|
---|
| 153 | * BN_DEBUG builds)
|
---|
| 154 | */
|
---|
| 155 | if ((num->top > 0 && num->d[num->top - 1] == 0) ||
|
---|
| 156 | (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
|
---|
| 157 | BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
|
---|
| 158 | return 0;
|
---|
| 159 | }
|
---|
| 160 |
|
---|
| 161 | bn_check_top(num);
|
---|
| 162 | bn_check_top(divisor);
|
---|
| 163 |
|
---|
| 164 | if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
|
---|
| 165 | || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
|
---|
| 166 | no_branch = 1;
|
---|
| 167 | }
|
---|
| 168 |
|
---|
| 169 | bn_check_top(dv);
|
---|
| 170 | bn_check_top(rm);
|
---|
| 171 | /*- bn_check_top(num); *//*
|
---|
| 172 | * 'num' has been checked already
|
---|
| 173 | */
|
---|
| 174 | /*- bn_check_top(divisor); *//*
|
---|
| 175 | * 'divisor' has been checked already
|
---|
| 176 | */
|
---|
| 177 |
|
---|
| 178 | if (BN_is_zero(divisor)) {
|
---|
| 179 | BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
|
---|
| 180 | return (0);
|
---|
| 181 | }
|
---|
| 182 |
|
---|
| 183 | if (!no_branch && BN_ucmp(num, divisor) < 0) {
|
---|
| 184 | if (rm != NULL) {
|
---|
| 185 | if (BN_copy(rm, num) == NULL)
|
---|
| 186 | return (0);
|
---|
| 187 | }
|
---|
| 188 | if (dv != NULL)
|
---|
| 189 | BN_zero(dv);
|
---|
| 190 | return (1);
|
---|
| 191 | }
|
---|
| 192 |
|
---|
| 193 | BN_CTX_start(ctx);
|
---|
| 194 | tmp = BN_CTX_get(ctx);
|
---|
| 195 | snum = BN_CTX_get(ctx);
|
---|
| 196 | sdiv = BN_CTX_get(ctx);
|
---|
| 197 | if (dv == NULL)
|
---|
| 198 | res = BN_CTX_get(ctx);
|
---|
| 199 | else
|
---|
| 200 | res = dv;
|
---|
| 201 | if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
|
---|
| 202 | goto err;
|
---|
| 203 |
|
---|
| 204 | /* First we normalise the numbers */
|
---|
| 205 | norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
|
---|
| 206 | if (!(BN_lshift(sdiv, divisor, norm_shift)))
|
---|
| 207 | goto err;
|
---|
| 208 | sdiv->neg = 0;
|
---|
| 209 | norm_shift += BN_BITS2;
|
---|
| 210 | if (!(BN_lshift(snum, num, norm_shift)))
|
---|
| 211 | goto err;
|
---|
| 212 | snum->neg = 0;
|
---|
| 213 |
|
---|
| 214 | if (no_branch) {
|
---|
| 215 | /*
|
---|
| 216 | * Since we don't know whether snum is larger than sdiv, we pad snum
|
---|
| 217 | * with enough zeroes without changing its value.
|
---|
| 218 | */
|
---|
| 219 | if (snum->top <= sdiv->top + 1) {
|
---|
| 220 | if (bn_wexpand(snum, sdiv->top + 2) == NULL)
|
---|
| 221 | goto err;
|
---|
| 222 | for (i = snum->top; i < sdiv->top + 2; i++)
|
---|
| 223 | snum->d[i] = 0;
|
---|
| 224 | snum->top = sdiv->top + 2;
|
---|
| 225 | } else {
|
---|
| 226 | if (bn_wexpand(snum, snum->top + 1) == NULL)
|
---|
| 227 | goto err;
|
---|
| 228 | snum->d[snum->top] = 0;
|
---|
| 229 | snum->top++;
|
---|
| 230 | }
|
---|
| 231 | }
|
---|
| 232 |
|
---|
| 233 | div_n = sdiv->top;
|
---|
| 234 | num_n = snum->top;
|
---|
| 235 | loop = num_n - div_n;
|
---|
| 236 | /*
|
---|
| 237 | * Lets setup a 'window' into snum This is the part that corresponds to
|
---|
| 238 | * the current 'area' being divided
|
---|
| 239 | */
|
---|
| 240 | wnum.neg = 0;
|
---|
| 241 | wnum.d = &(snum->d[loop]);
|
---|
| 242 | wnum.top = div_n;
|
---|
| 243 | /*
|
---|
| 244 | * only needed when BN_ucmp messes up the values between top and max
|
---|
| 245 | */
|
---|
| 246 | wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
|
---|
| 247 |
|
---|
| 248 | /* Get the top 2 words of sdiv */
|
---|
| 249 | /* div_n=sdiv->top; */
|
---|
| 250 | d0 = sdiv->d[div_n - 1];
|
---|
| 251 | d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
|
---|
| 252 |
|
---|
| 253 | /* pointer to the 'top' of snum */
|
---|
| 254 | wnump = &(snum->d[num_n - 1]);
|
---|
| 255 |
|
---|
| 256 | /* Setup to 'res' */
|
---|
| 257 | if (!bn_wexpand(res, (loop + 1)))
|
---|
| 258 | goto err;
|
---|
| 259 | res->neg = (num->neg ^ divisor->neg);
|
---|
| 260 | res->top = loop - no_branch;
|
---|
| 261 | resp = &(res->d[loop - 1]);
|
---|
| 262 |
|
---|
| 263 | /* space for temp */
|
---|
| 264 | if (!bn_wexpand(tmp, (div_n + 1)))
|
---|
| 265 | goto err;
|
---|
| 266 |
|
---|
| 267 | if (!no_branch) {
|
---|
| 268 | if (BN_ucmp(&wnum, sdiv) >= 0) {
|
---|
| 269 | /*
|
---|
| 270 | * If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
|
---|
| 271 | * the const bignum arguments => clean the values between top and
|
---|
| 272 | * max again
|
---|
| 273 | */
|
---|
| 274 | bn_clear_top2max(&wnum);
|
---|
| 275 | bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
|
---|
| 276 | *resp = 1;
|
---|
| 277 | } else
|
---|
| 278 | res->top--;
|
---|
| 279 | }
|
---|
| 280 |
|
---|
| 281 | /* Increase the resp pointer so that we never create an invalid pointer. */
|
---|
| 282 | resp++;
|
---|
| 283 |
|
---|
| 284 | /*
|
---|
| 285 | * if res->top == 0 then clear the neg value otherwise decrease the resp
|
---|
| 286 | * pointer
|
---|
| 287 | */
|
---|
| 288 | if (res->top == 0)
|
---|
| 289 | res->neg = 0;
|
---|
| 290 | else
|
---|
| 291 | resp--;
|
---|
| 292 |
|
---|
| 293 | for (i = 0; i < loop - 1; i++, wnump--) {
|
---|
| 294 | BN_ULONG q, l0;
|
---|
| 295 | /*
|
---|
| 296 | * the first part of the loop uses the top two words of snum and sdiv
|
---|
| 297 | * to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
|
---|
| 298 | */
|
---|
| 299 | # if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
|
---|
| 300 | BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
|
---|
| 301 | q = bn_div_3_words(wnump, d1, d0);
|
---|
| 302 | # else
|
---|
| 303 | BN_ULONG n0, n1, rem = 0;
|
---|
| 304 |
|
---|
| 305 | n0 = wnump[0];
|
---|
| 306 | n1 = wnump[-1];
|
---|
| 307 | if (n0 == d0)
|
---|
| 308 | q = BN_MASK2;
|
---|
| 309 | else { /* n0 < d0 */
|
---|
| 310 |
|
---|
| 311 | # ifdef BN_LLONG
|
---|
| 312 | BN_ULLONG t2;
|
---|
| 313 |
|
---|
| 314 | # if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
|
---|
| 315 | q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
|
---|
| 316 | # else
|
---|
| 317 | q = bn_div_words(n0, n1, d0);
|
---|
| 318 | # endif
|
---|
| 319 |
|
---|
| 320 | # ifndef REMAINDER_IS_ALREADY_CALCULATED
|
---|
| 321 | /*
|
---|
| 322 | * rem doesn't have to be BN_ULLONG. The least we
|
---|
| 323 | * know it's less that d0, isn't it?
|
---|
| 324 | */
|
---|
| 325 | rem = (n1 - q * d0) & BN_MASK2;
|
---|
| 326 | # endif
|
---|
| 327 | t2 = (BN_ULLONG) d1 *q;
|
---|
| 328 |
|
---|
| 329 | for (;;) {
|
---|
| 330 | if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))
|
---|
| 331 | break;
|
---|
| 332 | q--;
|
---|
| 333 | rem += d0;
|
---|
| 334 | if (rem < d0)
|
---|
| 335 | break; /* don't let rem overflow */
|
---|
| 336 | t2 -= d1;
|
---|
| 337 | }
|
---|
| 338 | # else /* !BN_LLONG */
|
---|
| 339 | BN_ULONG t2l, t2h;
|
---|
| 340 |
|
---|
| 341 | q = bn_div_words(n0, n1, d0);
|
---|
| 342 | # ifndef REMAINDER_IS_ALREADY_CALCULATED
|
---|
| 343 | rem = (n1 - q * d0) & BN_MASK2;
|
---|
| 344 | # endif
|
---|
| 345 |
|
---|
| 346 | # if defined(BN_UMULT_LOHI)
|
---|
| 347 | BN_UMULT_LOHI(t2l, t2h, d1, q);
|
---|
| 348 | # elif defined(BN_UMULT_HIGH)
|
---|
| 349 | t2l = d1 * q;
|
---|
| 350 | t2h = BN_UMULT_HIGH(d1, q);
|
---|
| 351 | # else
|
---|
| 352 | {
|
---|
| 353 | BN_ULONG ql, qh;
|
---|
| 354 | t2l = LBITS(d1);
|
---|
| 355 | t2h = HBITS(d1);
|
---|
| 356 | ql = LBITS(q);
|
---|
| 357 | qh = HBITS(q);
|
---|
| 358 | mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
|
---|
| 359 | }
|
---|
| 360 | # endif
|
---|
| 361 |
|
---|
| 362 | for (;;) {
|
---|
| 363 | if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
|
---|
| 364 | break;
|
---|
| 365 | q--;
|
---|
| 366 | rem += d0;
|
---|
| 367 | if (rem < d0)
|
---|
| 368 | break; /* don't let rem overflow */
|
---|
| 369 | if (t2l < d1)
|
---|
| 370 | t2h--;
|
---|
| 371 | t2l -= d1;
|
---|
| 372 | }
|
---|
| 373 | # endif /* !BN_LLONG */
|
---|
| 374 | }
|
---|
| 375 | # endif /* !BN_DIV3W */
|
---|
| 376 |
|
---|
| 377 | l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
|
---|
| 378 | tmp->d[div_n] = l0;
|
---|
| 379 | wnum.d--;
|
---|
| 380 | /*
|
---|
| 381 | * ingore top values of the bignums just sub the two BN_ULONG arrays
|
---|
| 382 | * with bn_sub_words
|
---|
| 383 | */
|
---|
| 384 | if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
|
---|
| 385 | /*
|
---|
| 386 | * Note: As we have considered only the leading two BN_ULONGs in
|
---|
| 387 | * the calculation of q, sdiv * q might be greater than wnum (but
|
---|
| 388 | * then (q-1) * sdiv is less or equal than wnum)
|
---|
| 389 | */
|
---|
| 390 | q--;
|
---|
| 391 | if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
|
---|
| 392 | /*
|
---|
| 393 | * we can't have an overflow here (assuming that q != 0, but
|
---|
| 394 | * if q == 0 then tmp is zero anyway)
|
---|
| 395 | */
|
---|
| 396 | (*wnump)++;
|
---|
| 397 | }
|
---|
| 398 | /* store part of the result */
|
---|
| 399 | resp--;
|
---|
| 400 | *resp = q;
|
---|
| 401 | }
|
---|
| 402 | bn_correct_top(snum);
|
---|
| 403 | if (rm != NULL) {
|
---|
| 404 | /*
|
---|
| 405 | * Keep a copy of the neg flag in num because if rm==num BN_rshift()
|
---|
| 406 | * will overwrite it.
|
---|
| 407 | */
|
---|
| 408 | int neg = num->neg;
|
---|
| 409 | BN_rshift(rm, snum, norm_shift);
|
---|
| 410 | if (!BN_is_zero(rm))
|
---|
| 411 | rm->neg = neg;
|
---|
| 412 | bn_check_top(rm);
|
---|
| 413 | }
|
---|
| 414 | if (no_branch)
|
---|
| 415 | bn_correct_top(res);
|
---|
| 416 | BN_CTX_end(ctx);
|
---|
| 417 | return (1);
|
---|
| 418 | err:
|
---|
| 419 | bn_check_top(rm);
|
---|
| 420 | BN_CTX_end(ctx);
|
---|
| 421 | return (0);
|
---|
| 422 | }
|
---|
| 423 | #endif
|
---|