[331] | 1 | /*
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| 2 | * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
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| 3 | *
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| 4 | * Licensed under the OpenSSL license (the "License"). You may not use
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| 5 | * this file except in compliance with the License. You can obtain a copy
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| 6 | * in the file LICENSE in the source distribution or at
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| 7 | * https://www.openssl.org/source/license.html
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| 8 | */
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| 9 |
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| 10 | #include "internal/cryptlib.h"
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| 11 | #include "bn_lcl.h"
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| 12 |
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| 13 | /* r must not be a */
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| 14 | /*
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| 15 | * I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96
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| 16 | */
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| 17 | int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
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| 18 | {
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| 19 | int max, al;
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| 20 | int ret = 0;
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| 21 | BIGNUM *tmp, *rr;
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| 22 |
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| 23 | bn_check_top(a);
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| 24 |
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| 25 | al = a->top;
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| 26 | if (al <= 0) {
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| 27 | r->top = 0;
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| 28 | r->neg = 0;
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| 29 | return 1;
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| 30 | }
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| 31 |
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| 32 | BN_CTX_start(ctx);
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| 33 | rr = (a != r) ? r : BN_CTX_get(ctx);
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| 34 | tmp = BN_CTX_get(ctx);
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| 35 | if (!rr || !tmp)
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| 36 | goto err;
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| 37 |
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| 38 | max = 2 * al; /* Non-zero (from above) */
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| 39 | if (bn_wexpand(rr, max) == NULL)
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| 40 | goto err;
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| 41 |
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| 42 | if (al == 4) {
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| 43 | #ifndef BN_SQR_COMBA
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| 44 | BN_ULONG t[8];
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| 45 | bn_sqr_normal(rr->d, a->d, 4, t);
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| 46 | #else
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| 47 | bn_sqr_comba4(rr->d, a->d);
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| 48 | #endif
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| 49 | } else if (al == 8) {
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| 50 | #ifndef BN_SQR_COMBA
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| 51 | BN_ULONG t[16];
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| 52 | bn_sqr_normal(rr->d, a->d, 8, t);
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| 53 | #else
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| 54 | bn_sqr_comba8(rr->d, a->d);
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| 55 | #endif
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| 56 | } else {
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| 57 | #if defined(BN_RECURSION)
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| 58 | if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
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| 59 | BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
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| 60 | bn_sqr_normal(rr->d, a->d, al, t);
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| 61 | } else {
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| 62 | int j, k;
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| 63 |
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| 64 | j = BN_num_bits_word((BN_ULONG)al);
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| 65 | j = 1 << (j - 1);
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| 66 | k = j + j;
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| 67 | if (al == j) {
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| 68 | if (bn_wexpand(tmp, k * 2) == NULL)
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| 69 | goto err;
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| 70 | bn_sqr_recursive(rr->d, a->d, al, tmp->d);
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| 71 | } else {
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| 72 | if (bn_wexpand(tmp, max) == NULL)
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| 73 | goto err;
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| 74 | bn_sqr_normal(rr->d, a->d, al, tmp->d);
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| 75 | }
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| 76 | }
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| 77 | #else
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| 78 | if (bn_wexpand(tmp, max) == NULL)
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| 79 | goto err;
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| 80 | bn_sqr_normal(rr->d, a->d, al, tmp->d);
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| 81 | #endif
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| 82 | }
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| 83 |
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| 84 | rr->neg = 0;
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| 85 | /*
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| 86 | * If the most-significant half of the top word of 'a' is zero, then the
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| 87 | * square of 'a' will max-1 words.
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| 88 | */
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| 89 | if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l))
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| 90 | rr->top = max - 1;
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| 91 | else
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| 92 | rr->top = max;
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| 93 | if (r != rr && BN_copy(r, rr) == NULL)
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| 94 | goto err;
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| 95 |
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| 96 | ret = 1;
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| 97 | err:
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| 98 | bn_check_top(rr);
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| 99 | bn_check_top(tmp);
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| 100 | BN_CTX_end(ctx);
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| 101 | return (ret);
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| 102 | }
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| 103 |
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| 104 | /* tmp must have 2*n words */
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| 105 | void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp)
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| 106 | {
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| 107 | int i, j, max;
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| 108 | const BN_ULONG *ap;
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| 109 | BN_ULONG *rp;
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| 110 |
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| 111 | max = n * 2;
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| 112 | ap = a;
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| 113 | rp = r;
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| 114 | rp[0] = rp[max - 1] = 0;
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| 115 | rp++;
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| 116 | j = n;
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| 117 |
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| 118 | if (--j > 0) {
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| 119 | ap++;
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| 120 | rp[j] = bn_mul_words(rp, ap, j, ap[-1]);
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| 121 | rp += 2;
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| 122 | }
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| 123 |
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| 124 | for (i = n - 2; i > 0; i--) {
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| 125 | j--;
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| 126 | ap++;
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| 127 | rp[j] = bn_mul_add_words(rp, ap, j, ap[-1]);
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| 128 | rp += 2;
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| 129 | }
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| 130 |
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| 131 | bn_add_words(r, r, r, max);
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| 132 |
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| 133 | /* There will not be a carry */
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| 134 |
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| 135 | bn_sqr_words(tmp, a, n);
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| 136 |
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| 137 | bn_add_words(r, r, tmp, max);
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| 138 | }
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| 139 |
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| 140 | #ifdef BN_RECURSION
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| 141 | /*-
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| 142 | * r is 2*n words in size,
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| 143 | * a and b are both n words in size. (There's not actually a 'b' here ...)
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| 144 | * n must be a power of 2.
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| 145 | * We multiply and return the result.
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| 146 | * t must be 2*n words in size
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| 147 | * We calculate
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| 148 | * a[0]*b[0]
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| 149 | * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
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| 150 | * a[1]*b[1]
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| 151 | */
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| 152 | void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t)
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| 153 | {
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| 154 | int n = n2 / 2;
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| 155 | int zero, c1;
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| 156 | BN_ULONG ln, lo, *p;
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| 157 |
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| 158 | if (n2 == 4) {
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| 159 | # ifndef BN_SQR_COMBA
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| 160 | bn_sqr_normal(r, a, 4, t);
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| 161 | # else
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| 162 | bn_sqr_comba4(r, a);
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| 163 | # endif
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| 164 | return;
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| 165 | } else if (n2 == 8) {
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| 166 | # ifndef BN_SQR_COMBA
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| 167 | bn_sqr_normal(r, a, 8, t);
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| 168 | # else
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| 169 | bn_sqr_comba8(r, a);
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| 170 | # endif
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| 171 | return;
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| 172 | }
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| 173 | if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
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| 174 | bn_sqr_normal(r, a, n2, t);
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| 175 | return;
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| 176 | }
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| 177 | /* r=(a[0]-a[1])*(a[1]-a[0]) */
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| 178 | c1 = bn_cmp_words(a, &(a[n]), n);
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| 179 | zero = 0;
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| 180 | if (c1 > 0)
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| 181 | bn_sub_words(t, a, &(a[n]), n);
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| 182 | else if (c1 < 0)
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| 183 | bn_sub_words(t, &(a[n]), a, n);
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| 184 | else
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| 185 | zero = 1;
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| 186 |
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| 187 | /* The result will always be negative unless it is zero */
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| 188 | p = &(t[n2 * 2]);
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| 189 |
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| 190 | if (!zero)
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| 191 | bn_sqr_recursive(&(t[n2]), t, n, p);
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| 192 | else
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| 193 | memset(&t[n2], 0, sizeof(*t) * n2);
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| 194 | bn_sqr_recursive(r, a, n, p);
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| 195 | bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);
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| 196 |
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| 197 | /*-
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| 198 | * t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
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| 199 | * r[10] holds (a[0]*b[0])
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| 200 | * r[32] holds (b[1]*b[1])
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| 201 | */
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| 202 |
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| 203 | c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
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| 204 |
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| 205 | /* t[32] is negative */
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| 206 | c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
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| 207 |
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| 208 | /*-
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| 209 | * t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
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| 210 | * r[10] holds (a[0]*a[0])
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| 211 | * r[32] holds (a[1]*a[1])
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| 212 | * c1 holds the carry bits
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| 213 | */
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| 214 | c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
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| 215 | if (c1) {
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| 216 | p = &(r[n + n2]);
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| 217 | lo = *p;
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| 218 | ln = (lo + c1) & BN_MASK2;
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| 219 | *p = ln;
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| 220 |
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| 221 | /*
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| 222 | * The overflow will stop before we over write words we should not
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| 223 | * overwrite
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| 224 | */
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| 225 | if (ln < (BN_ULONG)c1) {
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| 226 | do {
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| 227 | p++;
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| 228 | lo = *p;
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| 229 | ln = (lo + 1) & BN_MASK2;
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| 230 | *p = ln;
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| 231 | } while (ln == 0);
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| 232 | }
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| 233 | }
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| 234 | }
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| 235 | #endif
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