2 * Copyright 2002-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
14 #include "internal/cryptlib.h"
17 #ifndef OPENSSL_NO_EC2M
20 * Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should
23 # define MAX_ITERATIONS 50
25 # define SQR_nibble(w) ((((w) & 8) << 3) \
31 /* Platform-specific macros to accelerate squaring. */
32 # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
34 SQR_nibble((w) >> 60) << 56 | SQR_nibble((w) >> 56) << 48 | \
35 SQR_nibble((w) >> 52) << 40 | SQR_nibble((w) >> 48) << 32 | \
36 SQR_nibble((w) >> 44) << 24 | SQR_nibble((w) >> 40) << 16 | \
37 SQR_nibble((w) >> 36) << 8 | SQR_nibble((w) >> 32)
39 SQR_nibble((w) >> 28) << 56 | SQR_nibble((w) >> 24) << 48 | \
40 SQR_nibble((w) >> 20) << 40 | SQR_nibble((w) >> 16) << 32 | \
41 SQR_nibble((w) >> 12) << 24 | SQR_nibble((w) >> 8) << 16 | \
42 SQR_nibble((w) >> 4) << 8 | SQR_nibble((w) )
44 # ifdef THIRTY_TWO_BIT
46 SQR_nibble((w) >> 28) << 24 | SQR_nibble((w) >> 24) << 16 | \
47 SQR_nibble((w) >> 20) << 8 | SQR_nibble((w) >> 16)
49 SQR_nibble((w) >> 12) << 24 | SQR_nibble((w) >> 8) << 16 | \
50 SQR_nibble((w) >> 4) << 8 | SQR_nibble((w) )
53 # if !defined(OPENSSL_BN_ASM_GF2m)
55 * Product of two polynomials a, b each with degree < BN_BITS2 - 1, result is
56 * a polynomial r with degree < 2 * BN_BITS - 1 The caller MUST ensure that
57 * the variables have the right amount of space allocated.
59 # ifdef THIRTY_TWO_BIT
60 static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
63 register BN_ULONG h, l, s;
64 BN_ULONG tab[8], top2b = a >> 30;
65 register BN_ULONG a1, a2, a4;
67 a1 = a & (0x3FFFFFFF);
78 tab[7] = a1 ^ a2 ^ a4;
82 s = tab[b >> 3 & 0x7];
85 s = tab[b >> 6 & 0x7];
88 s = tab[b >> 9 & 0x7];
91 s = tab[b >> 12 & 0x7];
94 s = tab[b >> 15 & 0x7];
97 s = tab[b >> 18 & 0x7];
100 s = tab[b >> 21 & 0x7];
103 s = tab[b >> 24 & 0x7];
106 s = tab[b >> 27 & 0x7];
113 /* compensate for the top two bits of a */
128 # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
129 static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
132 register BN_ULONG h, l, s;
133 BN_ULONG tab[16], top3b = a >> 61;
134 register BN_ULONG a1, a2, a4, a8;
136 a1 = a & (0x1FFFFFFFFFFFFFFFULL);
148 tab[7] = a1 ^ a2 ^ a4;
152 tab[11] = a1 ^ a2 ^ a8;
154 tab[13] = a1 ^ a4 ^ a8;
155 tab[14] = a2 ^ a4 ^ a8;
156 tab[15] = a1 ^ a2 ^ a4 ^ a8;
160 s = tab[b >> 4 & 0xF];
163 s = tab[b >> 8 & 0xF];
166 s = tab[b >> 12 & 0xF];
169 s = tab[b >> 16 & 0xF];
172 s = tab[b >> 20 & 0xF];
175 s = tab[b >> 24 & 0xF];
178 s = tab[b >> 28 & 0xF];
181 s = tab[b >> 32 & 0xF];
184 s = tab[b >> 36 & 0xF];
187 s = tab[b >> 40 & 0xF];
190 s = tab[b >> 44 & 0xF];
193 s = tab[b >> 48 & 0xF];
196 s = tab[b >> 52 & 0xF];
199 s = tab[b >> 56 & 0xF];
206 /* compensate for the top three bits of a */
227 * Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
228 * result is a polynomial r with degree < 4 * BN_BITS2 - 1 The caller MUST
229 * ensure that the variables have the right amount of space allocated.
231 static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0,
232 const BN_ULONG b1, const BN_ULONG b0)
235 /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
236 bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1);
237 bn_GF2m_mul_1x1(r + 1, r, a0, b0);
238 bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
239 /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
240 r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */
241 r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */
244 void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1,
249 * Add polynomials a and b and store result in r; r could be a or b, a and b
250 * could be equal; r is the bitwise XOR of a and b.
252 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
255 const BIGNUM *at, *bt;
260 if (a->top < b->top) {
268 if (bn_wexpand(r, at->top) == NULL)
271 for (i = 0; i < bt->top; i++) {
272 r->d[i] = at->d[i] ^ bt->d[i];
274 for (; i < at->top; i++) {
285 * Some functions allow for representation of the irreducible polynomials
286 * as an int[], say p. The irreducible f(t) is then of the form:
287 * t^p[0] + t^p[1] + ... + t^p[k]
288 * where m = p[0] > p[1] > ... > p[k] = 0.
291 /* Performs modular reduction of a and store result in r. r could be a. */
292 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[])
301 /* reduction mod 1 => return 0 */
307 * Since the algorithm does reduction in the r value, if a != r, copy the
308 * contents of a into r so we can do reduction in r.
311 if (!bn_wexpand(r, a->top))
313 for (j = 0; j < a->top; j++) {
320 /* start reduction */
321 dN = p[0] / BN_BITS2;
322 for (j = r->top - 1; j > dN;) {
330 for (k = 1; p[k] != 0; k++) {
331 /* reducing component t^p[k] */
336 z[j - n] ^= (zz >> d0);
338 z[j - n - 1] ^= (zz << d1);
341 /* reducing component t^0 */
343 d0 = p[0] % BN_BITS2;
345 z[j - n] ^= (zz >> d0);
347 z[j - n - 1] ^= (zz << d1);
350 /* final round of reduction */
353 d0 = p[0] % BN_BITS2;
359 /* clear up the top d1 bits */
361 z[dN] = (z[dN] << d1) >> d1;
364 z[0] ^= zz; /* reduction t^0 component */
366 for (k = 1; p[k] != 0; k++) {
369 /* reducing component t^p[k] */
371 d0 = p[k] % BN_BITS2;
374 if (d0 && (tmp_ulong = zz >> d1))
375 z[n + 1] ^= tmp_ulong;
385 * Performs modular reduction of a by p and store result in r. r could be a.
386 * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
387 * function is only provided for convenience; for best performance, use the
388 * BN_GF2m_mod_arr function.
390 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)
396 ret = BN_GF2m_poly2arr(p, arr, OSSL_NELEM(arr));
397 if (!ret || ret > (int)OSSL_NELEM(arr)) {
398 BNerr(BN_F_BN_GF2M_MOD, BN_R_INVALID_LENGTH);
401 ret = BN_GF2m_mod_arr(r, a, arr);
407 * Compute the product of two polynomials a and b, reduce modulo p, and store
408 * the result in r. r could be a or b; a could be b.
410 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
411 const int p[], BN_CTX *ctx)
413 int zlen, i, j, k, ret = 0;
415 BN_ULONG x1, x0, y1, y0, zz[4];
421 return BN_GF2m_mod_sqr_arr(r, a, p, ctx);
425 if ((s = BN_CTX_get(ctx)) == NULL)
428 zlen = a->top + b->top + 4;
429 if (!bn_wexpand(s, zlen))
433 for (i = 0; i < zlen; i++)
436 for (j = 0; j < b->top; j += 2) {
438 y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1];
439 for (i = 0; i < a->top; i += 2) {
441 x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1];
442 bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);
443 for (k = 0; k < 4; k++)
444 s->d[i + j + k] ^= zz[k];
449 if (BN_GF2m_mod_arr(r, s, p))
459 * Compute the product of two polynomials a and b, reduce modulo p, and store
460 * the result in r. r could be a or b; a could equal b. This function calls
461 * down to the BN_GF2m_mod_mul_arr implementation; this wrapper function is
462 * only provided for convenience; for best performance, use the
463 * BN_GF2m_mod_mul_arr function.
465 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
466 const BIGNUM *p, BN_CTX *ctx)
469 const int max = BN_num_bits(p) + 1;
474 if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
476 ret = BN_GF2m_poly2arr(p, arr, max);
477 if (!ret || ret > max) {
478 BNerr(BN_F_BN_GF2M_MOD_MUL, BN_R_INVALID_LENGTH);
481 ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);
488 /* Square a, reduce the result mod p, and store it in a. r could be a. */
489 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
497 if ((s = BN_CTX_get(ctx)) == NULL)
499 if (!bn_wexpand(s, 2 * a->top))
502 for (i = a->top - 1; i >= 0; i--) {
503 s->d[2 * i + 1] = SQR1(a->d[i]);
504 s->d[2 * i] = SQR0(a->d[i]);
509 if (!BN_GF2m_mod_arr(r, s, p))
519 * Square a, reduce the result mod p, and store it in a. r could be a. This
520 * function calls down to the BN_GF2m_mod_sqr_arr implementation; this
521 * wrapper function is only provided for convenience; for best performance,
522 * use the BN_GF2m_mod_sqr_arr function.
524 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
527 const int max = BN_num_bits(p) + 1;
532 if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
534 ret = BN_GF2m_poly2arr(p, arr, max);
535 if (!ret || ret > max) {
536 BNerr(BN_F_BN_GF2M_MOD_SQR, BN_R_INVALID_LENGTH);
539 ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
547 * Invert a, reduce modulo p, and store the result in r. r could be a. Uses
548 * Modified Almost Inverse Algorithm (Algorithm 10) from Hankerson, D.,
549 * Hernandez, J.L., and Menezes, A. "Software Implementation of Elliptic
550 * Curve Cryptography Over Binary Fields".
552 static int BN_GF2m_mod_inv_vartime(BIGNUM *r, const BIGNUM *a,
553 const BIGNUM *p, BN_CTX *ctx)
555 BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp;
570 if (!BN_GF2m_mod(u, a, p))
582 while (!BN_is_odd(u)) {
585 if (!BN_rshift1(u, u))
588 if (!BN_GF2m_add(b, b, p))
591 if (!BN_rshift1(b, b))
595 if (BN_abs_is_word(u, 1))
598 if (BN_num_bits(u) < BN_num_bits(v)) {
607 if (!BN_GF2m_add(u, u, v))
609 if (!BN_GF2m_add(b, b, c))
615 int ubits = BN_num_bits(u);
616 int vbits = BN_num_bits(v); /* v is copy of p */
618 BN_ULONG *udp, *bdp, *vdp, *cdp;
620 if (!bn_wexpand(u, top))
623 for (i = u->top; i < top; i++)
626 if (!bn_wexpand(b, top))
630 for (i = 1; i < top; i++)
633 if (!bn_wexpand(c, top))
636 for (i = 0; i < top; i++)
639 vdp = v->d; /* It pays off to "cache" *->d pointers,
640 * because it allows optimizer to be more
641 * aggressive. But we don't have to "cache"
642 * p->d, because *p is declared 'const'... */
644 while (ubits && !(udp[0] & 1)) {
645 BN_ULONG u0, u1, b0, b1, mask;
649 mask = (BN_ULONG)0 - (b0 & 1);
650 b0 ^= p->d[0] & mask;
651 for (i = 0; i < top - 1; i++) {
653 udp[i] = ((u0 >> 1) | (u1 << (BN_BITS2 - 1))) & BN_MASK2;
655 b1 = bdp[i + 1] ^ (p->d[i + 1] & mask);
656 bdp[i] = ((b0 >> 1) | (b1 << (BN_BITS2 - 1))) & BN_MASK2;
664 if (ubits <= BN_BITS2) {
665 if (udp[0] == 0) /* poly was reducible */
686 for (i = 0; i < top; i++) {
690 if (ubits == vbits) {
692 int utop = (ubits - 1) / BN_BITS2;
694 while ((ul = udp[utop]) == 0 && utop)
696 ubits = utop * BN_BITS2 + BN_num_bits_word(ul);
709 # ifdef BN_DEBUG /* BN_CTX_end would complain about the
720 * Wrapper for BN_GF2m_mod_inv_vartime that blinds the input before calling.
721 * This is not constant time.
722 * But it does eliminate first order deduction on the input.
724 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
730 if ((b = BN_CTX_get(ctx)) == NULL)
733 /* generate blinding value */
735 if (!BN_priv_rand(b, BN_num_bits(p) - 1,
736 BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY))
738 } while (BN_is_zero(b));
741 if (!BN_GF2m_mod_mul(r, a, b, p, ctx))
745 if (!BN_GF2m_mod_inv_vartime(r, r, p, ctx))
748 /* r := b/(a * b) = 1/a */
749 if (!BN_GF2m_mod_mul(r, r, b, p, ctx))
760 * Invert xx, reduce modulo p, and store the result in r. r could be xx.
761 * This function calls down to the BN_GF2m_mod_inv implementation; this
762 * wrapper function is only provided for convenience; for best performance,
763 * use the BN_GF2m_mod_inv function.
765 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[],
773 if ((field = BN_CTX_get(ctx)) == NULL)
775 if (!BN_GF2m_arr2poly(p, field))
778 ret = BN_GF2m_mod_inv(r, xx, field, ctx);
787 * Divide y by x, reduce modulo p, and store the result in r. r could be x
788 * or y, x could equal y.
790 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x,
791 const BIGNUM *p, BN_CTX *ctx)
801 xinv = BN_CTX_get(ctx);
805 if (!BN_GF2m_mod_inv(xinv, x, p, ctx))
807 if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx))
818 * Divide yy by xx, reduce modulo p, and store the result in r. r could be xx
819 * * or yy, xx could equal yy. This function calls down to the
820 * BN_GF2m_mod_div implementation; this wrapper function is only provided for
821 * convenience; for best performance, use the BN_GF2m_mod_div function.
823 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx,
824 const int p[], BN_CTX *ctx)
833 if ((field = BN_CTX_get(ctx)) == NULL)
835 if (!BN_GF2m_arr2poly(p, field))
838 ret = BN_GF2m_mod_div(r, yy, xx, field, ctx);
847 * Compute the bth power of a, reduce modulo p, and store the result in r. r
848 * could be a. Uses simple square-and-multiply algorithm A.5.1 from IEEE
851 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
852 const int p[], BN_CTX *ctx)
863 if (BN_abs_is_word(b, 1))
864 return (BN_copy(r, a) != NULL);
867 if ((u = BN_CTX_get(ctx)) == NULL)
870 if (!BN_GF2m_mod_arr(u, a, p))
873 n = BN_num_bits(b) - 1;
874 for (i = n - 1; i >= 0; i--) {
875 if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx))
877 if (BN_is_bit_set(b, i)) {
878 if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx))
892 * Compute the bth power of a, reduce modulo p, and store the result in r. r
893 * could be a. This function calls down to the BN_GF2m_mod_exp_arr
894 * implementation; this wrapper function is only provided for convenience;
895 * for best performance, use the BN_GF2m_mod_exp_arr function.
897 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
898 const BIGNUM *p, BN_CTX *ctx)
901 const int max = BN_num_bits(p) + 1;
906 if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
908 ret = BN_GF2m_poly2arr(p, arr, max);
909 if (!ret || ret > max) {
910 BNerr(BN_F_BN_GF2M_MOD_EXP, BN_R_INVALID_LENGTH);
913 ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);
921 * Compute the square root of a, reduce modulo p, and store the result in r.
922 * r could be a. Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
924 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[],
933 /* reduction mod 1 => return 0 */
939 if ((u = BN_CTX_get(ctx)) == NULL)
942 if (!BN_set_bit(u, p[0] - 1))
944 ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
953 * Compute the square root of a, reduce modulo p, and store the result in r.
954 * r could be a. This function calls down to the BN_GF2m_mod_sqrt_arr
955 * implementation; this wrapper function is only provided for convenience;
956 * for best performance, use the BN_GF2m_mod_sqrt_arr function.
958 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
961 const int max = BN_num_bits(p) + 1;
965 if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
967 ret = BN_GF2m_poly2arr(p, arr, max);
968 if (!ret || ret > max) {
969 BNerr(BN_F_BN_GF2M_MOD_SQRT, BN_R_INVALID_LENGTH);
972 ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
980 * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
981 * 0. Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
983 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[],
986 int ret = 0, count = 0, j;
987 BIGNUM *a, *z, *rho, *w, *w2, *tmp;
992 /* reduction mod 1 => return 0 */
1000 w = BN_CTX_get(ctx);
1004 if (!BN_GF2m_mod_arr(a, a_, p))
1007 if (BN_is_zero(a)) {
1013 if (p[0] & 0x1) { /* m is odd */
1014 /* compute half-trace of a */
1017 for (j = 1; j <= (p[0] - 1) / 2; j++) {
1018 if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
1020 if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
1022 if (!BN_GF2m_add(z, z, a))
1026 } else { /* m is even */
1028 rho = BN_CTX_get(ctx);
1029 w2 = BN_CTX_get(ctx);
1030 tmp = BN_CTX_get(ctx);
1034 if (!BN_priv_rand(rho, p[0], BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
1036 if (!BN_GF2m_mod_arr(rho, rho, p))
1039 if (!BN_copy(w, rho))
1041 for (j = 1; j <= p[0] - 1; j++) {
1042 if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
1044 if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx))
1046 if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx))
1048 if (!BN_GF2m_add(z, z, tmp))
1050 if (!BN_GF2m_add(w, w2, rho))
1054 } while (BN_is_zero(w) && (count < MAX_ITERATIONS));
1055 if (BN_is_zero(w)) {
1056 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_TOO_MANY_ITERATIONS);
1061 if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx))
1063 if (!BN_GF2m_add(w, z, w))
1065 if (BN_GF2m_cmp(w, a)) {
1066 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION);
1082 * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
1083 * 0. This function calls down to the BN_GF2m_mod_solve_quad_arr
1084 * implementation; this wrapper function is only provided for convenience;
1085 * for best performance, use the BN_GF2m_mod_solve_quad_arr function.
1087 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1091 const int max = BN_num_bits(p) + 1;
1095 if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
1097 ret = BN_GF2m_poly2arr(p, arr, max);
1098 if (!ret || ret > max) {
1099 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD, BN_R_INVALID_LENGTH);
1102 ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);
1110 * Convert the bit-string representation of a polynomial ( \sum_{i=0}^n a_i *
1111 * x^i) into an array of integers corresponding to the bits with non-zero
1112 * coefficient. Array is terminated with -1. Up to max elements of the array
1113 * will be filled. Return value is total number of array elements that would
1114 * be filled if array was large enough.
1116 int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max)
1124 for (i = a->top - 1; i >= 0; i--) {
1126 /* skip word if a->d[i] == 0 */
1129 for (j = BN_BITS2 - 1; j >= 0; j--) {
1130 if (a->d[i] & mask) {
1132 p[k] = BN_BITS2 * i + j;
1148 * Convert the coefficient array representation of a polynomial to a
1149 * bit-string. The array must be terminated by -1.
1151 int BN_GF2m_arr2poly(const int p[], BIGNUM *a)
1157 for (i = 0; p[i] != -1; i++) {
1158 if (BN_set_bit(a, p[i]) == 0)