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Diffstat (limited to 'openssl-1.1.0h/crypto/bn/bn_gf2m.c')
-rw-r--r--openssl-1.1.0h/crypto/bn/bn_gf2m.c1224
1 files changed, 1224 insertions, 0 deletions
diff --git a/openssl-1.1.0h/crypto/bn/bn_gf2m.c b/openssl-1.1.0h/crypto/bn/bn_gf2m.c
new file mode 100644
index 0000000..b1987f5
--- /dev/null
+++ b/openssl-1.1.0h/crypto/bn/bn_gf2m.c
@@ -0,0 +1,1224 @@
+/*
+ * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved.
+ *
+ * Licensed under the OpenSSL license (the "License"). You may not use
+ * this file except in compliance with the License. You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
+ */
+
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ *
+ * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
+ * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
+ * to the OpenSSL project.
+ *
+ * The ECC Code is licensed pursuant to the OpenSSL open source
+ * license provided below.
+ */
+
+#include <assert.h>
+#include <limits.h>
+#include <stdio.h>
+#include "internal/cryptlib.h"
+#include "bn_lcl.h"
+
+#ifndef OPENSSL_NO_EC2M
+
+/*
+ * Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should
+ * fail.
+ */
+# define MAX_ITERATIONS 50
+
+static const BN_ULONG SQR_tb[16] = { 0, 1, 4, 5, 16, 17, 20, 21,
+ 64, 65, 68, 69, 80, 81, 84, 85
+};
+
+/* Platform-specific macros to accelerate squaring. */
+# if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
+# define SQR1(w) \
+ SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \
+ SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \
+ SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \
+ SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF]
+# define SQR0(w) \
+ SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \
+ SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \
+ SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
+ SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
+# endif
+# ifdef THIRTY_TWO_BIT
+# define SQR1(w) \
+ SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \
+ SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF]
+# define SQR0(w) \
+ SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
+ SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
+# endif
+
+# if !defined(OPENSSL_BN_ASM_GF2m)
+/*
+ * Product of two polynomials a, b each with degree < BN_BITS2 - 1, result is
+ * a polynomial r with degree < 2 * BN_BITS - 1 The caller MUST ensure that
+ * the variables have the right amount of space allocated.
+ */
+# ifdef THIRTY_TWO_BIT
+static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
+ const BN_ULONG b)
+{
+ register BN_ULONG h, l, s;
+ BN_ULONG tab[8], top2b = a >> 30;
+ register BN_ULONG a1, a2, a4;
+
+ a1 = a & (0x3FFFFFFF);
+ a2 = a1 << 1;
+ a4 = a2 << 1;
+
+ tab[0] = 0;
+ tab[1] = a1;
+ tab[2] = a2;
+ tab[3] = a1 ^ a2;
+ tab[4] = a4;
+ tab[5] = a1 ^ a4;
+ tab[6] = a2 ^ a4;
+ tab[7] = a1 ^ a2 ^ a4;
+
+ s = tab[b & 0x7];
+ l = s;
+ s = tab[b >> 3 & 0x7];
+ l ^= s << 3;
+ h = s >> 29;
+ s = tab[b >> 6 & 0x7];
+ l ^= s << 6;
+ h ^= s >> 26;
+ s = tab[b >> 9 & 0x7];
+ l ^= s << 9;
+ h ^= s >> 23;
+ s = tab[b >> 12 & 0x7];
+ l ^= s << 12;
+ h ^= s >> 20;
+ s = tab[b >> 15 & 0x7];
+ l ^= s << 15;
+ h ^= s >> 17;
+ s = tab[b >> 18 & 0x7];
+ l ^= s << 18;
+ h ^= s >> 14;
+ s = tab[b >> 21 & 0x7];
+ l ^= s << 21;
+ h ^= s >> 11;
+ s = tab[b >> 24 & 0x7];
+ l ^= s << 24;
+ h ^= s >> 8;
+ s = tab[b >> 27 & 0x7];
+ l ^= s << 27;
+ h ^= s >> 5;
+ s = tab[b >> 30];
+ l ^= s << 30;
+ h ^= s >> 2;
+
+ /* compensate for the top two bits of a */
+
+ if (top2b & 01) {
+ l ^= b << 30;
+ h ^= b >> 2;
+ }
+ if (top2b & 02) {
+ l ^= b << 31;
+ h ^= b >> 1;
+ }
+
+ *r1 = h;
+ *r0 = l;
+}
+# endif
+# if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
+static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
+ const BN_ULONG b)
+{
+ register BN_ULONG h, l, s;
+ BN_ULONG tab[16], top3b = a >> 61;
+ register BN_ULONG a1, a2, a4, a8;
+
+ a1 = a & (0x1FFFFFFFFFFFFFFFULL);
+ a2 = a1 << 1;
+ a4 = a2 << 1;
+ a8 = a4 << 1;
+
+ tab[0] = 0;
+ tab[1] = a1;
+ tab[2] = a2;
+ tab[3] = a1 ^ a2;
+ tab[4] = a4;
+ tab[5] = a1 ^ a4;
+ tab[6] = a2 ^ a4;
+ tab[7] = a1 ^ a2 ^ a4;
+ tab[8] = a8;
+ tab[9] = a1 ^ a8;
+ tab[10] = a2 ^ a8;
+ tab[11] = a1 ^ a2 ^ a8;
+ tab[12] = a4 ^ a8;
+ tab[13] = a1 ^ a4 ^ a8;
+ tab[14] = a2 ^ a4 ^ a8;
+ tab[15] = a1 ^ a2 ^ a4 ^ a8;
+
+ s = tab[b & 0xF];
+ l = s;
+ s = tab[b >> 4 & 0xF];
+ l ^= s << 4;
+ h = s >> 60;
+ s = tab[b >> 8 & 0xF];
+ l ^= s << 8;
+ h ^= s >> 56;
+ s = tab[b >> 12 & 0xF];
+ l ^= s << 12;
+ h ^= s >> 52;
+ s = tab[b >> 16 & 0xF];
+ l ^= s << 16;
+ h ^= s >> 48;
+ s = tab[b >> 20 & 0xF];
+ l ^= s << 20;
+ h ^= s >> 44;
+ s = tab[b >> 24 & 0xF];
+ l ^= s << 24;
+ h ^= s >> 40;
+ s = tab[b >> 28 & 0xF];
+ l ^= s << 28;
+ h ^= s >> 36;
+ s = tab[b >> 32 & 0xF];
+ l ^= s << 32;
+ h ^= s >> 32;
+ s = tab[b >> 36 & 0xF];
+ l ^= s << 36;
+ h ^= s >> 28;
+ s = tab[b >> 40 & 0xF];
+ l ^= s << 40;
+ h ^= s >> 24;
+ s = tab[b >> 44 & 0xF];
+ l ^= s << 44;
+ h ^= s >> 20;
+ s = tab[b >> 48 & 0xF];
+ l ^= s << 48;
+ h ^= s >> 16;
+ s = tab[b >> 52 & 0xF];
+ l ^= s << 52;
+ h ^= s >> 12;
+ s = tab[b >> 56 & 0xF];
+ l ^= s << 56;
+ h ^= s >> 8;
+ s = tab[b >> 60];
+ l ^= s << 60;
+ h ^= s >> 4;
+
+ /* compensate for the top three bits of a */
+
+ if (top3b & 01) {
+ l ^= b << 61;
+ h ^= b >> 3;
+ }
+ if (top3b & 02) {
+ l ^= b << 62;
+ h ^= b >> 2;
+ }
+ if (top3b & 04) {
+ l ^= b << 63;
+ h ^= b >> 1;
+ }
+
+ *r1 = h;
+ *r0 = l;
+}
+# endif
+
+/*
+ * Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
+ * result is a polynomial r with degree < 4 * BN_BITS2 - 1 The caller MUST
+ * ensure that the variables have the right amount of space allocated.
+ */
+static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0,
+ const BN_ULONG b1, const BN_ULONG b0)
+{
+ BN_ULONG m1, m0;
+ /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
+ bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1);
+ bn_GF2m_mul_1x1(r + 1, r, a0, b0);
+ bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
+ /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
+ r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */
+ r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */
+}
+# else
+void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1,
+ BN_ULONG b0);
+# endif
+
+/*
+ * Add polynomials a and b and store result in r; r could be a or b, a and b
+ * could be equal; r is the bitwise XOR of a and b.
+ */
+int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
+{
+ int i;
+ const BIGNUM *at, *bt;
+
+ bn_check_top(a);
+ bn_check_top(b);
+
+ if (a->top < b->top) {
+ at = b;
+ bt = a;
+ } else {
+ at = a;
+ bt = b;
+ }
+
+ if (bn_wexpand(r, at->top) == NULL)
+ return 0;
+
+ for (i = 0; i < bt->top; i++) {
+ r->d[i] = at->d[i] ^ bt->d[i];
+ }
+ for (; i < at->top; i++) {
+ r->d[i] = at->d[i];
+ }
+
+ r->top = at->top;
+ bn_correct_top(r);
+
+ return 1;
+}
+
+/*-
+ * Some functions allow for representation of the irreducible polynomials
+ * as an int[], say p. The irreducible f(t) is then of the form:
+ * t^p[0] + t^p[1] + ... + t^p[k]
+ * where m = p[0] > p[1] > ... > p[k] = 0.
+ */
+
+/* Performs modular reduction of a and store result in r. r could be a. */
+int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[])
+{
+ int j, k;
+ int n, dN, d0, d1;
+ BN_ULONG zz, *z;
+
+ bn_check_top(a);
+
+ if (!p[0]) {
+ /* reduction mod 1 => return 0 */
+ BN_zero(r);
+ return 1;
+ }
+
+ /*
+ * Since the algorithm does reduction in the r value, if a != r, copy the
+ * contents of a into r so we can do reduction in r.
+ */
+ if (a != r) {
+ if (!bn_wexpand(r, a->top))
+ return 0;
+ for (j = 0; j < a->top; j++) {
+ r->d[j] = a->d[j];
+ }
+ r->top = a->top;
+ }
+ z = r->d;
+
+ /* start reduction */
+ dN = p[0] / BN_BITS2;
+ for (j = r->top - 1; j > dN;) {
+ zz = z[j];
+ if (z[j] == 0) {
+ j--;
+ continue;
+ }
+ z[j] = 0;
+
+ for (k = 1; p[k] != 0; k++) {
+ /* reducing component t^p[k] */
+ n = p[0] - p[k];
+ d0 = n % BN_BITS2;
+ d1 = BN_BITS2 - d0;
+ n /= BN_BITS2;
+ z[j - n] ^= (zz >> d0);
+ if (d0)
+ z[j - n - 1] ^= (zz << d1);
+ }
+
+ /* reducing component t^0 */
+ n = dN;
+ d0 = p[0] % BN_BITS2;
+ d1 = BN_BITS2 - d0;
+ z[j - n] ^= (zz >> d0);
+ if (d0)
+ z[j - n - 1] ^= (zz << d1);
+ }
+
+ /* final round of reduction */
+ while (j == dN) {
+
+ d0 = p[0] % BN_BITS2;
+ zz = z[dN] >> d0;
+ if (zz == 0)
+ break;
+ d1 = BN_BITS2 - d0;
+
+ /* clear up the top d1 bits */
+ if (d0)
+ z[dN] = (z[dN] << d1) >> d1;
+ else
+ z[dN] = 0;
+ z[0] ^= zz; /* reduction t^0 component */
+
+ for (k = 1; p[k] != 0; k++) {
+ BN_ULONG tmp_ulong;
+
+ /* reducing component t^p[k] */
+ n = p[k] / BN_BITS2;
+ d0 = p[k] % BN_BITS2;
+ d1 = BN_BITS2 - d0;
+ z[n] ^= (zz << d0);
+ if (d0 && (tmp_ulong = zz >> d1))
+ z[n + 1] ^= tmp_ulong;
+ }
+
+ }
+
+ bn_correct_top(r);
+ return 1;
+}
+
+/*
+ * Performs modular reduction of a by p and store result in r. r could be a.
+ * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
+ * function is only provided for convenience; for best performance, use the
+ * BN_GF2m_mod_arr function.
+ */
+int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)
+{
+ int ret = 0;
+ int arr[6];
+ bn_check_top(a);
+ bn_check_top(p);
+ ret = BN_GF2m_poly2arr(p, arr, OSSL_NELEM(arr));
+ if (!ret || ret > (int)OSSL_NELEM(arr)) {
+ BNerr(BN_F_BN_GF2M_MOD, BN_R_INVALID_LENGTH);
+ return 0;
+ }
+ ret = BN_GF2m_mod_arr(r, a, arr);
+ bn_check_top(r);
+ return ret;
+}
+
+/*
+ * Compute the product of two polynomials a and b, reduce modulo p, and store
+ * the result in r. r could be a or b; a could be b.
+ */
+int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
+ const int p[], BN_CTX *ctx)
+{
+ int zlen, i, j, k, ret = 0;
+ BIGNUM *s;
+ BN_ULONG x1, x0, y1, y0, zz[4];
+
+ bn_check_top(a);
+ bn_check_top(b);
+
+ if (a == b) {
+ return BN_GF2m_mod_sqr_arr(r, a, p, ctx);
+ }
+
+ BN_CTX_start(ctx);
+ if ((s = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ zlen = a->top + b->top + 4;
+ if (!bn_wexpand(s, zlen))
+ goto err;
+ s->top = zlen;
+
+ for (i = 0; i < zlen; i++)
+ s->d[i] = 0;
+
+ for (j = 0; j < b->top; j += 2) {
+ y0 = b->d[j];
+ y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1];
+ for (i = 0; i < a->top; i += 2) {
+ x0 = a->d[i];
+ x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1];
+ bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);
+ for (k = 0; k < 4; k++)
+ s->d[i + j + k] ^= zz[k];
+ }
+ }
+
+ bn_correct_top(s);
+ if (BN_GF2m_mod_arr(r, s, p))
+ ret = 1;
+ bn_check_top(r);
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*
+ * Compute the product of two polynomials a and b, reduce modulo p, and store
+ * the result in r. r could be a or b; a could equal b. This function calls
+ * down to the BN_GF2m_mod_mul_arr implementation; this wrapper function is
+ * only provided for convenience; for best performance, use the
+ * BN_GF2m_mod_mul_arr function.
+ */
+int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
+ const BIGNUM *p, BN_CTX *ctx)
+{
+ int ret = 0;
+ const int max = BN_num_bits(p) + 1;
+ int *arr = NULL;
+ bn_check_top(a);
+ bn_check_top(b);
+ bn_check_top(p);
+ if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
+ goto err;
+ ret = BN_GF2m_poly2arr(p, arr, max);
+ if (!ret || ret > max) {
+ BNerr(BN_F_BN_GF2M_MOD_MUL, BN_R_INVALID_LENGTH);
+ goto err;
+ }
+ ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);
+ bn_check_top(r);
+ err:
+ OPENSSL_free(arr);
+ return ret;
+}
+
+/* Square a, reduce the result mod p, and store it in a. r could be a. */
+int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
+ BN_CTX *ctx)
+{
+ int i, ret = 0;
+ BIGNUM *s;
+
+ bn_check_top(a);
+ BN_CTX_start(ctx);
+ if ((s = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if (!bn_wexpand(s, 2 * a->top))
+ goto err;
+
+ for (i = a->top - 1; i >= 0; i--) {
+ s->d[2 * i + 1] = SQR1(a->d[i]);
+ s->d[2 * i] = SQR0(a->d[i]);
+ }
+
+ s->top = 2 * a->top;
+ bn_correct_top(s);
+ if (!BN_GF2m_mod_arr(r, s, p))
+ goto err;
+ bn_check_top(r);
+ ret = 1;
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*
+ * Square a, reduce the result mod p, and store it in a. r could be a. This
+ * function calls down to the BN_GF2m_mod_sqr_arr implementation; this
+ * wrapper function is only provided for convenience; for best performance,
+ * use the BN_GF2m_mod_sqr_arr function.
+ */
+int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
+{
+ int ret = 0;
+ const int max = BN_num_bits(p) + 1;
+ int *arr = NULL;
+
+ bn_check_top(a);
+ bn_check_top(p);
+ if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
+ goto err;
+ ret = BN_GF2m_poly2arr(p, arr, max);
+ if (!ret || ret > max) {
+ BNerr(BN_F_BN_GF2M_MOD_SQR, BN_R_INVALID_LENGTH);
+ goto err;
+ }
+ ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
+ bn_check_top(r);
+ err:
+ OPENSSL_free(arr);
+ return ret;
+}
+
+/*
+ * Invert a, reduce modulo p, and store the result in r. r could be a. Uses
+ * Modified Almost Inverse Algorithm (Algorithm 10) from Hankerson, D.,
+ * Hernandez, J.L., and Menezes, A. "Software Implementation of Elliptic
+ * Curve Cryptography Over Binary Fields".
+ */
+int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
+{
+ BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp;
+ int ret = 0;
+
+ bn_check_top(a);
+ bn_check_top(p);
+
+ BN_CTX_start(ctx);
+
+ if ((b = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((c = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((u = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if ((v = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ if (!BN_GF2m_mod(u, a, p))
+ goto err;
+ if (BN_is_zero(u))
+ goto err;
+
+ if (!BN_copy(v, p))
+ goto err;
+# if 0
+ if (!BN_one(b))
+ goto err;
+
+ while (1) {
+ while (!BN_is_odd(u)) {
+ if (BN_is_zero(u))
+ goto err;
+ if (!BN_rshift1(u, u))
+ goto err;
+ if (BN_is_odd(b)) {
+ if (!BN_GF2m_add(b, b, p))
+ goto err;
+ }
+ if (!BN_rshift1(b, b))
+ goto err;
+ }
+
+ if (BN_abs_is_word(u, 1))
+ break;
+
+ if (BN_num_bits(u) < BN_num_bits(v)) {
+ tmp = u;
+ u = v;
+ v = tmp;
+ tmp = b;
+ b = c;
+ c = tmp;
+ }
+
+ if (!BN_GF2m_add(u, u, v))
+ goto err;
+ if (!BN_GF2m_add(b, b, c))
+ goto err;
+ }
+# else
+ {
+ int i;
+ int ubits = BN_num_bits(u);
+ int vbits = BN_num_bits(v); /* v is copy of p */
+ int top = p->top;
+ BN_ULONG *udp, *bdp, *vdp, *cdp;
+
+ if (!bn_wexpand(u, top))
+ goto err;
+ udp = u->d;
+ for (i = u->top; i < top; i++)
+ udp[i] = 0;
+ u->top = top;
+ if (!bn_wexpand(b, top))
+ goto err;
+ bdp = b->d;
+ bdp[0] = 1;
+ for (i = 1; i < top; i++)
+ bdp[i] = 0;
+ b->top = top;
+ if (!bn_wexpand(c, top))
+ goto err;
+ cdp = c->d;
+ for (i = 0; i < top; i++)
+ cdp[i] = 0;
+ c->top = top;
+ vdp = v->d; /* It pays off to "cache" *->d pointers,
+ * because it allows optimizer to be more
+ * aggressive. But we don't have to "cache"
+ * p->d, because *p is declared 'const'... */
+ while (1) {
+ while (ubits && !(udp[0] & 1)) {
+ BN_ULONG u0, u1, b0, b1, mask;
+
+ u0 = udp[0];
+ b0 = bdp[0];
+ mask = (BN_ULONG)0 - (b0 & 1);
+ b0 ^= p->d[0] & mask;
+ for (i = 0; i < top - 1; i++) {
+ u1 = udp[i + 1];
+ udp[i] = ((u0 >> 1) | (u1 << (BN_BITS2 - 1))) & BN_MASK2;
+ u0 = u1;
+ b1 = bdp[i + 1] ^ (p->d[i + 1] & mask);
+ bdp[i] = ((b0 >> 1) | (b1 << (BN_BITS2 - 1))) & BN_MASK2;
+ b0 = b1;
+ }
+ udp[i] = u0 >> 1;
+ bdp[i] = b0 >> 1;
+ ubits--;
+ }
+
+ if (ubits <= BN_BITS2) {
+ if (udp[0] == 0) /* poly was reducible */
+ goto err;
+ if (udp[0] == 1)
+ break;
+ }
+
+ if (ubits < vbits) {
+ i = ubits;
+ ubits = vbits;
+ vbits = i;
+ tmp = u;
+ u = v;
+ v = tmp;
+ tmp = b;
+ b = c;
+ c = tmp;
+ udp = vdp;
+ vdp = v->d;
+ bdp = cdp;
+ cdp = c->d;
+ }
+ for (i = 0; i < top; i++) {
+ udp[i] ^= vdp[i];
+ bdp[i] ^= cdp[i];
+ }
+ if (ubits == vbits) {
+ BN_ULONG ul;
+ int utop = (ubits - 1) / BN_BITS2;
+
+ while ((ul = udp[utop]) == 0 && utop)
+ utop--;
+ ubits = utop * BN_BITS2 + BN_num_bits_word(ul);
+ }
+ }
+ bn_correct_top(b);
+ }
+# endif
+
+ if (!BN_copy(r, b))
+ goto err;
+ bn_check_top(r);
+ ret = 1;
+
+ err:
+# ifdef BN_DEBUG /* BN_CTX_end would complain about the
+ * expanded form */
+ bn_correct_top(c);
+ bn_correct_top(u);
+ bn_correct_top(v);
+# endif
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*
+ * Invert xx, reduce modulo p, and store the result in r. r could be xx.
+ * This function calls down to the BN_GF2m_mod_inv implementation; this
+ * wrapper function is only provided for convenience; for best performance,
+ * use the BN_GF2m_mod_inv function.
+ */
+int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[],
+ BN_CTX *ctx)
+{
+ BIGNUM *field;
+ int ret = 0;
+
+ bn_check_top(xx);
+ BN_CTX_start(ctx);
+ if ((field = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if (!BN_GF2m_arr2poly(p, field))
+ goto err;
+
+ ret = BN_GF2m_mod_inv(r, xx, field, ctx);
+ bn_check_top(r);
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+# ifndef OPENSSL_SUN_GF2M_DIV
+/*
+ * Divide y by x, reduce modulo p, and store the result in r. r could be x
+ * or y, x could equal y.
+ */
+int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x,
+ const BIGNUM *p, BN_CTX *ctx)
+{
+ BIGNUM *xinv = NULL;
+ int ret = 0;
+
+ bn_check_top(y);
+ bn_check_top(x);
+ bn_check_top(p);
+
+ BN_CTX_start(ctx);
+ xinv = BN_CTX_get(ctx);
+ if (xinv == NULL)
+ goto err;
+
+ if (!BN_GF2m_mod_inv(xinv, x, p, ctx))
+ goto err;
+ if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx))
+ goto err;
+ bn_check_top(r);
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+# else
+/*
+ * Divide y by x, reduce modulo p, and store the result in r. r could be x
+ * or y, x could equal y. Uses algorithm Modular_Division_GF(2^m) from
+ * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to the
+ * Great Divide".
+ */
+int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x,
+ const BIGNUM *p, BN_CTX *ctx)
+{
+ BIGNUM *a, *b, *u, *v;
+ int ret = 0;
+
+ bn_check_top(y);
+ bn_check_top(x);
+ bn_check_top(p);
+
+ BN_CTX_start(ctx);
+
+ a = BN_CTX_get(ctx);
+ b = BN_CTX_get(ctx);
+ u = BN_CTX_get(ctx);
+ v = BN_CTX_get(ctx);
+ if (v == NULL)
+ goto err;
+
+ /* reduce x and y mod p */
+ if (!BN_GF2m_mod(u, y, p))
+ goto err;
+ if (!BN_GF2m_mod(a, x, p))
+ goto err;
+ if (!BN_copy(b, p))
+ goto err;
+
+ while (!BN_is_odd(a)) {
+ if (!BN_rshift1(a, a))
+ goto err;
+ if (BN_is_odd(u))
+ if (!BN_GF2m_add(u, u, p))
+ goto err;
+ if (!BN_rshift1(u, u))
+ goto err;
+ }
+
+ do {
+ if (BN_GF2m_cmp(b, a) > 0) {
+ if (!BN_GF2m_add(b, b, a))
+ goto err;
+ if (!BN_GF2m_add(v, v, u))
+ goto err;
+ do {
+ if (!BN_rshift1(b, b))
+ goto err;
+ if (BN_is_odd(v))
+ if (!BN_GF2m_add(v, v, p))
+ goto err;
+ if (!BN_rshift1(v, v))
+ goto err;
+ } while (!BN_is_odd(b));
+ } else if (BN_abs_is_word(a, 1))
+ break;
+ else {
+ if (!BN_GF2m_add(a, a, b))
+ goto err;
+ if (!BN_GF2m_add(u, u, v))
+ goto err;
+ do {
+ if (!BN_rshift1(a, a))
+ goto err;
+ if (BN_is_odd(u))
+ if (!BN_GF2m_add(u, u, p))
+ goto err;
+ if (!BN_rshift1(u, u))
+ goto err;
+ } while (!BN_is_odd(a));
+ }
+ } while (1);
+
+ if (!BN_copy(r, u))
+ goto err;
+ bn_check_top(r);
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+# endif
+
+/*
+ * Divide yy by xx, reduce modulo p, and store the result in r. r could be xx
+ * * or yy, xx could equal yy. This function calls down to the
+ * BN_GF2m_mod_div implementation; this wrapper function is only provided for
+ * convenience; for best performance, use the BN_GF2m_mod_div function.
+ */
+int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx,
+ const int p[], BN_CTX *ctx)
+{
+ BIGNUM *field;
+ int ret = 0;
+
+ bn_check_top(yy);
+ bn_check_top(xx);
+
+ BN_CTX_start(ctx);
+ if ((field = BN_CTX_get(ctx)) == NULL)
+ goto err;
+ if (!BN_GF2m_arr2poly(p, field))
+ goto err;
+
+ ret = BN_GF2m_mod_div(r, yy, xx, field, ctx);
+ bn_check_top(r);
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*
+ * Compute the bth power of a, reduce modulo p, and store the result in r. r
+ * could be a. Uses simple square-and-multiply algorithm A.5.1 from IEEE
+ * P1363.
+ */
+int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
+ const int p[], BN_CTX *ctx)
+{
+ int ret = 0, i, n;
+ BIGNUM *u;
+
+ bn_check_top(a);
+ bn_check_top(b);
+
+ if (BN_is_zero(b))
+ return (BN_one(r));
+
+ if (BN_abs_is_word(b, 1))
+ return (BN_copy(r, a) != NULL);
+
+ BN_CTX_start(ctx);
+ if ((u = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ if (!BN_GF2m_mod_arr(u, a, p))
+ goto err;
+
+ n = BN_num_bits(b) - 1;
+ for (i = n - 1; i >= 0; i--) {
+ if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx))
+ goto err;
+ if (BN_is_bit_set(b, i)) {
+ if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx))
+ goto err;
+ }
+ }
+ if (!BN_copy(r, u))
+ goto err;
+ bn_check_top(r);
+ ret = 1;
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*
+ * Compute the bth power of a, reduce modulo p, and store the result in r. r
+ * could be a. This function calls down to the BN_GF2m_mod_exp_arr
+ * implementation; this wrapper function is only provided for convenience;
+ * for best performance, use the BN_GF2m_mod_exp_arr function.
+ */
+int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
+ const BIGNUM *p, BN_CTX *ctx)
+{
+ int ret = 0;
+ const int max = BN_num_bits(p) + 1;
+ int *arr = NULL;
+ bn_check_top(a);
+ bn_check_top(b);
+ bn_check_top(p);
+ if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
+ goto err;
+ ret = BN_GF2m_poly2arr(p, arr, max);
+ if (!ret || ret > max) {
+ BNerr(BN_F_BN_GF2M_MOD_EXP, BN_R_INVALID_LENGTH);
+ goto err;
+ }
+ ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);
+ bn_check_top(r);
+ err:
+ OPENSSL_free(arr);
+ return ret;
+}
+
+/*
+ * Compute the square root of a, reduce modulo p, and store the result in r.
+ * r could be a. Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
+ */
+int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[],
+ BN_CTX *ctx)
+{
+ int ret = 0;
+ BIGNUM *u;
+
+ bn_check_top(a);
+
+ if (!p[0]) {
+ /* reduction mod 1 => return 0 */
+ BN_zero(r);
+ return 1;
+ }
+
+ BN_CTX_start(ctx);
+ if ((u = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ if (!BN_set_bit(u, p[0] - 1))
+ goto err;
+ ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
+ bn_check_top(r);
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*
+ * Compute the square root of a, reduce modulo p, and store the result in r.
+ * r could be a. This function calls down to the BN_GF2m_mod_sqrt_arr
+ * implementation; this wrapper function is only provided for convenience;
+ * for best performance, use the BN_GF2m_mod_sqrt_arr function.
+ */
+int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
+{
+ int ret = 0;
+ const int max = BN_num_bits(p) + 1;
+ int *arr = NULL;
+ bn_check_top(a);
+ bn_check_top(p);
+ if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
+ goto err;
+ ret = BN_GF2m_poly2arr(p, arr, max);
+ if (!ret || ret > max) {
+ BNerr(BN_F_BN_GF2M_MOD_SQRT, BN_R_INVALID_LENGTH);
+ goto err;
+ }
+ ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
+ bn_check_top(r);
+ err:
+ OPENSSL_free(arr);
+ return ret;
+}
+
+/*
+ * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
+ * 0. Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
+ */
+int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[],
+ BN_CTX *ctx)
+{
+ int ret = 0, count = 0, j;
+ BIGNUM *a, *z, *rho, *w, *w2, *tmp;
+
+ bn_check_top(a_);
+
+ if (!p[0]) {
+ /* reduction mod 1 => return 0 */
+ BN_zero(r);
+ return 1;
+ }
+
+ BN_CTX_start(ctx);
+ a = BN_CTX_get(ctx);
+ z = BN_CTX_get(ctx);
+ w = BN_CTX_get(ctx);
+ if (w == NULL)
+ goto err;
+
+ if (!BN_GF2m_mod_arr(a, a_, p))
+ goto err;
+
+ if (BN_is_zero(a)) {
+ BN_zero(r);
+ ret = 1;
+ goto err;
+ }
+
+ if (p[0] & 0x1) { /* m is odd */
+ /* compute half-trace of a */
+ if (!BN_copy(z, a))
+ goto err;
+ for (j = 1; j <= (p[0] - 1) / 2; j++) {
+ if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
+ goto err;
+ if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
+ goto err;
+ if (!BN_GF2m_add(z, z, a))
+ goto err;
+ }
+
+ } else { /* m is even */
+
+ rho = BN_CTX_get(ctx);
+ w2 = BN_CTX_get(ctx);
+ tmp = BN_CTX_get(ctx);
+ if (tmp == NULL)
+ goto err;
+ do {
+ if (!BN_rand(rho, p[0], BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
+ goto err;
+ if (!BN_GF2m_mod_arr(rho, rho, p))
+ goto err;
+ BN_zero(z);
+ if (!BN_copy(w, rho))
+ goto err;
+ for (j = 1; j <= p[0] - 1; j++) {
+ if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
+ goto err;
+ if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx))
+ goto err;
+ if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx))
+ goto err;
+ if (!BN_GF2m_add(z, z, tmp))
+ goto err;
+ if (!BN_GF2m_add(w, w2, rho))
+ goto err;
+ }
+ count++;
+ } while (BN_is_zero(w) && (count < MAX_ITERATIONS));
+ if (BN_is_zero(w)) {
+ BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_TOO_MANY_ITERATIONS);
+ goto err;
+ }
+ }
+
+ if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx))
+ goto err;
+ if (!BN_GF2m_add(w, z, w))
+ goto err;
+ if (BN_GF2m_cmp(w, a)) {
+ BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION);
+ goto err;
+ }
+
+ if (!BN_copy(r, z))
+ goto err;
+ bn_check_top(r);
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+/*
+ * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
+ * 0. This function calls down to the BN_GF2m_mod_solve_quad_arr
+ * implementation; this wrapper function is only provided for convenience;
+ * for best performance, use the BN_GF2m_mod_solve_quad_arr function.
+ */
+int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
+ BN_CTX *ctx)
+{
+ int ret = 0;
+ const int max = BN_num_bits(p) + 1;
+ int *arr = NULL;
+ bn_check_top(a);
+ bn_check_top(p);
+ if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
+ goto err;
+ ret = BN_GF2m_poly2arr(p, arr, max);
+ if (!ret || ret > max) {
+ BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD, BN_R_INVALID_LENGTH);
+ goto err;
+ }
+ ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);
+ bn_check_top(r);
+ err:
+ OPENSSL_free(arr);
+ return ret;
+}
+
+/*
+ * Convert the bit-string representation of a polynomial ( \sum_{i=0}^n a_i *
+ * x^i) into an array of integers corresponding to the bits with non-zero
+ * coefficient. Array is terminated with -1. Up to max elements of the array
+ * will be filled. Return value is total number of array elements that would
+ * be filled if array was large enough.
+ */
+int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max)
+{
+ int i, j, k = 0;
+ BN_ULONG mask;
+
+ if (BN_is_zero(a))
+ return 0;
+
+ for (i = a->top - 1; i >= 0; i--) {
+ if (!a->d[i])
+ /* skip word if a->d[i] == 0 */
+ continue;
+ mask = BN_TBIT;
+ for (j = BN_BITS2 - 1; j >= 0; j--) {
+ if (a->d[i] & mask) {
+ if (k < max)
+ p[k] = BN_BITS2 * i + j;
+ k++;
+ }
+ mask >>= 1;
+ }
+ }
+
+ if (k < max) {
+ p[k] = -1;
+ k++;
+ }
+
+ return k;
+}
+
+/*
+ * Convert the coefficient array representation of a polynomial to a
+ * bit-string. The array must be terminated by -1.
+ */
+int BN_GF2m_arr2poly(const int p[], BIGNUM *a)
+{
+ int i;
+
+ bn_check_top(a);
+ BN_zero(a);
+ for (i = 0; p[i] != -1; i++) {
+ if (BN_set_bit(a, p[i]) == 0)
+ return 0;
+ }
+ bn_check_top(a);
+
+ return 1;
+}
+
+#endif
generated by cgit