+/* crypto/bn/bn_gf2m.c */
+/* ====================================================================
+ * 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.
+ *
+ * In addition, Sun covenants to all licensees who provide a reciprocal
+ * covenant with respect to their own patents if any, not to sue under
+ * current and future patent claims necessarily infringed by the making,
+ * using, practicing, selling, offering for sale and/or otherwise
+ * disposing of the ECC Code as delivered hereunder (or portions thereof),
+ * provided that such covenant shall not apply:
+ * 1) for code that a licensee deletes from the ECC Code;
+ * 2) separates from the ECC Code; or
+ * 3) for infringements caused by:
+ * i) the modification of the ECC Code or
+ * ii) the combination of the ECC Code with other software or
+ * devices where such combination causes the infringement.
+ *
+ * The software is originally written by Sheueling Chang Shantz and
+ * Douglas Stebila of Sun Microsystems Laboratories.
+ *
+ */
+
+/* ====================================================================
+ * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in
+ * the documentation and/or other materials provided with the
+ * distribution.
+ *
+ * 3. All advertising materials mentioning features or use of this
+ * software must display the following acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
+ *
+ * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
+ * endorse or promote products derived from this software without
+ * prior written permission. For written permission, please contact
+ * openssl-core@openssl.org.
+ *
+ * 5. Products derived from this software may not be called "OpenSSL"
+ * nor may "OpenSSL" appear in their names without prior written
+ * permission of the OpenSSL Project.
+ *
+ * 6. Redistributions of any form whatsoever must retain the following
+ * acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
+ * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
+ * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+ * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
+ * OF THE POSSIBILITY OF SUCH DAMAGE.
+ * ====================================================================
+ *
+ * This product includes cryptographic software written by Eric Young
+ * (eay@cryptsoft.com). This product includes software written by Tim
+ * Hudson (tjh@cryptsoft.com).
+ *
+ */
+
+#include <assert.h>
+#include <limits.h>
+#include <stdio.h>
+#include "cryptlib.h"
+#include "bn_lcl.h"
+
+/* 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
+#ifdef SIXTEEN_BIT
+#define SQR1(w) \
+ SQR_tb[(w) >> 12 & 0xF] << 8 | SQR_tb[(w) >> 8 & 0xF]
+#define SQR0(w) \
+ SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
+#endif
+#ifdef EIGHT_BIT
+#define SQR1(w) \
+ SQR_tb[(w) >> 4 & 0xF]
+#define SQR0(w) \
+ SQR_tb[(w) & 15]
+#endif
+
+/* 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 EIGHT_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[4], top1b = a >> 7;
+ register BN_ULONG a1, a2;
+
+ a1 = a & (0x7F); a2 = a1 << 1;
+
+ tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2;
+
+ s = tab[b & 0x3]; l = s;
+ s = tab[b >> 2 & 0x3]; l ^= s << 2; h = s >> 6;
+ s = tab[b >> 4 & 0x3]; l ^= s << 4; h ^= s >> 4;
+ s = tab[b >> 6 ]; l ^= s << 6; h ^= s >> 2;
+
+ /* compensate for the top bit of a */
+
+ if (top1b & 01) { l ^= b << 7; h ^= b >> 1; }
+
+ *r1 = h; *r0 = l;
+ }
+#endif
+#ifdef SIXTEEN_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[4], top1b = a >> 15;
+ register BN_ULONG a1, a2;
+
+ a1 = a & (0x7FFF); a2 = a1 << 1;
+
+ tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2;
+
+ s = tab[b & 0x3]; l = s;
+ s = tab[b >> 2 & 0x3]; l ^= s << 2; h = s >> 14;
+ s = tab[b >> 4 & 0x3]; l ^= s << 4; h ^= s >> 12;
+ s = tab[b >> 6 & 0x3]; l ^= s << 6; h ^= s >> 10;
+ s = tab[b >> 8 & 0x3]; l ^= s << 8; h ^= s >> 8;
+ s = tab[b >>10 & 0x3]; l ^= s << 10; h ^= s >> 6;
+ s = tab[b >>12 & 0x3]; l ^= s << 12; h ^= s >> 4;
+ s = tab[b >>14 ]; l ^= s << 14; h ^= s >> 2;
+
+ /* compensate for the top bit of a */
+
+ if (top1b & 01) { l ^= b << 15; h ^= b >> 1; }
+
+ *r1 = h; *r0 = l;
+ }
+#endif
+#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 & (0x1FFFFFFFFFFFFFFF); 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; */
+ }
+
+
+/* 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;
+
+ if (a->top < b->top) { at = b; bt = a; }
+ else { at = a; bt = b; }
+
+ bn_expand2(r, at->top);
+
+ 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_fix_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 unsigned int p[])
+ {
+ int j, k;
+ int n, dN, d0, d1;
+ BN_ULONG zz, *z;
+
+ /* Since the algorithm does reduction in place, if a == r, copy the
+ * contents of a into r so we can do reduction in r.
+ */
+ if ((a != NULL) && (a->d != r->d))
+ {
+ 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;
+
+ if (d0) z[dN] = (z[dN] << d1) >> d1; /* clear up the top d1 bits */
+ z[0] ^= zz; /* reduction t^0 component */
+
+ for (k = 1; p[k] > 0; k++)
+ {
+ /* 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) z[n+1] ^= (zz >> d1);
+ }
+
+
+ }
+
+ bn_fix_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)
+ {
+ const int max = BN_num_bits(p);
+ unsigned int *arr=NULL, ret = 0;
+ if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+ if (BN_GF2m_poly2arr(p, arr, max) > max)
+ {
+ BNerr(BN_F_BN_GF2M_MOD,BN_R_INVALID_LENGTH);
+ goto err;
+ }
+ ret = BN_GF2m_mod_arr(r, a, arr);
+ err:
+ if (arr) OPENSSL_free(arr);
+ 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 unsigned int p[], BN_CTX *ctx)
+ {
+ int zlen, i, j, k, ret = 0;
+ BIGNUM *s;
+ BN_ULONG x1, x0, y1, y0, zz[4];
+
+ 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;
+ 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_fix_top(s);
+ BN_GF2m_mod_arr(r, s, p);
+ ret = 1;
+
+ 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)
+ {
+ const int max = BN_num_bits(p);
+ unsigned int *arr=NULL, ret = 0;
+ if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+ if (BN_GF2m_poly2arr(p, arr, max) > 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);
+ err:
+ if (arr) 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 unsigned int p[], BN_CTX *ctx)
+ {
+ int i, ret = 0;
+ BIGNUM *s;
+
+ BN_CTX_start(ctx);
+ if ((s = BN_CTX_get(ctx)) == NULL) return 0;
+ 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_fix_top(s);
+ if (!BN_GF2m_mod_arr(r, s, p)) goto err;
+ 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)
+ {
+ const int max = BN_num_bits(p);
+ unsigned int *arr=NULL, ret = 0;
+ if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+ if (BN_GF2m_poly2arr(p, arr, max) > max)
+ {
+ BNerr(BN_F_BN_GF2M_MOD_SQR,BN_R_INVALID_LENGTH);
+ goto err;
+ }
+ ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
+ err:
+ if (arr) 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, *u, *v, *tmp;
+ int ret = 0;
+
+ BN_CTX_start(ctx);
+
+ b = BN_CTX_get(ctx);
+ c = BN_CTX_get(ctx);
+ u = BN_CTX_get(ctx);
+ v = BN_CTX_get(ctx);
+ if (v == NULL) goto err;
+
+ if (!BN_one(b)) goto err;
+ if (!BN_zero(c)) goto err;
+ if (!BN_GF2m_mod(u, a, p)) goto err;
+ if (!BN_copy(v, p)) goto err;
+
+ u->neg = 0; /* Need to set u->neg = 0 because BN_is_one(u) checks
+ * the neg flag of the bignum.
+ */
+
+ if (BN_is_zero(u)) goto err;
+
+ while (1)
+ {
+ while (!BN_is_odd(u))
+ {
+ 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_is_one(u)) 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;
+ }
+
+
+ if (!BN_copy(r, b)) goto err;
+ ret = 1;
+
+ err:
+ 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 unsigned int p[], BN_CTX *ctx)
+ {
+ BIGNUM *field;
+ int ret = 0;
+
+ 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);
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+ }
+
+
+#ifdef OPENSSL_NO_SUN_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_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;
+ 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_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;
+ if (!BN_zero(v)) goto err;
+
+ a->neg = 0; /* Need to set a->neg = 0 because BN_is_one(a) checks
+ * the neg flag of the bignum.
+ */
+
+ 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_is_one(a))
+ 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;
+ 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 unsigned int p[], BN_CTX *ctx)
+ {
+ BIGNUM *field;
+ int ret = 0;
+
+ 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);
+
+ 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 unsigned int p[], BN_CTX *ctx)
+ {
+ int ret = 0, i, n;
+ BIGNUM *u;
+
+ if (BN_is_zero(b))
+ {
+ return(BN_one(r));
+ }
+
+
+ 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;
+
+ 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)
+ {
+ const int max = BN_num_bits(p);
+ unsigned int *arr=NULL, ret = 0;
+ if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+ if (BN_GF2m_poly2arr(p, arr, max) > 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);
+ err:
+ if (arr) 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 unsigned int p[], BN_CTX *ctx)
+ {
+ int ret = 0;
+ BIGNUM *u;
+
+ BN_CTX_start(ctx);
+ if ((u = BN_CTX_get(ctx)) == NULL) goto err;
+
+ if (!BN_zero(u)) goto err;
+ if (!BN_set_bit(u, p[0] - 1)) goto err;
+ ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
+
+ 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)
+ {
+ const int max = BN_num_bits(p);
+ unsigned int *arr=NULL, ret = 0;
+ if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+ if (BN_GF2m_poly2arr(p, arr, max) > max)
+ {
+ BNerr(BN_F_BN_GF2M_MOD_EXP,BN_R_INVALID_LENGTH);
+ goto err;
+ }
+ ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
+ err:
+ if (arr) 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 unsigned int p[], BN_CTX *ctx)
+ {
+ int ret = 0, i, count = 0;
+ BIGNUM *a, *z, *rho, *w, *w2, *tmp;
+
+ 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))
+ {
+ ret = BN_zero(r);
+ goto err;
+ }
+
+ if (p[0] & 0x1) /* m is odd */
+ {
+ /* compute half-trace of a */
+ if (!BN_copy(z, a)) goto err;
+ for (i = 1; i <= (p[0] - 1) / 2; i++)
+ {
+ 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], 0, 0)) goto err;
+ if (!BN_GF2m_mod_arr(rho, rho, p)) goto err;
+ if (!BN_zero(z)) goto err;
+ if (!BN_copy(w, rho)) goto err;
+ for (i = 1; i <= p[0] - 1; i++)
+ {
+ 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)) goto err;
+
+ if (!BN_copy(r, z)) goto err;
+
+ 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)
+ {
+ const int max = BN_num_bits(p);
+ unsigned int *arr=NULL, ret = 0;
+ if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;
+ if (BN_GF2m_poly2arr(p, arr, max) > 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);
+ err:
+ if (arr) OPENSSL_free(arr);
+ return ret;
+ }
+
+/* Convert the bit-string representation of a polynomial a into an array
+ * of integers corresponding to the bits with non-zero coefficient.
+ * Up to max elements of the array will be filled. Return value is total
+ * number of coefficients that would be extracted if array was large enough.
+ */
+int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max)
+ {
+ int i, j, k;
+ BN_ULONG mask;
+
+ for (k = 0; k < max; k++) p[k] = 0;
+ k = 0;
+
+ for (i = a->top - 1; i >= 0; i--)
+ {
+ 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;
+ }
+ }
+
+ return k;
+ }
+
+/* Convert the coefficient array representation of a polynomial to a
+ * bit-string. The array must be terminated by 0.
+ */
+int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a)
+ {
+ int i;
+
+ BN_zero(a);
+ for (i = 0; p[i] > 0; i++)
+ {
+ BN_set_bit(a, p[i]);
+ }
+ BN_set_bit(a, 0);
+
+ return 1;
+ }
+
projects / openssl.git / commitdiff