--- /dev/null
+/* crypto/ec/ec2_mult.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.
+ *
+ * The software is originally written by Sheueling Chang Shantz and
+ * Douglas Stebila of Sun Microsystems Laboratories.
+ *
+ */
+/* ====================================================================
+ * Copyright (c) 1998-2003 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 <openssl/err.h>
+
+#include "ec_lcl.h"
+
+#ifndef OPENSSL_NO_EC2M
+
+
+/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
+ * coordinates.
+ * Uses algorithm Mdouble in appendix of
+ * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
+ * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
+ * modified to not require precomputation of c=b^{2^{m-1}}.
+ */
+static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx)
+ {
+ BIGNUM *t1;
+ int ret = 0;
+
+ /* Since Mdouble is static we can guarantee that ctx != NULL. */
+ BN_CTX_start(ctx);
+ t1 = BN_CTX_get(ctx);
+ if (t1 == NULL) goto err;
+
+ if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
+ if (!group->meth->field_sqr(group, t1, z, ctx)) goto err;
+ if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err;
+ if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
+ if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err;
+ if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err;
+ if (!BN_GF2m_add(x, x, t1)) goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+ }
+
+/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
+ * projective coordinates.
+ * Uses algorithm Madd in appendix of
+ * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
+ * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
+ */
+static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1,
+ const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx)
+ {
+ BIGNUM *t1, *t2;
+ int ret = 0;
+
+ /* Since Madd is static we can guarantee that ctx != NULL. */
+ BN_CTX_start(ctx);
+ t1 = BN_CTX_get(ctx);
+ t2 = BN_CTX_get(ctx);
+ if (t2 == NULL) goto err;
+
+ if (!BN_copy(t1, x)) goto err;
+ if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err;
+ if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err;
+ if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err;
+ if (!BN_GF2m_add(z1, z1, x1)) goto err;
+ if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err;
+ if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err;
+ if (!BN_GF2m_add(x1, x1, t2)) goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+ }
+
+/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
+ * using Montgomery point multiplication algorithm Mxy() in appendix of
+ * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
+ * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
+ * Returns:
+ * 0 on error
+ * 1 if return value should be the point at infinity
+ * 2 otherwise
+ */
+static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1,
+ BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx)
+ {
+ BIGNUM *t3, *t4, *t5;
+ int ret = 0;
+
+ if (BN_is_zero(z1))
+ {
+ BN_zero(x2);
+ BN_zero(z2);
+ return 1;
+ }
+
+ if (BN_is_zero(z2))
+ {
+ if (!BN_copy(x2, x)) return 0;
+ if (!BN_GF2m_add(z2, x, y)) return 0;
+ return 2;
+ }
+
+ /* Since Mxy is static we can guarantee that ctx != NULL. */
+ BN_CTX_start(ctx);
+ t3 = BN_CTX_get(ctx);
+ t4 = BN_CTX_get(ctx);
+ t5 = BN_CTX_get(ctx);
+ if (t5 == NULL) goto err;
+
+ if (!BN_one(t5)) goto err;
+
+ if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err;
+
+ if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err;
+ if (!BN_GF2m_add(z1, z1, x1)) goto err;
+ if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err;
+ if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err;
+ if (!BN_GF2m_add(z2, z2, x2)) goto err;
+
+ if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err;
+ if (!group->meth->field_sqr(group, t4, x, ctx)) goto err;
+ if (!BN_GF2m_add(t4, t4, y)) goto err;
+ if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err;
+ if (!BN_GF2m_add(t4, t4, z2)) goto err;
+
+ if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err;
+ if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err;
+ if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err;
+ if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err;
+ if (!BN_GF2m_add(z2, x2, x)) goto err;
+
+ if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err;
+ if (!BN_GF2m_add(z2, z2, y)) goto err;
+
+ ret = 2;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+ }
+
+
+/* Computes scalar*point and stores the result in r.
+ * point can not equal r.
+ * Uses a modified algorithm 2P of
+ * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
+ * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
+ *
+ * To protect against side-channel attack the function uses constant time swap,
+ * avoiding conditional branches.
+ */
+static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+ const EC_POINT *point, BN_CTX *ctx)
+ {
+ BIGNUM *x1, *x2, *z1, *z2;
+ int ret = 0, i;
+ BN_ULONG mask,word;
+
+ if (r == point)
+ {
+ ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
+ return 0;
+ }
+
+ /* if result should be point at infinity */
+ if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
+ EC_POINT_is_at_infinity(group, point))
+ {
+ return EC_POINT_set_to_infinity(group, r);
+ }
+
+ /* only support affine coordinates */
+ if (!point->Z_is_one) return 0;
+
+ /* Since point_multiply is static we can guarantee that ctx != NULL. */
+ BN_CTX_start(ctx);
+ x1 = BN_CTX_get(ctx);
+ z1 = BN_CTX_get(ctx);
+ if (z1 == NULL) goto err;
+
+ x2 = &r->X;
+ z2 = &r->Y;
+
+ bn_wexpand(x1, group->field.top);
+ bn_wexpand(z1, group->field.top);
+ bn_wexpand(x2, group->field.top);
+ bn_wexpand(z2, group->field.top);
+
+ if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */
+ if (!BN_one(z1)) goto err; /* z1 = 1 */
+ if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */
+ if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err;
+ if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */
+
+ /* find top most bit and go one past it */
+ i = scalar->top - 1;
+ mask = BN_TBIT;
+ word = scalar->d[i];
+ while (!(word & mask)) mask >>= 1;
+ mask >>= 1;
+ /* if top most bit was at word break, go to next word */
+ if (!mask)
+ {
+ i--;
+ mask = BN_TBIT;
+ }
+
+ for (; i >= 0; i--)
+ {
+ word = scalar->d[i];
+ while (mask)
+ {
+ BN_consttime_swap(word & mask, x1, x2, group->field.top);
+ BN_consttime_swap(word & mask, z1, z2, group->field.top);
+ if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err;
+ if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err;
+ BN_consttime_swap(word & mask, x1, x2, group->field.top);
+ BN_consttime_swap(word & mask, z1, z2, group->field.top);
+ mask >>= 1;
+ }
+ mask = BN_TBIT;
+ }
+
+ /* convert out of "projective" coordinates */
+ i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
+ if (i == 0) goto err;
+ else if (i == 1)
+ {
+ if (!EC_POINT_set_to_infinity(group, r)) goto err;
+ }
+ else
+ {
+ if (!BN_one(&r->Z)) goto err;
+ r->Z_is_one = 1;
+ }
+
+ /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
+ BN_set_negative(&r->X, 0);
+ BN_set_negative(&r->Y, 0);
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ return ret;
+ }
+
+
+/* Computes the sum
+ * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
+ * gracefully ignoring NULL scalar values.
+ */
+int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+ size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
+ {
+ BN_CTX *new_ctx = NULL;
+ int ret = 0;
+ size_t i;
+ EC_POINT *p=NULL;
+ EC_POINT *acc = NULL;
+
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ /* This implementation is more efficient than the wNAF implementation for 2
+ * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points,
+ * or if we can perform a fast multiplication based on precomputation.
+ */
+ if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group)))
+ {
+ ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
+ goto err;
+ }
+
+ if ((p = EC_POINT_new(group)) == NULL) goto err;
+ if ((acc = EC_POINT_new(group)) == NULL) goto err;
+
+ if (!EC_POINT_set_to_infinity(group, acc)) goto err;
+
+ if (scalar)
+ {
+ if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err;
+ if (BN_is_negative(scalar))
+ if (!group->meth->invert(group, p, ctx)) goto err;
+ if (!group->meth->add(group, acc, acc, p, ctx)) goto err;
+ }
+
+ for (i = 0; i < num; i++)
+ {
+ if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err;
+ if (BN_is_negative(scalars[i]))
+ if (!group->meth->invert(group, p, ctx)) goto err;
+ if (!group->meth->add(group, acc, acc, p, ctx)) goto err;
+ }
+
+ if (!EC_POINT_copy(r, acc)) goto err;
+
+ ret = 1;
+
+ err:
+ if (p) EC_POINT_free(p);
+ if (acc) EC_POINT_free(acc);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
+
+
+/* Precomputation for point multiplication: fall back to wNAF methods
+ * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */
+
+int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
+ {
+ return ec_wNAF_precompute_mult(group, ctx);
+ }
+
+int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
+ {
+ return ec_wNAF_have_precompute_mult(group);
+ }
+
+#endif
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