/* * 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. * * The software is originally written by Sheueling Chang Shantz and * Douglas Stebila of Sun Microsystems Laboratories. * */ #include #include "internal/bn_int.h" #include "ec_lcl.h" #ifndef OPENSSL_NO_EC2M const EC_METHOD *EC_GF2m_simple_method(void) { static const EC_METHOD ret = { EC_FLAGS_DEFAULT_OCT, NID_X9_62_characteristic_two_field, ec_GF2m_simple_group_init, ec_GF2m_simple_group_finish, ec_GF2m_simple_group_clear_finish, ec_GF2m_simple_group_copy, ec_GF2m_simple_group_set_curve, ec_GF2m_simple_group_get_curve, ec_GF2m_simple_group_get_degree, ec_group_simple_order_bits, ec_GF2m_simple_group_check_discriminant, ec_GF2m_simple_point_init, ec_GF2m_simple_point_finish, ec_GF2m_simple_point_clear_finish, ec_GF2m_simple_point_copy, ec_GF2m_simple_point_set_to_infinity, 0 /* set_Jprojective_coordinates_GFp */ , 0 /* get_Jprojective_coordinates_GFp */ , ec_GF2m_simple_point_set_affine_coordinates, ec_GF2m_simple_point_get_affine_coordinates, 0, 0, 0, ec_GF2m_simple_add, ec_GF2m_simple_dbl, ec_GF2m_simple_invert, ec_GF2m_simple_is_at_infinity, ec_GF2m_simple_is_on_curve, ec_GF2m_simple_cmp, ec_GF2m_simple_make_affine, ec_GF2m_simple_points_make_affine, /* * the following three method functions are defined in ec2_mult.c */ ec_GF2m_simple_mul, ec_GF2m_precompute_mult, ec_GF2m_have_precompute_mult, ec_GF2m_simple_field_mul, ec_GF2m_simple_field_sqr, ec_GF2m_simple_field_div, 0 /* field_encode */ , 0 /* field_decode */ , 0, /* field_set_to_one */ ec_key_simple_priv2oct, ec_key_simple_oct2priv, 0, /* set private */ ec_key_simple_generate_key, ec_key_simple_check_key, ec_key_simple_generate_public_key, 0, /* keycopy */ 0, /* keyfinish */ ecdh_simple_compute_key }; return &ret; } /* * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members * are handled by EC_GROUP_new. */ int ec_GF2m_simple_group_init(EC_GROUP *group) { group->field = BN_new(); group->a = BN_new(); group->b = BN_new(); if (group->field == NULL || group->a == NULL || group->b == NULL) { BN_free(group->field); BN_free(group->a); BN_free(group->b); return 0; } return 1; } /* * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are * handled by EC_GROUP_free. */ void ec_GF2m_simple_group_finish(EC_GROUP *group) { BN_free(group->field); BN_free(group->a); BN_free(group->b); } /* * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other * members are handled by EC_GROUP_clear_free. */ void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) { BN_clear_free(group->field); BN_clear_free(group->a); BN_clear_free(group->b); group->poly[0] = 0; group->poly[1] = 0; group->poly[2] = 0; group->poly[3] = 0; group->poly[4] = 0; group->poly[5] = -1; } /* * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are * handled by EC_GROUP_copy. */ int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) { if (!BN_copy(dest->field, src->field)) return 0; if (!BN_copy(dest->a, src->a)) return 0; if (!BN_copy(dest->b, src->b)) return 0; dest->poly[0] = src->poly[0]; dest->poly[1] = src->poly[1]; dest->poly[2] = src->poly[2]; dest->poly[3] = src->poly[3]; dest->poly[4] = src->poly[4]; dest->poly[5] = src->poly[5]; if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; bn_set_all_zero(dest->a); bn_set_all_zero(dest->b); return 1; } /* Set the curve parameters of an EC_GROUP structure. */ int ec_GF2m_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { int ret = 0, i; /* group->field */ if (!BN_copy(group->field, p)) goto err; i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1; if ((i != 5) && (i != 3)) { ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); goto err; } /* group->a */ if (!BN_GF2m_mod_arr(group->a, a, group->poly)) goto err; if (bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; bn_set_all_zero(group->a); /* group->b */ if (!BN_GF2m_mod_arr(group->b, b, group->poly)) goto err; if (bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err; bn_set_all_zero(group->b); ret = 1; err: return ret; } /* * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL * then there values will not be set but the method will return with success. */ int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) { int ret = 0; if (p != NULL) { if (!BN_copy(p, group->field)) return 0; } if (a != NULL) { if (!BN_copy(a, group->a)) goto err; } if (b != NULL) { if (!BN_copy(b, group->b)) goto err; } ret = 1; err: return ret; } /* * Gets the degree of the field. For a curve over GF(2^m) this is the value * m. */ int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) { return BN_num_bits(group->field) - 1; } /* * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an * elliptic curve <=> b != 0 (mod p) */ int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) { int ret = 0; BIGNUM *b; BN_CTX *new_ctx = NULL; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) { ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE); goto err; } } BN_CTX_start(ctx); b = BN_CTX_get(ctx); if (b == NULL) goto err; if (!BN_GF2m_mod_arr(b, group->b, group->poly)) goto err; /* * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic * curve <=> b != 0 (mod p) */ if (BN_is_zero(b)) goto err; ret = 1; err: if (ctx != NULL) BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; } /* Initializes an EC_POINT. */ int ec_GF2m_simple_point_init(EC_POINT *point) { point->X = BN_new(); point->Y = BN_new(); point->Z = BN_new(); if (point->X == NULL || point->Y == NULL || point->Z == NULL) { BN_free(point->X); BN_free(point->Y); BN_free(point->Z); return 0; } return 1; } /* Frees an EC_POINT. */ void ec_GF2m_simple_point_finish(EC_POINT *point) { BN_free(point->X); BN_free(point->Y); BN_free(point->Z); } /* Clears and frees an EC_POINT. */ void ec_GF2m_simple_point_clear_finish(EC_POINT *point) { BN_clear_free(point->X); BN_clear_free(point->Y); BN_clear_free(point->Z); point->Z_is_one = 0; } /* * Copy the contents of one EC_POINT into another. Assumes dest is * initialized. */ int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) { if (!BN_copy(dest->X, src->X)) return 0; if (!BN_copy(dest->Y, src->Y)) return 0; if (!BN_copy(dest->Z, src->Z)) return 0; dest->Z_is_one = src->Z_is_one; return 1; } /* * Set an EC_POINT to the point at infinity. A point at infinity is * represented by having Z=0. */ int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point) { point->Z_is_one = 0; BN_zero(point->Z); return 1; } /* * Set the coordinates of an EC_POINT using affine coordinates. Note that * the simple implementation only uses affine coordinates. */ int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) { int ret = 0; if (x == NULL || y == NULL) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER); return 0; } if (!BN_copy(point->X, x)) goto err; BN_set_negative(point->X, 0); if (!BN_copy(point->Y, y)) goto err; BN_set_negative(point->Y, 0); if (!BN_copy(point->Z, BN_value_one())) goto err; BN_set_negative(point->Z, 0); point->Z_is_one = 1; ret = 1; err: return ret; } /* * Gets the affine coordinates of an EC_POINT. Note that the simple * implementation only uses affine coordinates. */ int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) { int ret = 0; if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY); return 0; } if (BN_cmp(point->Z, BN_value_one())) { ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } if (x != NULL) { if (!BN_copy(x, point->X)) goto err; BN_set_negative(x, 0); } if (y != NULL) { if (!BN_copy(y, point->Y)) goto err; BN_set_negative(y, 0); } ret = 1; err: return ret; } /* * Computes a + b and stores the result in r. r could be a or b, a could be * b. Uses algorithm A.10.2 of IEEE P1363. */ int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { BN_CTX *new_ctx = NULL; BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; int ret = 0; if (EC_POINT_is_at_infinity(group, a)) { if (!EC_POINT_copy(r, b)) return 0; return 1; } if (EC_POINT_is_at_infinity(group, b)) { if (!EC_POINT_copy(r, a)) return 0; return 1; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); x0 = BN_CTX_get(ctx); y0 = BN_CTX_get(ctx); x1 = BN_CTX_get(ctx); y1 = BN_CTX_get(ctx); x2 = BN_CTX_get(ctx); y2 = BN_CTX_get(ctx); s = BN_CTX_get(ctx); t = BN_CTX_get(ctx); if (t == NULL) goto err; if (a->Z_is_one) { if (!BN_copy(x0, a->X)) goto err; if (!BN_copy(y0, a->Y)) goto err; } else { if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err; } if (b->Z_is_one) { if (!BN_copy(x1, b->X)) goto err; if (!BN_copy(y1, b->Y)) goto err; } else { if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err; } if (BN_GF2m_cmp(x0, x1)) { if (!BN_GF2m_add(t, x0, x1)) goto err; if (!BN_GF2m_add(s, y0, y1)) goto err; if (!group->meth->field_div(group, s, s, t, ctx)) goto err; if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; if (!BN_GF2m_add(x2, x2, group->a)) goto err; if (!BN_GF2m_add(x2, x2, s)) goto err; if (!BN_GF2m_add(x2, x2, t)) goto err; } else { if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { if (!EC_POINT_set_to_infinity(group, r)) goto err; ret = 1; goto err; } if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err; if (!BN_GF2m_add(s, s, x1)) goto err; if (!group->meth->field_sqr(group, x2, s, ctx)) goto err; if (!BN_GF2m_add(x2, x2, s)) goto err; if (!BN_GF2m_add(x2, x2, group->a)) goto err; } if (!BN_GF2m_add(y2, x1, x2)) goto err; if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err; if (!BN_GF2m_add(y2, y2, x2)) goto err; if (!BN_GF2m_add(y2, y2, y1)) goto err; if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err; ret = 1; err: BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; } /* * Computes 2 * a and stores the result in r. r could be a. Uses algorithm * A.10.2 of IEEE P1363. */ int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) { return ec_GF2m_simple_add(group, r, a, a, ctx); } int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) { if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) /* point is its own inverse */ return 1; if (!EC_POINT_make_affine(group, point, ctx)) return 0; return BN_GF2m_add(point->Y, point->X, point->Y); } /* Indicates whether the given point is the point at infinity. */ int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) { return BN_is_zero(point->Z); } /*- * Determines whether the given EC_POINT is an actual point on the curve defined * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: * y^2 + x*y = x^3 + a*x^2 + b. */ int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) { int ret = -1; BN_CTX *new_ctx = NULL; BIGNUM *lh, *y2; int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); if (EC_POINT_is_at_infinity(group, point)) return 1; field_mul = group->meth->field_mul; field_sqr = group->meth->field_sqr; /* only support affine coordinates */ if (!point->Z_is_one) return -1; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; } BN_CTX_start(ctx); y2 = BN_CTX_get(ctx); lh = BN_CTX_get(ctx); if (lh == NULL) goto err; /*- * We have a curve defined by a Weierstrass equation * y^2 + x*y = x^3 + a*x^2 + b. * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 * <=> ((x + a) * x + y ) * x + b + y^2 = 0 */ if (!BN_GF2m_add(lh, point->X, group->a)) goto err; if (!field_mul(group, lh, lh, point->X, ctx)) goto err; if (!BN_GF2m_add(lh, lh, point->Y)) goto err; if (!field_mul(group, lh, lh, point->X, ctx)) goto err; if (!BN_GF2m_add(lh, lh, group->b)) goto err; if (!field_sqr(group, y2, point->Y, ctx)) goto err; if (!BN_GF2m_add(lh, lh, y2)) goto err; ret = BN_is_zero(lh); err: if (ctx) BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; } /*- * Indicates whether two points are equal. * Return values: * -1 error * 0 equal (in affine coordinates) * 1 not equal */ int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { BIGNUM *aX, *aY, *bX, *bY; BN_CTX *new_ctx = NULL; int ret = -1; if (EC_POINT_is_at_infinity(group, a)) { return EC_POINT_is_at_infinity(group, b) ? 0 : 1; } if (EC_POINT_is_at_infinity(group, b)) return 1; if (a->Z_is_one && b->Z_is_one) { return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return -1; } BN_CTX_start(ctx); aX = BN_CTX_get(ctx); aY = BN_CTX_get(ctx); bX = BN_CTX_get(ctx); bY = BN_CTX_get(ctx); if (bY == NULL) goto err; if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err; if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err; ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; err: if (ctx) BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; } /* Forces the given EC_POINT to internally use affine coordinates. */ int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) { BN_CTX *new_ctx = NULL; BIGNUM *x, *y; int ret = 0; if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) return 1; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) return 0; } BN_CTX_start(ctx); x = BN_CTX_get(ctx); y = BN_CTX_get(ctx); if (y == NULL) goto err; if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; if (!BN_copy(point->X, x)) goto err; if (!BN_copy(point->Y, y)) goto err; if (!BN_one(point->Z)) goto err; point->Z_is_one = 1; ret = 1; err: if (ctx) BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; } /* * Forces each of the EC_POINTs in the given array to use affine coordinates. */ int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx) { size_t i; for (i = 0; i < num; i++) { if (!group->meth->make_affine(group, points[i], ctx)) return 0; } return 1; } /* Wrapper to simple binary polynomial field multiplication implementation. */ int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); } /* Wrapper to simple binary polynomial field squaring implementation. */ int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) { return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); } /* Wrapper to simple binary polynomial field division implementation. */ int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { return BN_GF2m_mod_div(r, a, b, group->field, ctx); } #endif