1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357
|
/* Originally written by Bodo Moeller for the OpenSSL project.
* ====================================================================
* Copyright (c) 1998-2005 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).
*
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the OpenSSL open source
* license provided above.
*
* The elliptic curve binary polynomial software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
* Laboratories. */
#include <CNIOBoringSSL_ec.h>
#include <string.h>
#include <CNIOBoringSSL_bn.h>
#include <CNIOBoringSSL_err.h>
#include <CNIOBoringSSL_mem.h>
#include "internal.h"
#include "../../internal.h"
// Most method functions in this file are designed to work with non-trivial
// representations of field elements if necessary (see ecp_mont.c): while
// standard modular addition and subtraction are used, the field_mul and
// field_sqr methods will be used for multiplication, and field_encode and
// field_decode (if defined) will be used for converting between
// representations.
//
// Functions here specifically assume that if a non-trivial representation is
// used, it is a Montgomery representation (i.e. 'encoding' means multiplying
// by some factor R).
int ec_GFp_simple_group_init(EC_GROUP *group) {
BN_init(&group->field);
group->a_is_minus3 = 0;
return 1;
}
void ec_GFp_simple_group_finish(EC_GROUP *group) {
BN_free(&group->field);
}
int ec_GFp_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p,
const BIGNUM *a, const BIGNUM *b,
BN_CTX *ctx) {
// p must be a prime > 3
if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FIELD);
return 0;
}
int ret = 0;
BN_CTX_start(ctx);
BIGNUM *tmp = BN_CTX_get(ctx);
if (tmp == NULL) {
goto err;
}
// group->field
if (!BN_copy(&group->field, p)) {
goto err;
}
BN_set_negative(&group->field, 0);
// Store the field in minimal form, so it can be used with |BN_ULONG| arrays.
bn_set_minimal_width(&group->field);
if (!ec_bignum_to_felem(group, &group->a, a) ||
!ec_bignum_to_felem(group, &group->b, b) ||
!ec_bignum_to_felem(group, &group->one, BN_value_one())) {
goto err;
}
// group->a_is_minus3
if (!BN_copy(tmp, a) ||
!BN_add_word(tmp, 3)) {
goto err;
}
group->a_is_minus3 = (0 == BN_cmp(tmp, &group->field));
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
BIGNUM *b) {
if ((p != NULL && !BN_copy(p, &group->field)) ||
(a != NULL && !ec_felem_to_bignum(group, a, &group->a)) ||
(b != NULL && !ec_felem_to_bignum(group, b, &group->b))) {
return 0;
}
return 1;
}
void ec_GFp_simple_point_init(EC_RAW_POINT *point) {
OPENSSL_memset(&point->X, 0, sizeof(EC_FELEM));
OPENSSL_memset(&point->Y, 0, sizeof(EC_FELEM));
OPENSSL_memset(&point->Z, 0, sizeof(EC_FELEM));
}
void ec_GFp_simple_point_copy(EC_RAW_POINT *dest, const EC_RAW_POINT *src) {
OPENSSL_memcpy(&dest->X, &src->X, sizeof(EC_FELEM));
OPENSSL_memcpy(&dest->Y, &src->Y, sizeof(EC_FELEM));
OPENSSL_memcpy(&dest->Z, &src->Z, sizeof(EC_FELEM));
}
void ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
EC_RAW_POINT *point) {
// Although it is strictly only necessary to zero Z, we zero the entire point
// in case |point| was stack-allocated and yet to be initialized.
ec_GFp_simple_point_init(point);
}
void ec_GFp_simple_invert(const EC_GROUP *group, EC_RAW_POINT *point) {
ec_felem_neg(group, &point->Y, &point->Y);
}
int ec_GFp_simple_is_at_infinity(const EC_GROUP *group,
const EC_RAW_POINT *point) {
return ec_felem_non_zero_mask(group, &point->Z) == 0;
}
int ec_GFp_simple_is_on_curve(const EC_GROUP *group,
const EC_RAW_POINT *point) {
// We have a curve defined by a Weierstrass equation
// y^2 = x^3 + a*x + b.
// The point to consider is given in Jacobian projective coordinates
// where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
// Substituting this and multiplying by Z^6 transforms the above equation
// into
// Y^2 = X^3 + a*X*Z^4 + b*Z^6.
// To test this, we add up the right-hand side in 'rh'.
//
// This function may be used when double-checking the secret result of a point
// multiplication, so we proceed in constant-time.
void (*const felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a,
const EC_FELEM *b) = group->meth->felem_mul;
void (*const felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a) =
group->meth->felem_sqr;
// rh := X^2
EC_FELEM rh;
felem_sqr(group, &rh, &point->X);
EC_FELEM tmp, Z4, Z6;
felem_sqr(group, &tmp, &point->Z);
felem_sqr(group, &Z4, &tmp);
felem_mul(group, &Z6, &Z4, &tmp);
// rh := rh + a*Z^4
if (group->a_is_minus3) {
ec_felem_add(group, &tmp, &Z4, &Z4);
ec_felem_add(group, &tmp, &tmp, &Z4);
ec_felem_sub(group, &rh, &rh, &tmp);
} else {
felem_mul(group, &tmp, &Z4, &group->a);
ec_felem_add(group, &rh, &rh, &tmp);
}
// rh := (rh + a*Z^4)*X
felem_mul(group, &rh, &rh, &point->X);
// rh := rh + b*Z^6
felem_mul(group, &tmp, &group->b, &Z6);
ec_felem_add(group, &rh, &rh, &tmp);
// 'lh' := Y^2
felem_sqr(group, &tmp, &point->Y);
ec_felem_sub(group, &tmp, &tmp, &rh);
BN_ULONG not_equal = ec_felem_non_zero_mask(group, &tmp);
// If Z = 0, the point is infinity, which is always on the curve.
BN_ULONG not_infinity = ec_felem_non_zero_mask(group, &point->Z);
return 1 & ~(not_infinity & not_equal);
}
int ec_GFp_simple_points_equal(const EC_GROUP *group, const EC_RAW_POINT *a,
const EC_RAW_POINT *b) {
// This function is implemented in constant-time for two reasons. First,
// although EC points are usually public, their Jacobian Z coordinates may be
// secret, or at least are not obviously public. Second, more complex
// protocols will sometimes manipulate secret points.
//
// This does mean that we pay a 6M+2S Jacobian comparison when comparing two
// publicly affine points costs no field operations at all. If needed, we can
// restore this optimization by keeping better track of affine vs. Jacobian
// forms. See https://crbug.com/boringssl/326.
// If neither |a| or |b| is infinity, we have to decide whether
// (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
// or equivalently, whether
// (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
void (*const felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a,
const EC_FELEM *b) = group->meth->felem_mul;
void (*const felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a) =
group->meth->felem_sqr;
EC_FELEM tmp1, tmp2, Za23, Zb23;
felem_sqr(group, &Zb23, &b->Z); // Zb23 = Z_b^2
felem_mul(group, &tmp1, &a->X, &Zb23); // tmp1 = X_a * Z_b^2
felem_sqr(group, &Za23, &a->Z); // Za23 = Z_a^2
felem_mul(group, &tmp2, &b->X, &Za23); // tmp2 = X_b * Z_a^2
ec_felem_sub(group, &tmp1, &tmp1, &tmp2);
const BN_ULONG x_not_equal = ec_felem_non_zero_mask(group, &tmp1);
felem_mul(group, &Zb23, &Zb23, &b->Z); // Zb23 = Z_b^3
felem_mul(group, &tmp1, &a->Y, &Zb23); // tmp1 = Y_a * Z_b^3
felem_mul(group, &Za23, &Za23, &a->Z); // Za23 = Z_a^3
felem_mul(group, &tmp2, &b->Y, &Za23); // tmp2 = Y_b * Z_a^3
ec_felem_sub(group, &tmp1, &tmp1, &tmp2);
const BN_ULONG y_not_equal = ec_felem_non_zero_mask(group, &tmp1);
const BN_ULONG x_and_y_equal = ~(x_not_equal | y_not_equal);
const BN_ULONG a_not_infinity = ec_felem_non_zero_mask(group, &a->Z);
const BN_ULONG b_not_infinity = ec_felem_non_zero_mask(group, &b->Z);
const BN_ULONG a_and_b_infinity = ~(a_not_infinity | b_not_infinity);
const BN_ULONG equal =
a_and_b_infinity | (a_not_infinity & b_not_infinity & x_and_y_equal);
return equal & 1;
}
int ec_affine_jacobian_equal(const EC_GROUP *group, const EC_AFFINE *a,
const EC_RAW_POINT *b) {
// If |b| is not infinity, we have to decide whether
// (X_a, Y_a) = (X_b/Z_b^2, Y_b/Z_b^3),
// or equivalently, whether
// (X_a*Z_b^2, Y_a*Z_b^3) = (X_b, Y_b).
void (*const felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a,
const EC_FELEM *b) = group->meth->felem_mul;
void (*const felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a) =
group->meth->felem_sqr;
EC_FELEM tmp, Zb2;
felem_sqr(group, &Zb2, &b->Z); // Zb2 = Z_b^2
felem_mul(group, &tmp, &a->X, &Zb2); // tmp = X_a * Z_b^2
ec_felem_sub(group, &tmp, &tmp, &b->X);
const BN_ULONG x_not_equal = ec_felem_non_zero_mask(group, &tmp);
felem_mul(group, &tmp, &a->Y, &Zb2); // tmp = Y_a * Z_b^2
felem_mul(group, &tmp, &tmp, &b->Z); // tmp = Y_a * Z_b^3
ec_felem_sub(group, &tmp, &tmp, &b->Y);
const BN_ULONG y_not_equal = ec_felem_non_zero_mask(group, &tmp);
const BN_ULONG x_and_y_equal = ~(x_not_equal | y_not_equal);
const BN_ULONG b_not_infinity = ec_felem_non_zero_mask(group, &b->Z);
const BN_ULONG equal = b_not_infinity & x_and_y_equal;
return equal & 1;
}
int ec_GFp_simple_cmp_x_coordinate(const EC_GROUP *group, const EC_RAW_POINT *p,
const EC_SCALAR *r) {
if (ec_GFp_simple_is_at_infinity(group, p)) {
// |ec_get_x_coordinate_as_scalar| will check this internally, but this way
// we do not push to the error queue.
return 0;
}
EC_SCALAR x;
return ec_get_x_coordinate_as_scalar(group, &x, p) &&
ec_scalar_equal_vartime(group, &x, r);
}
void ec_GFp_simple_felem_to_bytes(const EC_GROUP *group, uint8_t *out,
size_t *out_len, const EC_FELEM *in) {
size_t len = BN_num_bytes(&group->field);
for (size_t i = 0; i < len; i++) {
out[i] = in->bytes[len - 1 - i];
}
*out_len = len;
}
int ec_GFp_simple_felem_from_bytes(const EC_GROUP *group, EC_FELEM *out,
const uint8_t *in, size_t len) {
if (len != BN_num_bytes(&group->field)) {
OPENSSL_PUT_ERROR(EC, EC_R_DECODE_ERROR);
return 0;
}
OPENSSL_memset(out, 0, sizeof(EC_FELEM));
for (size_t i = 0; i < len; i++) {
out->bytes[i] = in[len - 1 - i];
}
if (!bn_less_than_words(out->words, group->field.d, group->field.width)) {
OPENSSL_PUT_ERROR(EC, EC_R_DECODE_ERROR);
return 0;
}
return 1;
}
|