blob: 39403362e4b47c7a582563e04f59e167125120c8 [file] [log] [blame]
/* Copyright (c) 2020, Google Inc.
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
#include <openssl/ec.h>
#include <openssl/digest.h>
#include <openssl/err.h>
#include <openssl/nid.h>
#include <assert.h>
#include "internal.h"
#include "../fipsmodule/bn/internal.h"
#include "../fipsmodule/ec/internal.h"
#include "../internal.h"
// This file implements hash-to-curve, as described in
// draft-irtf-cfrg-hash-to-curve-16.
//
// This hash-to-curve implementation is written generically with the
// expectation that we will eventually wish to support other curves. If it
// becomes a performance bottleneck, some possible optimizations by
// specializing it to the curve:
//
// - Rather than using a generic |felem_exp|, specialize the exponentation to
// c2 with a faster addition chain.
//
// - |felem_mul| and |felem_sqr| are indirect calls to generic Montgomery
// code. Given the few curves, we could specialize
// |map_to_curve_simple_swu|. But doing this reasonably without duplicating
// code in C is difficult. (C++ templates would be useful here.)
//
// - P-521's Z and c2 have small power-of-two absolute values. We could save
// two multiplications in SSWU. (Other curves have reasonable values of Z
// and inconvenient c2.) This is unlikely to be worthwhile without C++
// templates to make specializing more convenient.
// expand_message_xmd implements the operation described in section 5.3.1 of
// draft-irtf-cfrg-hash-to-curve-16. It returns one on success and zero on
// error.
static int expand_message_xmd(const EVP_MD *md, uint8_t *out, size_t out_len,
const uint8_t *msg, size_t msg_len,
const uint8_t *dst, size_t dst_len) {
// See https://github.com/cfrg/draft-irtf-cfrg-hash-to-curve/issues/352
if (dst_len == 0) {
OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return 0;
}
int ret = 0;
const size_t block_size = EVP_MD_block_size(md);
const size_t md_size = EVP_MD_size(md);
EVP_MD_CTX ctx;
EVP_MD_CTX_init(&ctx);
// Long DSTs are hashed down to size. See section 5.3.3.
static_assert(EVP_MAX_MD_SIZE < 256, "hashed DST still too large");
uint8_t dst_buf[EVP_MAX_MD_SIZE];
if (dst_len >= 256) {
static const char kPrefix[] = "H2C-OVERSIZE-DST-";
if (!EVP_DigestInit_ex(&ctx, md, NULL) ||
!EVP_DigestUpdate(&ctx, kPrefix, sizeof(kPrefix) - 1) ||
!EVP_DigestUpdate(&ctx, dst, dst_len) ||
!EVP_DigestFinal_ex(&ctx, dst_buf, NULL)) {
goto err;
}
dst = dst_buf;
dst_len = md_size;
}
uint8_t dst_len_u8 = (uint8_t)dst_len;
// Compute b_0.
static const uint8_t kZeros[EVP_MAX_MD_BLOCK_SIZE] = {0};
// If |out_len| exceeds 16 bits then |i| will wrap below causing an error to
// be returned. This depends on the static assert above.
uint8_t l_i_b_str_zero[3] = {out_len >> 8, out_len, 0};
uint8_t b_0[EVP_MAX_MD_SIZE];
if (!EVP_DigestInit_ex(&ctx, md, NULL) ||
!EVP_DigestUpdate(&ctx, kZeros, block_size) ||
!EVP_DigestUpdate(&ctx, msg, msg_len) ||
!EVP_DigestUpdate(&ctx, l_i_b_str_zero, sizeof(l_i_b_str_zero)) ||
!EVP_DigestUpdate(&ctx, dst, dst_len) ||
!EVP_DigestUpdate(&ctx, &dst_len_u8, 1) ||
!EVP_DigestFinal_ex(&ctx, b_0, NULL)) {
goto err;
}
uint8_t b_i[EVP_MAX_MD_SIZE];
uint8_t i = 1;
while (out_len > 0) {
if (i == 0) {
// Input was too large.
OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
goto err;
}
if (i > 1) {
for (size_t j = 0; j < md_size; j++) {
b_i[j] ^= b_0[j];
}
} else {
OPENSSL_memcpy(b_i, b_0, md_size);
}
if (!EVP_DigestInit_ex(&ctx, md, NULL) ||
!EVP_DigestUpdate(&ctx, b_i, md_size) ||
!EVP_DigestUpdate(&ctx, &i, 1) ||
!EVP_DigestUpdate(&ctx, dst, dst_len) ||
!EVP_DigestUpdate(&ctx, &dst_len_u8, 1) ||
!EVP_DigestFinal_ex(&ctx, b_i, NULL)) {
goto err;
}
size_t todo = out_len >= md_size ? md_size : out_len;
OPENSSL_memcpy(out, b_i, todo);
out += todo;
out_len -= todo;
i++;
}
ret = 1;
err:
EVP_MD_CTX_cleanup(&ctx);
return ret;
}
// num_bytes_to_derive determines the number of bytes to derive when hashing to
// a number modulo |modulus|. See the hash_to_field operation defined in
// section 5.2 of draft-irtf-cfrg-hash-to-curve-16.
static int num_bytes_to_derive(size_t *out, const BIGNUM *modulus, unsigned k) {
size_t bits = BN_num_bits(modulus);
size_t L = (bits + k + 7) / 8;
// We require 2^(8*L) < 2^(2*bits - 2) <= n^2 so to fit in bounds for
// |felem_reduce| and |ec_scalar_reduce|. All defined hash-to-curve suites
// define |k| to be well under this bound. (|k| is usually around half of
// |p_bits|.)
if (L * 8 >= 2 * bits - 2 ||
L > 2 * EC_MAX_BYTES) {
assert(0);
OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
return 0;
}
*out = L;
return 1;
}
// big_endian_to_words decodes |in| as a big-endian integer and writes the
// result to |out|. |num_words| must be large enough to contain the output.
static void big_endian_to_words(BN_ULONG *out, size_t num_words,
const uint8_t *in, size_t len) {
assert(len <= num_words * sizeof(BN_ULONG));
// Ensure any excess bytes are zeroed.
OPENSSL_memset(out, 0, num_words * sizeof(BN_ULONG));
uint8_t *out_u8 = (uint8_t *)out;
for (size_t i = 0; i < len; i++) {
out_u8[len - 1 - i] = in[i];
}
}
// hash_to_field implements the operation described in section 5.2
// of draft-irtf-cfrg-hash-to-curve-16, with count = 2. |k| is the security
// factor.
static int hash_to_field2(const EC_GROUP *group, const EVP_MD *md,
EC_FELEM *out1, EC_FELEM *out2, const uint8_t *dst,
size_t dst_len, unsigned k, const uint8_t *msg,
size_t msg_len) {
size_t L;
uint8_t buf[4 * EC_MAX_BYTES];
if (!num_bytes_to_derive(&L, &group->field, k) ||
!expand_message_xmd(md, buf, 2 * L, msg, msg_len, dst, dst_len)) {
return 0;
}
BN_ULONG words[2 * EC_MAX_WORDS];
size_t num_words = 2 * group->field.width;
big_endian_to_words(words, num_words, buf, L);
group->meth->felem_reduce(group, out1, words, num_words);
big_endian_to_words(words, num_words, buf + L, L);
group->meth->felem_reduce(group, out2, words, num_words);
return 1;
}
// hash_to_scalar behaves like |hash_to_field2| but returns a value modulo the
// group order rather than a field element. |k| is the security factor.
static int hash_to_scalar(const EC_GROUP *group, const EVP_MD *md,
EC_SCALAR *out, const uint8_t *dst, size_t dst_len,
unsigned k, const uint8_t *msg, size_t msg_len) {
size_t L;
uint8_t buf[EC_MAX_BYTES * 2];
if (!num_bytes_to_derive(&L, &group->order, k) ||
!expand_message_xmd(md, buf, L, msg, msg_len, dst, dst_len)) {
return 0;
}
BN_ULONG words[2 * EC_MAX_WORDS];
size_t num_words = 2 * group->order.width;
big_endian_to_words(words, num_words, buf, L);
ec_scalar_reduce(group, out, words, num_words);
return 1;
}
static inline void mul_A(const EC_GROUP *group, EC_FELEM *out,
const EC_FELEM *in) {
assert(group->a_is_minus3);
EC_FELEM tmp;
ec_felem_add(group, &tmp, in, in); // tmp = 2*in
ec_felem_add(group, &tmp, &tmp, &tmp); // tmp = 4*in
ec_felem_sub(group, out, in, &tmp); // out = -3*in
}
// sgn0 implements the operation described in section 4.1.2 of
// draft-irtf-cfrg-hash-to-curve-16.
static BN_ULONG sgn0(const EC_GROUP *group, const EC_FELEM *a) {
uint8_t buf[EC_MAX_BYTES];
size_t len;
ec_felem_to_bytes(group, buf, &len, a);
return buf[len - 1] & 1;
}
OPENSSL_UNUSED static int is_3mod4(const EC_GROUP *group) {
return group->field.width > 0 && (group->field.d[0] & 3) == 3;
}
// sqrt_ratio_3mod4 implements the operation described in appendix F.2.1.2
// of draft-irtf-cfrg-hash-to-curve-16.
static BN_ULONG sqrt_ratio_3mod4(const EC_GROUP *group, const EC_FELEM *Z,
const BN_ULONG *c1, size_t num_c1,
const EC_FELEM *c2, EC_FELEM *out_y,
const EC_FELEM *u, const EC_FELEM *v) {
assert(is_3mod4(group));
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 tv1, tv2, tv3, y1, y2;
felem_sqr(group, &tv1, v); // 1. tv1 = v^2
felem_mul(group, &tv2, u, v); // 2. tv2 = u * v
felem_mul(group, &tv1, &tv1, &tv2); // 3. tv1 = tv1 * tv2
group->meth->felem_exp(group, &y1, &tv1, c1, num_c1); // 4. y1 = tv1^c1
felem_mul(group, &y1, &y1, &tv2); // 5. y1 = y1 * tv2
felem_mul(group, &y2, &y1, c2); // 6. y2 = y1 * c2
felem_sqr(group, &tv3, &y1); // 7. tv3 = y1^2
felem_mul(group, &tv3, &tv3, v); // 8. tv3 = tv3 * v
// 9. isQR = tv3 == u
// 10. y = CMOV(y2, y1, isQR)
// 11. return (isQR, y)
//
// Note the specification's CMOV function and our |ec_felem_select| have the
// opposite argument order.
ec_felem_sub(group, &tv1, &tv3, u);
const BN_ULONG isQR = ~ec_felem_non_zero_mask(group, &tv1);
ec_felem_select(group, out_y, isQR, &y1, &y2);
return isQR;
}
// map_to_curve_simple_swu implements the operation described in section 6.6.2
// of draft-irtf-cfrg-hash-to-curve-16, using the straight-line implementation
// in appendix F.2.
static void map_to_curve_simple_swu(const EC_GROUP *group, const EC_FELEM *Z,
const BN_ULONG *c1, size_t num_c1,
const EC_FELEM *c2, EC_JACOBIAN *out,
const EC_FELEM *u) {
// This function requires the prime be 3 mod 4, and that A = -3.
assert(is_3mod4(group));
assert(group->a_is_minus3);
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 tv1, tv2, tv3, tv4, tv5, tv6, x, y, y1;
felem_sqr(group, &tv1, u); // 1. tv1 = u^2
felem_mul(group, &tv1, Z, &tv1); // 2. tv1 = Z * tv1
felem_sqr(group, &tv2, &tv1); // 3. tv2 = tv1^2
ec_felem_add(group, &tv2, &tv2, &tv1); // 4. tv2 = tv2 + tv1
ec_felem_add(group, &tv3, &tv2, &group->one); // 5. tv3 = tv2 + 1
felem_mul(group, &tv3, &group->b, &tv3); // 6. tv3 = B * tv3
// 7. tv4 = CMOV(Z, -tv2, tv2 != 0)
const BN_ULONG tv2_non_zero = ec_felem_non_zero_mask(group, &tv2);
ec_felem_neg(group, &tv4, &tv2);
ec_felem_select(group, &tv4, tv2_non_zero, &tv4, Z);
mul_A(group, &tv4, &tv4); // 8. tv4 = A * tv4
felem_sqr(group, &tv2, &tv3); // 9. tv2 = tv3^2
felem_sqr(group, &tv6, &tv4); // 10. tv6 = tv4^2
mul_A(group, &tv5, &tv6); // 11. tv5 = A * tv6
ec_felem_add(group, &tv2, &tv2, &tv5); // 12. tv2 = tv2 + tv5
felem_mul(group, &tv2, &tv2, &tv3); // 13. tv2 = tv2 * tv3
felem_mul(group, &tv6, &tv6, &tv4); // 14. tv6 = tv6 * tv4
felem_mul(group, &tv5, &group->b, &tv6); // 15. tv5 = B * tv6
ec_felem_add(group, &tv2, &tv2, &tv5); // 16. tv2 = tv2 + tv5
felem_mul(group, &x, &tv1, &tv3); // 17. x = tv1 * tv3
// 18. (is_gx1_square, y1) = sqrt_ratio(tv2, tv6)
const BN_ULONG is_gx1_square =
sqrt_ratio_3mod4(group, Z, c1, num_c1, c2, &y1, &tv2, &tv6);
felem_mul(group, &y, &tv1, u); // 19. y = tv1 * u
felem_mul(group, &y, &y, &y1); // 20. y = y * y1
// 21. x = CMOV(x, tv3, is_gx1_square)
ec_felem_select(group, &x, is_gx1_square, &tv3, &x);
// 22. y = CMOV(y, y1, is_gx1_square)
ec_felem_select(group, &y, is_gx1_square, &y1, &y);
// 23. e1 = sgn0(u) == sgn0(y)
BN_ULONG sgn0_u = sgn0(group, u);
BN_ULONG sgn0_y = sgn0(group, &y);
BN_ULONG not_e1 = sgn0_u ^ sgn0_y;
not_e1 = ((BN_ULONG)0) - not_e1;
// 24. y = CMOV(-y, y, e1)
ec_felem_neg(group, &tv1, &y);
ec_felem_select(group, &y, not_e1, &tv1, &y);
// 25. x = x / tv4
//
// Our output is in projective coordinates, so rather than inverting |tv4|
// now, represent (x / tv4, y) as (x * tv4, y * tv4^3, tv4). This is much more
// efficient if the caller will do further computation on the output. (If the
// caller will immediately convert to affine coordinates, it is slightly less
// efficient, but only by a few field multiplications.)
felem_mul(group, &out->X, &x, &tv4);
felem_mul(group, &out->Y, &y, &tv6);
out->Z = tv4;
}
static int hash_to_curve(const EC_GROUP *group, const EVP_MD *md,
const EC_FELEM *Z, const EC_FELEM *c2, unsigned k,
EC_JACOBIAN *out, const uint8_t *dst, size_t dst_len,
const uint8_t *msg, size_t msg_len) {
EC_FELEM u0, u1;
if (!hash_to_field2(group, md, &u0, &u1, dst, dst_len, k, msg, msg_len)) {
return 0;
}
// Compute |c1| = (p - 3) / 4.
BN_ULONG c1[EC_MAX_WORDS];
size_t num_c1 = group->field.width;
if (!bn_copy_words(c1, num_c1, &group->field)) {
return 0;
}
bn_rshift_words(c1, c1, /*shift=*/2, /*num=*/num_c1);
EC_JACOBIAN Q0, Q1;
map_to_curve_simple_swu(group, Z, c1, num_c1, c2, &Q0, &u0);
map_to_curve_simple_swu(group, Z, c1, num_c1, c2, &Q1, &u1);
group->meth->add(group, out, &Q0, &Q1); // R = Q0 + Q1
// All our curves have cofactor one, so |clear_cofactor| is a no-op.
return 1;
}
static int felem_from_u8(const EC_GROUP *group, EC_FELEM *out, uint8_t a) {
uint8_t bytes[EC_MAX_BYTES] = {0};
size_t len = BN_num_bytes(&group->field);
bytes[len - 1] = a;
return ec_felem_from_bytes(group, out, bytes, len);
}
// kP256Sqrt10 is sqrt(10) in P-256's field. It was computed as follows in
// python3:
//
// p = 2**256 - 2**224 + 2**192 + 2**96 - 1
// c2 = pow(10, (p+1)//4, p)
// assert pow(c2, 2, p) == 10
// ", ".join("0x%02x" % b for b in c2.to_bytes(256//8, 'big'))
static const uint8_t kP256Sqrt10[] = {
0xda, 0x53, 0x8e, 0x3b, 0xe1, 0xd8, 0x9b, 0x99, 0xc9, 0x78, 0xfc,
0x67, 0x51, 0x80, 0xaa, 0xb2, 0x7b, 0x8d, 0x1f, 0xf8, 0x4c, 0x55,
0xd5, 0xb6, 0x2c, 0xcd, 0x34, 0x27, 0xe4, 0x33, 0xc4, 0x7f};
// kP384Sqrt12 is sqrt(12) in P-384's field. It was computed as follows in
// python3:
//
// p = 2**384 - 2**128 - 2**96 + 2**32 - 1
// c2 = pow(12, (p+1)//4, p)
// assert pow(c2, 2, p) == 12
// ", ".join("0x%02x" % b for b in c2.to_bytes(384//8, 'big'))
static const uint8_t kP384Sqrt12[] = {
0x2a, 0xcc, 0xb4, 0xa6, 0x56, 0xb0, 0x24, 0x9c, 0x71, 0xf0, 0x50, 0x0e,
0x83, 0xda, 0x2f, 0xdd, 0x7f, 0x98, 0xe3, 0x83, 0xd6, 0x8b, 0x53, 0x87,
0x1f, 0x87, 0x2f, 0xcb, 0x9c, 0xcb, 0x80, 0xc5, 0x3c, 0x0d, 0xe1, 0xf8,
0xa8, 0x0f, 0x7e, 0x19, 0x14, 0xe2, 0xec, 0x69, 0xf5, 0xa6, 0x26, 0xb3};
int ec_hash_to_curve_p256_xmd_sha256_sswu(const EC_GROUP *group,
EC_JACOBIAN *out, const uint8_t *dst,
size_t dst_len, const uint8_t *msg,
size_t msg_len) {
// See section 8.3 of draft-irtf-cfrg-hash-to-curve-16.
if (EC_GROUP_get_curve_name(group) != NID_X9_62_prime256v1) {
OPENSSL_PUT_ERROR(EC, EC_R_GROUP_MISMATCH);
return 0;
}
// Z = -10, c2 = sqrt(10)
EC_FELEM Z, c2;
if (!felem_from_u8(group, &Z, 10) ||
!ec_felem_from_bytes(group, &c2, kP256Sqrt10, sizeof(kP256Sqrt10))) {
return 0;
}
ec_felem_neg(group, &Z, &Z);
return hash_to_curve(group, EVP_sha256(), &Z, &c2, /*k=*/128, out, dst,
dst_len, msg, msg_len);
}
int EC_hash_to_curve_p256_xmd_sha256_sswu(const EC_GROUP *group, EC_POINT *out,
const uint8_t *dst, size_t dst_len,
const uint8_t *msg, size_t msg_len) {
if (EC_GROUP_cmp(group, out->group, NULL) != 0) {
OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
return 0;
}
return ec_hash_to_curve_p256_xmd_sha256_sswu(group, &out->raw, dst, dst_len,
msg, msg_len);
}
int ec_hash_to_curve_p384_xmd_sha384_sswu(const EC_GROUP *group,
EC_JACOBIAN *out, const uint8_t *dst,
size_t dst_len, const uint8_t *msg,
size_t msg_len) {
// See section 8.3 of draft-irtf-cfrg-hash-to-curve-16.
if (EC_GROUP_get_curve_name(group) != NID_secp384r1) {
OPENSSL_PUT_ERROR(EC, EC_R_GROUP_MISMATCH);
return 0;
}
// Z = -12, c2 = sqrt(12)
EC_FELEM Z, c2;
if (!felem_from_u8(group, &Z, 12) ||
!ec_felem_from_bytes(group, &c2, kP384Sqrt12, sizeof(kP384Sqrt12))) {
return 0;
}
ec_felem_neg(group, &Z, &Z);
return hash_to_curve(group, EVP_sha384(), &Z, &c2, /*k=*/192, out, dst,
dst_len, msg, msg_len);
}
int EC_hash_to_curve_p384_xmd_sha384_sswu(const EC_GROUP *group, EC_POINT *out,
const uint8_t *dst, size_t dst_len,
const uint8_t *msg, size_t msg_len) {
if (EC_GROUP_cmp(group, out->group, NULL) != 0) {
OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
return 0;
}
return ec_hash_to_curve_p384_xmd_sha384_sswu(group, &out->raw, dst, dst_len,
msg, msg_len);
}
int ec_hash_to_scalar_p384_xmd_sha384(
const EC_GROUP *group, EC_SCALAR *out, const uint8_t *dst, size_t dst_len,
const uint8_t *msg, size_t msg_len) {
if (EC_GROUP_get_curve_name(group) != NID_secp384r1) {
OPENSSL_PUT_ERROR(EC, EC_R_GROUP_MISMATCH);
return 0;
}
return hash_to_scalar(group, EVP_sha384(), out, dst, dst_len, /*k=*/192, msg,
msg_len);
}
int ec_hash_to_curve_p384_xmd_sha512_sswu_draft07(
const EC_GROUP *group, EC_JACOBIAN *out, const uint8_t *dst,
size_t dst_len, const uint8_t *msg, size_t msg_len) {
// See section 8.3 of draft-irtf-cfrg-hash-to-curve-07.
if (EC_GROUP_get_curve_name(group) != NID_secp384r1) {
OPENSSL_PUT_ERROR(EC, EC_R_GROUP_MISMATCH);
return 0;
}
// Z = -12, c2 = sqrt(12)
EC_FELEM Z, c2;
if (!felem_from_u8(group, &Z, 12) ||
!ec_felem_from_bytes(group, &c2, kP384Sqrt12, sizeof(kP384Sqrt12))) {
return 0;
}
ec_felem_neg(group, &Z, &Z);
return hash_to_curve(group, EVP_sha512(), &Z, &c2, /*k=*/192, out, dst,
dst_len, msg, msg_len);
}
int ec_hash_to_scalar_p384_xmd_sha512_draft07(
const EC_GROUP *group, EC_SCALAR *out, const uint8_t *dst, size_t dst_len,
const uint8_t *msg, size_t msg_len) {
if (EC_GROUP_get_curve_name(group) != NID_secp384r1) {
OPENSSL_PUT_ERROR(EC, EC_R_GROUP_MISMATCH);
return 0;
}
return hash_to_scalar(group, EVP_sha512(), out, dst, dst_len, /*k=*/192, msg,
msg_len);
}