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boringssl / boringssl / 6f13380d27835e70ec7caf807da7a1f239b10da6 / . / crypto / trust_token / pmbtoken.c
blob: 93a0191f3a3dc18ea6d7446592b2f71a655d0224 [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/trust_token.h>
#include <openssl/bn.h>
#include <openssl/bytestring.h>
#include <openssl/ec.h>
#include <openssl/err.h>
#include <openssl/mem.h>
#include <openssl/nid.h>
#include <openssl/rand.h>
#include <openssl/sha.h>
#include "../ec_extra/internal.h"
#include "../fipsmodule/bn/internal.h"
#include "../fipsmodule/ec/internal.h"
#include "internal.h"
typedef int (*hash_t_func_t)(const EC_GROUP *group, EC_JACOBIAN *out,
const uint8_t t[TRUST_TOKEN_NONCE_SIZE]);
typedef int (*hash_s_func_t)(const EC_GROUP *group, EC_JACOBIAN *out,
const EC_AFFINE *t,
const uint8_t s[TRUST_TOKEN_NONCE_SIZE]);
typedef int (*hash_c_func_t)(const EC_GROUP *group, EC_SCALAR *out,
uint8_t *buf, size_t len);
typedef int (*hash_to_scalar_func_t)(const EC_GROUP *group, EC_SCALAR *out,
uint8_t *buf, size_t len);
typedef struct {
const EC_GROUP *group;
EC_PRECOMP g_precomp;
EC_PRECOMP h_precomp;
EC_JACOBIAN h;
// hash_t implements the H_t operation in PMBTokens. It returns one on success
// and zero on error.
hash_t_func_t hash_t;
// hash_s implements the H_s operation in PMBTokens. It returns one on success
// and zero on error.
hash_s_func_t hash_s;
// hash_c implements the H_c operation in PMBTokens. It returns one on success
// and zero on error.
hash_c_func_t hash_c;
// hash_to_scalar implements the HashToScalar operation for PMBTokens. It
// returns one on success and zero on error.
hash_to_scalar_func_t hash_to_scalar;
int prefix_point : 1;
} PMBTOKEN_METHOD;
static const uint8_t kDefaultAdditionalData[32] = {0};
static int pmbtoken_init_method(PMBTOKEN_METHOD *method, int curve_nid,
const uint8_t *h_bytes, size_t h_len,
hash_t_func_t hash_t, hash_s_func_t hash_s,
hash_c_func_t hash_c,
hash_to_scalar_func_t hash_to_scalar,
int prefix_point) {
method->group = EC_GROUP_new_by_curve_name(curve_nid);
if (method->group == NULL) {
return 0;
}
method->hash_t = hash_t;
method->hash_s = hash_s;
method->hash_c = hash_c;
method->hash_to_scalar = hash_to_scalar;
method->prefix_point = prefix_point;
EC_AFFINE h;
if (!ec_point_from_uncompressed(method->group, &h, h_bytes, h_len)) {
return 0;
}
ec_affine_to_jacobian(method->group, &method->h, &h);
if (!ec_init_precomp(method->group, &method->g_precomp,
&method->group->generator->raw) ||
!ec_init_precomp(method->group, &method->h_precomp, &method->h)) {
return 0;
}
return 1;
}
static int derive_scalar_from_secret(const PMBTOKEN_METHOD *method,
EC_SCALAR *out, const uint8_t *secret,
size_t secret_len, uint8_t scalar_id) {
static const uint8_t kKeygenLabel[] = "TrustTokenPMBTokenKeyGen";
int ok = 0;
CBB cbb;
CBB_zero(&cbb);
uint8_t *buf = NULL;
size_t len;
if (!CBB_init(&cbb, 0) ||
!CBB_add_bytes(&cbb, kKeygenLabel, sizeof(kKeygenLabel)) ||
!CBB_add_u8(&cbb, scalar_id) ||
!CBB_add_bytes(&cbb, secret, secret_len) ||
!CBB_finish(&cbb, &buf, &len) ||
!method->hash_to_scalar(method->group, out, buf, len)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_KEYGEN_FAILURE);
goto err;
}
ok = 1;
err:
CBB_cleanup(&cbb);
OPENSSL_free(buf);
return ok;
}
static int point_to_cbb(CBB *out, const EC_GROUP *group,
const EC_AFFINE *point) {
size_t len = ec_point_byte_len(group, POINT_CONVERSION_UNCOMPRESSED);
if (len == 0) {
return 0;
}
uint8_t *p;
return CBB_add_space(out, &p, len) &&
ec_point_to_bytes(group, point, POINT_CONVERSION_UNCOMPRESSED, p,
len) == len;
}
static int cbb_add_prefixed_point(CBB *out, const EC_GROUP *group,
const EC_AFFINE *point, int prefix_point) {
if (prefix_point) {
CBB child;
if (!CBB_add_u16_length_prefixed(out, &child) ||
!point_to_cbb(&child, group, point) ||
!CBB_flush(out)) {
return 0;
}
} else {
if (!point_to_cbb(out, group, point) ||
!CBB_flush(out)) {
return 0;
}
}
return 1;
}
static int cbs_get_prefixed_point(CBS *cbs, const EC_GROUP *group,
EC_AFFINE *out, int prefix_point) {
CBS child;
if (prefix_point) {
if (!CBS_get_u16_length_prefixed(cbs, &child)) {
return 0;
}
} else {
size_t plen = 1 + 2 * BN_num_bytes(&group->field);
if (!CBS_get_bytes(cbs, &child, plen)) {
return 0;
}
}
if (!ec_point_from_uncompressed(group, out, CBS_data(&child),
CBS_len(&child))) {
return 0;
}
return 1;
}
static int mul_public_3(const EC_GROUP *group, EC_JACOBIAN *out,
const EC_JACOBIAN *p0, const EC_SCALAR *scalar0,
const EC_JACOBIAN *p1, const EC_SCALAR *scalar1,
const EC_JACOBIAN *p2, const EC_SCALAR *scalar2) {
EC_JACOBIAN points[3] = {*p0, *p1, *p2};
EC_SCALAR scalars[3] = {*scalar0, *scalar1, *scalar2};
return ec_point_mul_scalar_public_batch(group, out, /*g_scalar=*/NULL, points,
scalars, 3);
}
static int pmbtoken_compute_keys(const PMBTOKEN_METHOD *method,
CBB *out_private, CBB *out_public,
const EC_SCALAR *x0, const EC_SCALAR *y0,
const EC_SCALAR *x1, const EC_SCALAR *y1,
const EC_SCALAR *xs, const EC_SCALAR *ys) {
const EC_GROUP *group = method->group;
EC_JACOBIAN pub[3];
if (!ec_point_mul_scalar_precomp(group, &pub[0], &method->g_precomp,
x0, &method->h_precomp, y0, NULL, NULL) ||
!ec_point_mul_scalar_precomp(group, &pub[1], &method->g_precomp,
x1, &method->h_precomp, y1, NULL, NULL) ||
!ec_point_mul_scalar_precomp(method->group, &pub[2], &method->g_precomp,
xs, &method->h_precomp, ys, NULL, NULL)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_KEYGEN_FAILURE);
return 0;
}
const EC_SCALAR *scalars[] = {x0, y0, x1, y1, xs, ys};
size_t scalar_len = BN_num_bytes(EC_GROUP_get0_order(group));
for (size_t i = 0; i < OPENSSL_ARRAY_SIZE(scalars); i++) {
uint8_t *buf;
if (!CBB_add_space(out_private, &buf, scalar_len)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_BUFFER_TOO_SMALL);
return 0;
}
ec_scalar_to_bytes(group, buf, &scalar_len, scalars[i]);
}
EC_AFFINE pub_affine[3];
if (!ec_jacobian_to_affine_batch(group, pub_affine, pub, 3)) {
return 0;
}
if (!cbb_add_prefixed_point(out_public, group, &pub_affine[0],
method->prefix_point) ||
!cbb_add_prefixed_point(out_public, group, &pub_affine[1],
method->prefix_point) ||
!cbb_add_prefixed_point(out_public, group, &pub_affine[2],
method->prefix_point)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_BUFFER_TOO_SMALL);
return 0;
}
return 1;
}
static int pmbtoken_generate_key(const PMBTOKEN_METHOD *method,
CBB *out_private, CBB *out_public) {
EC_SCALAR x0, y0, x1, y1, xs, ys;
if (!ec_random_nonzero_scalar(method->group, &x0, kDefaultAdditionalData) ||
!ec_random_nonzero_scalar(method->group, &y0, kDefaultAdditionalData) ||
!ec_random_nonzero_scalar(method->group, &x1, kDefaultAdditionalData) ||
!ec_random_nonzero_scalar(method->group, &y1, kDefaultAdditionalData) ||
!ec_random_nonzero_scalar(method->group, &xs, kDefaultAdditionalData) ||
!ec_random_nonzero_scalar(method->group, &ys, kDefaultAdditionalData)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_KEYGEN_FAILURE);
return 0;
}
return pmbtoken_compute_keys(method, out_private, out_public, &x0, &y0, &x1,
&y1, &xs, &ys);
}
static int pmbtoken_derive_key_from_secret(const PMBTOKEN_METHOD *method,
CBB *out_private, CBB *out_public,
const uint8_t *secret,
size_t secret_len) {
EC_SCALAR x0, y0, x1, y1, xs, ys;
if (!derive_scalar_from_secret(method, &x0, secret, secret_len, 0) ||
!derive_scalar_from_secret(method, &y0, secret, secret_len, 1) ||
!derive_scalar_from_secret(method, &x1, secret, secret_len, 2) ||
!derive_scalar_from_secret(method, &y1, secret, secret_len, 3) ||
!derive_scalar_from_secret(method, &xs, secret, secret_len, 4) ||
!derive_scalar_from_secret(method, &ys, secret, secret_len, 5)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_KEYGEN_FAILURE);
return 0;
}
return pmbtoken_compute_keys(method, out_private, out_public, &x0, &y0, &x1,
&y1, &xs, &ys);
}
static int pmbtoken_client_key_from_bytes(const PMBTOKEN_METHOD *method,
TRUST_TOKEN_CLIENT_KEY *key,
const uint8_t *in, size_t len) {
CBS cbs;
CBS_init(&cbs, in, len);
if (!cbs_get_prefixed_point(&cbs, method->group, &key->pub0,
method->prefix_point) ||
!cbs_get_prefixed_point(&cbs, method->group, &key->pub1,
method->prefix_point) ||
!cbs_get_prefixed_point(&cbs, method->group, &key->pubs,
method->prefix_point) ||
CBS_len(&cbs) != 0) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE);
return 0;
}
return 1;
}
static int pmbtoken_issuer_key_from_bytes(const PMBTOKEN_METHOD *method,
TRUST_TOKEN_ISSUER_KEY *key,
const uint8_t *in, size_t len) {
const EC_GROUP *group = method->group;
CBS cbs, tmp;
CBS_init(&cbs, in, len);
size_t scalar_len = BN_num_bytes(EC_GROUP_get0_order(group));
EC_SCALAR *scalars[] = {&key->x0, &key->y0, &key->x1,
&key->y1, &key->xs, &key->ys};
for (size_t i = 0; i < OPENSSL_ARRAY_SIZE(scalars); i++) {
if (!CBS_get_bytes(&cbs, &tmp, scalar_len) ||
!ec_scalar_from_bytes(group, scalars[i], CBS_data(&tmp),
CBS_len(&tmp))) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE);
return 0;
}
}
// Recompute the public key.
EC_JACOBIAN pub[3];
EC_AFFINE pub_affine[3];
if (!ec_point_mul_scalar_precomp(group, &pub[0], &method->g_precomp, &key->x0,
&method->h_precomp, &key->y0, NULL, NULL) ||
!ec_init_precomp(group, &key->pub0_precomp, &pub[0]) ||
!ec_point_mul_scalar_precomp(group, &pub[1], &method->g_precomp, &key->x1,
&method->h_precomp, &key->y1, NULL, NULL) ||
!ec_init_precomp(group, &key->pub1_precomp, &pub[1]) ||
!ec_point_mul_scalar_precomp(group, &pub[2], &method->g_precomp, &key->xs,
&method->h_precomp, &key->ys, NULL, NULL) ||
!ec_init_precomp(group, &key->pubs_precomp, &pub[2]) ||
!ec_jacobian_to_affine_batch(group, pub_affine, pub, 3)) {
return 0;
}
key->pub0 = pub_affine[0];
key->pub1 = pub_affine[1];
key->pubs = pub_affine[2];
return 1;
}
static STACK_OF(TRUST_TOKEN_PRETOKEN) *pmbtoken_blind(
const PMBTOKEN_METHOD *method, CBB *cbb, size_t count, int include_message,
const uint8_t *msg, size_t msg_len) {
SHA512_CTX hash_ctx;
const EC_GROUP *group = method->group;
STACK_OF(TRUST_TOKEN_PRETOKEN) *pretokens = sk_TRUST_TOKEN_PRETOKEN_new_null();
if (pretokens == NULL) {
goto err;
}
for (size_t i = 0; i < count; i++) {
// Insert |pretoken| into |pretokens| early to simplify error-handling.
TRUST_TOKEN_PRETOKEN *pretoken = OPENSSL_malloc(sizeof(TRUST_TOKEN_PRETOKEN));
if (pretoken == NULL ||
!sk_TRUST_TOKEN_PRETOKEN_push(pretokens, pretoken)) {
TRUST_TOKEN_PRETOKEN_free(pretoken);
goto err;
}
RAND_bytes(pretoken->salt, sizeof(pretoken->salt));
if (include_message) {
assert(SHA512_DIGEST_LENGTH == TRUST_TOKEN_NONCE_SIZE);
SHA512_Init(&hash_ctx);
SHA512_Update(&hash_ctx, pretoken->salt, sizeof(pretoken->salt));
SHA512_Update(&hash_ctx, msg, msg_len);
SHA512_Final(pretoken->t, &hash_ctx);
} else {
OPENSSL_memcpy(pretoken->t, pretoken->salt, TRUST_TOKEN_NONCE_SIZE);
}
// We sample |pretoken->r| in Montgomery form to simplify inverting.
if (!ec_random_nonzero_scalar(group, &pretoken->r,
kDefaultAdditionalData)) {
goto err;
}
EC_SCALAR rinv;
ec_scalar_inv0_montgomery(group, &rinv, &pretoken->r);
// Convert both out of Montgomery form.
ec_scalar_from_montgomery(group, &pretoken->r, &pretoken->r);
ec_scalar_from_montgomery(group, &rinv, &rinv);
EC_JACOBIAN T, Tp;
if (!method->hash_t(group, &T, pretoken->t) ||
!ec_point_mul_scalar(group, &Tp, &T, &rinv) ||
!ec_jacobian_to_affine(group, &pretoken->Tp, &Tp)) {
goto err;
}
if (!cbb_add_prefixed_point(cbb, group, &pretoken->Tp,
method->prefix_point)) {
goto err;
}
}
return pretokens;
err:
sk_TRUST_TOKEN_PRETOKEN_pop_free(pretokens, TRUST_TOKEN_PRETOKEN_free);
return NULL;
}
static int scalar_to_cbb(CBB *out, const EC_GROUP *group,
const EC_SCALAR *scalar) {
uint8_t *buf;
size_t scalar_len = BN_num_bytes(EC_GROUP_get0_order(group));
if (!CBB_add_space(out, &buf, scalar_len)) {
return 0;
}
ec_scalar_to_bytes(group, buf, &scalar_len, scalar);
return 1;
}
static int scalar_from_cbs(CBS *cbs, const EC_GROUP *group, EC_SCALAR *out) {
size_t scalar_len = BN_num_bytes(EC_GROUP_get0_order(group));
CBS tmp;
if (!CBS_get_bytes(cbs, &tmp, scalar_len)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE);
return 0;
}
ec_scalar_from_bytes(group, out, CBS_data(&tmp), CBS_len(&tmp));
return 1;
}
static int hash_c_dleq(const PMBTOKEN_METHOD *method, EC_SCALAR *out,
const EC_AFFINE *X, const EC_AFFINE *T,
const EC_AFFINE *S, const EC_AFFINE *W,
const EC_AFFINE *K0, const EC_AFFINE *K1) {
static const uint8_t kDLEQ2Label[] = "DLEQ2";
int ok = 0;
CBB cbb;
CBB_zero(&cbb);
uint8_t *buf = NULL;
size_t len;
if (!CBB_init(&cbb, 0) ||
!CBB_add_bytes(&cbb, kDLEQ2Label, sizeof(kDLEQ2Label)) ||
!point_to_cbb(&cbb, method->group, X) ||
!point_to_cbb(&cbb, method->group, T) ||
!point_to_cbb(&cbb, method->group, S) ||
!point_to_cbb(&cbb, method->group, W) ||
!point_to_cbb(&cbb, method->group, K0) ||
!point_to_cbb(&cbb, method->group, K1) ||
!CBB_finish(&cbb, &buf, &len) ||
!method->hash_c(method->group, out, buf, len)) {
goto err;
}
ok = 1;
err:
CBB_cleanup(&cbb);
OPENSSL_free(buf);
return ok;
}
static int hash_c_dleqor(const PMBTOKEN_METHOD *method, EC_SCALAR *out,
const EC_AFFINE *X0, const EC_AFFINE *X1,
const EC_AFFINE *T, const EC_AFFINE *S,
const EC_AFFINE *W, const EC_AFFINE *K00,
const EC_AFFINE *K01, const EC_AFFINE *K10,
const EC_AFFINE *K11) {
static const uint8_t kDLEQOR2Label[] = "DLEQOR2";
int ok = 0;
CBB cbb;
CBB_zero(&cbb);
uint8_t *buf = NULL;
size_t len;
if (!CBB_init(&cbb, 0) ||
!CBB_add_bytes(&cbb, kDLEQOR2Label, sizeof(kDLEQOR2Label)) ||
!point_to_cbb(&cbb, method->group, X0) ||
!point_to_cbb(&cbb, method->group, X1) ||
!point_to_cbb(&cbb, method->group, T) ||
!point_to_cbb(&cbb, method->group, S) ||
!point_to_cbb(&cbb, method->group, W) ||
!point_to_cbb(&cbb, method->group, K00) ||
!point_to_cbb(&cbb, method->group, K01) ||
!point_to_cbb(&cbb, method->group, K10) ||
!point_to_cbb(&cbb, method->group, K11) ||
!CBB_finish(&cbb, &buf, &len) ||
!method->hash_c(method->group, out, buf, len)) {
goto err;
}
ok = 1;
err:
CBB_cleanup(&cbb);
OPENSSL_free(buf);
return ok;
}
static int hash_c_batch(const PMBTOKEN_METHOD *method, EC_SCALAR *out,
const CBB *points, size_t index) {
static const uint8_t kDLEQBatchLabel[] = "DLEQ BATCH";
if (index > 0xffff) {
// The protocol supports only two-byte batches.
OPENSSL_PUT_ERROR(TRUST_TOKEN, ERR_R_OVERFLOW);
return 0;
}
int ok = 0;
CBB cbb;
CBB_zero(&cbb);
uint8_t *buf = NULL;
size_t len;
if (!CBB_init(&cbb, 0) ||
!CBB_add_bytes(&cbb, kDLEQBatchLabel, sizeof(kDLEQBatchLabel)) ||
!CBB_add_bytes(&cbb, CBB_data(points), CBB_len(points)) ||
!CBB_add_u16(&cbb, (uint16_t)index) ||
!CBB_finish(&cbb, &buf, &len) ||
!method->hash_c(method->group, out, buf, len)) {
goto err;
}
ok = 1;
err:
CBB_cleanup(&cbb);
OPENSSL_free(buf);
return ok;
}
// The DLEQ2 and DLEQOR2 constructions are described in appendix B of
// https://eprint.iacr.org/2020/072/20200324:214215. DLEQ2 is an instance of
// DLEQOR2 with only one value (n=1).
static int dleq_generate(const PMBTOKEN_METHOD *method, CBB *cbb,
const TRUST_TOKEN_ISSUER_KEY *priv,
const EC_JACOBIAN *T, const EC_JACOBIAN *S,
const EC_JACOBIAN *W, const EC_JACOBIAN *Ws,
uint8_t private_metadata) {
const EC_GROUP *group = method->group;
// We generate a DLEQ proof for the validity token and a DLEQOR2 proof for the
// private metadata token. To allow amortizing Jacobian-to-affine conversions,
// we compute Ki for both proofs first.
enum {
idx_T,
idx_S,
idx_W,
idx_Ws,
idx_Ks0,
idx_Ks1,
idx_Kb0,
idx_Kb1,
idx_Ko0,
idx_Ko1,
num_idx,
};
EC_JACOBIAN jacobians[num_idx];
// Setup the DLEQ proof.
EC_SCALAR ks0, ks1;
if (// ks0, ks1 <- Zp
!ec_random_nonzero_scalar(group, &ks0, kDefaultAdditionalData) ||
!ec_random_nonzero_scalar(group, &ks1, kDefaultAdditionalData) ||
// Ks = ks0*(G;T) + ks1*(H;S)
!ec_point_mul_scalar_precomp(group, &jacobians[idx_Ks0],
&method->g_precomp, &ks0, &method->h_precomp,
&ks1, NULL, NULL) ||
!ec_point_mul_scalar_batch(group, &jacobians[idx_Ks1], T, &ks0, S, &ks1,
NULL, NULL)) {
return 0;
}
// Setup the DLEQOR proof. First, select values of xb, yb (keys corresponding
// to the private metadata value) and pubo (public key corresponding to the
// other value) in constant time.
BN_ULONG mask = ((BN_ULONG)0) - (private_metadata & 1);
EC_PRECOMP pubo_precomp;
EC_SCALAR xb, yb;
ec_scalar_select(group, &xb, mask, &priv->x1, &priv->x0);
ec_scalar_select(group, &yb, mask, &priv->y1, &priv->y0);
ec_precomp_select(group, &pubo_precomp, mask, &priv->pub0_precomp,
&priv->pub1_precomp);
EC_SCALAR k0, k1, minus_co, uo, vo;
if (// k0, k1 <- Zp
!ec_random_nonzero_scalar(group, &k0, kDefaultAdditionalData) ||
!ec_random_nonzero_scalar(group, &k1, kDefaultAdditionalData) ||
// Kb = k0*(G;T) + k1*(H;S)
!ec_point_mul_scalar_precomp(group, &jacobians[idx_Kb0],
&method->g_precomp, &k0, &method->h_precomp,
&k1, NULL, NULL) ||
!ec_point_mul_scalar_batch(group, &jacobians[idx_Kb1], T, &k0, S, &k1,
NULL, NULL) ||
// co, uo, vo <- Zp
!ec_random_nonzero_scalar(group, &minus_co, kDefaultAdditionalData) ||
!ec_random_nonzero_scalar(group, &uo, kDefaultAdditionalData) ||
!ec_random_nonzero_scalar(group, &vo, kDefaultAdditionalData) ||
// Ko = uo*(G;T) + vo*(H;S) - co*(pubo;W)
!ec_point_mul_scalar_precomp(group, &jacobians[idx_Ko0],
&method->g_precomp, &uo, &method->h_precomp,
&vo, &pubo_precomp, &minus_co) ||
!ec_point_mul_scalar_batch(group, &jacobians[idx_Ko1], T, &uo, S, &vo, W,
&minus_co)) {
return 0;
}
EC_AFFINE affines[num_idx];
jacobians[idx_T] = *T;
jacobians[idx_S] = *S;
jacobians[idx_W] = *W;
jacobians[idx_Ws] = *Ws;
if (!ec_jacobian_to_affine_batch(group, affines, jacobians, num_idx)) {
return 0;
}
// Select the K corresponding to K0 and K1 in constant-time.
EC_AFFINE K00, K01, K10, K11;
ec_affine_select(group, &K00, mask, &affines[idx_Ko0], &affines[idx_Kb0]);
ec_affine_select(group, &K01, mask, &affines[idx_Ko1], &affines[idx_Kb1]);
ec_affine_select(group, &K10, mask, &affines[idx_Kb0], &affines[idx_Ko0]);
ec_affine_select(group, &K11, mask, &affines[idx_Kb1], &affines[idx_Ko1]);
// Compute c = Hc(...) for the two proofs.
EC_SCALAR cs, c;
if (!hash_c_dleq(method, &cs, &priv->pubs, &affines[idx_T], &affines[idx_S],
&affines[idx_Ws], &affines[idx_Ks0], &affines[idx_Ks1]) ||
!hash_c_dleqor(method, &c, &priv->pub0, &priv->pub1, &affines[idx_T],
&affines[idx_S], &affines[idx_W], &K00, &K01, &K10,
&K11)) {
return 0;
}
// Compute cb, ub, and ub for the two proofs. In each of these products, only
// one operand is in Montgomery form, so the product does not need to be
// converted.
EC_SCALAR cs_mont;
ec_scalar_to_montgomery(group, &cs_mont, &cs);
// us = ks0 + cs*xs
EC_SCALAR us, vs;
ec_scalar_mul_montgomery(group, &us, &priv->xs, &cs_mont);
ec_scalar_add(group, &us, &ks0, &us);
// vs = ks1 + cs*ys
ec_scalar_mul_montgomery(group, &vs, &priv->ys, &cs_mont);
ec_scalar_add(group, &vs, &ks1, &vs);
// Store DLEQ2 proof in transcript.
if (!scalar_to_cbb(cbb, group, &cs) ||
!scalar_to_cbb(cbb, group, &us) ||
!scalar_to_cbb(cbb, group, &vs)) {
return 0;
}
// cb = c - co
EC_SCALAR cb, ub, vb;
ec_scalar_add(group, &cb, &c, &minus_co);
EC_SCALAR cb_mont;
ec_scalar_to_montgomery(group, &cb_mont, &cb);
// ub = k0 + cb*xb
ec_scalar_mul_montgomery(group, &ub, &xb, &cb_mont);
ec_scalar_add(group, &ub, &k0, &ub);
// vb = k1 + cb*yb
ec_scalar_mul_montgomery(group, &vb, &yb, &cb_mont);
ec_scalar_add(group, &vb, &k1, &vb);
// Select c, u, v in constant-time.
EC_SCALAR co, c0, c1, u0, u1, v0, v1;
ec_scalar_neg(group, &co, &minus_co);
ec_scalar_select(group, &c0, mask, &co, &cb);
ec_scalar_select(group, &u0, mask, &uo, &ub);
ec_scalar_select(group, &v0, mask, &vo, &vb);
ec_scalar_select(group, &c1, mask, &cb, &co);
ec_scalar_select(group, &u1, mask, &ub, &uo);
ec_scalar_select(group, &v1, mask, &vb, &vo);
// Store DLEQOR2 proof in transcript.
if (!scalar_to_cbb(cbb, group, &c0) ||
!scalar_to_cbb(cbb, group, &c1) ||
!scalar_to_cbb(cbb, group, &u0) ||
!scalar_to_cbb(cbb, group, &u1) ||
!scalar_to_cbb(cbb, group, &v0) ||
!scalar_to_cbb(cbb, group, &v1)) {
return 0;
}
return 1;
}
static int dleq_verify(const PMBTOKEN_METHOD *method, CBS *cbs,
const TRUST_TOKEN_CLIENT_KEY *pub, const EC_JACOBIAN *T,
const EC_JACOBIAN *S, const EC_JACOBIAN *W,
const EC_JACOBIAN *Ws) {
const EC_GROUP *group = method->group;
const EC_JACOBIAN *g = &group->generator->raw;
// We verify a DLEQ proof for the validity token and a DLEQOR2 proof for the
// private metadata token. To allow amortizing Jacobian-to-affine conversions,
// we compute Ki for both proofs first. Additionally, all inputs to this
// function are public, so we can use the faster variable-time
// multiplications.
enum {
idx_T,
idx_S,
idx_W,
idx_Ws,
idx_Ks0,
idx_Ks1,
idx_K00,
idx_K01,
idx_K10,
idx_K11,
num_idx,
};
EC_JACOBIAN jacobians[num_idx];
// Decode the DLEQ proof.
EC_SCALAR cs, us, vs;
if (!scalar_from_cbs(cbs, group, &cs) ||
!scalar_from_cbs(cbs, group, &us) ||
!scalar_from_cbs(cbs, group, &vs)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE);
return 0;
}
// Ks = us*(G;T) + vs*(H;S) - cs*(pubs;Ws)
EC_JACOBIAN pubs;
ec_affine_to_jacobian(group, &pubs, &pub->pubs);
EC_SCALAR minus_cs;
ec_scalar_neg(group, &minus_cs, &cs);
if (!mul_public_3(group, &jacobians[idx_Ks0], g, &us, &method->h, &vs, &pubs,
&minus_cs) ||
!mul_public_3(group, &jacobians[idx_Ks1], T, &us, S, &vs, Ws,
&minus_cs)) {
return 0;
}
// Decode the DLEQOR proof.
EC_SCALAR c0, c1, u0, u1, v0, v1;
if (!scalar_from_cbs(cbs, group, &c0) ||
!scalar_from_cbs(cbs, group, &c1) ||
!scalar_from_cbs(cbs, group, &u0) ||
!scalar_from_cbs(cbs, group, &u1) ||
!scalar_from_cbs(cbs, group, &v0) ||
!scalar_from_cbs(cbs, group, &v1)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE);
return 0;
}
EC_JACOBIAN pub0, pub1;
ec_affine_to_jacobian(group, &pub0, &pub->pub0);
ec_affine_to_jacobian(group, &pub1, &pub->pub1);
EC_SCALAR minus_c0, minus_c1;
ec_scalar_neg(group, &minus_c0, &c0);
ec_scalar_neg(group, &minus_c1, &c1);
if (// K0 = u0*(G;T) + v0*(H;S) - c0*(pub0;W)
!mul_public_3(group, &jacobians[idx_K00], g, &u0, &method->h, &v0, &pub0,
&minus_c0) ||
!mul_public_3(group, &jacobians[idx_K01], T, &u0, S, &v0, W, &minus_c0) ||
// K1 = u1*(G;T) + v1*(H;S) - c1*(pub1;W)
!mul_public_3(group, &jacobians[idx_K10], g, &u1, &method->h, &v1, &pub1,
&minus_c1) ||
!mul_public_3(group, &jacobians[idx_K11], T, &u1, S, &v1, W, &minus_c1)) {
return 0;
}
EC_AFFINE affines[num_idx];
jacobians[idx_T] = *T;
jacobians[idx_S] = *S;
jacobians[idx_W] = *W;
jacobians[idx_Ws] = *Ws;
if (!ec_jacobian_to_affine_batch(group, affines, jacobians, num_idx)) {
return 0;
}
// Check the DLEQ proof.
EC_SCALAR calculated;
if (!hash_c_dleq(method, &calculated, &pub->pubs, &affines[idx_T],
&affines[idx_S], &affines[idx_Ws], &affines[idx_Ks0],
&affines[idx_Ks1])) {
return 0;
}
// cs == calculated
if (!ec_scalar_equal_vartime(group, &cs, &calculated)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_INVALID_PROOF);
return 0;
}
// Check the DLEQOR proof.
if (!hash_c_dleqor(method, &calculated, &pub->pub0, &pub->pub1,
&affines[idx_T], &affines[idx_S], &affines[idx_W],
&affines[idx_K00], &affines[idx_K01], &affines[idx_K10],
&affines[idx_K11])) {
return 0;
}
// c0 + c1 == calculated
EC_SCALAR c;
ec_scalar_add(group, &c, &c0, &c1);
if (!ec_scalar_equal_vartime(group, &c, &calculated)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_INVALID_PROOF);
return 0;
}
return 1;
}
static int pmbtoken_sign(const PMBTOKEN_METHOD *method,
const TRUST_TOKEN_ISSUER_KEY *key, CBB *cbb, CBS *cbs,
size_t num_requested, size_t num_to_issue,
uint8_t private_metadata) {
const EC_GROUP *group = method->group;
if (num_requested < num_to_issue) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, ERR_R_INTERNAL_ERROR);
return 0;
}
if (num_to_issue > ((size_t)-1) / sizeof(EC_JACOBIAN) ||
num_to_issue > ((size_t)-1) / sizeof(EC_SCALAR)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, ERR_R_OVERFLOW);
return 0;
}
int ret = 0;
EC_JACOBIAN *Tps = OPENSSL_malloc(num_to_issue * sizeof(EC_JACOBIAN));
EC_JACOBIAN *Sps = OPENSSL_malloc(num_to_issue * sizeof(EC_JACOBIAN));
EC_JACOBIAN *Wps = OPENSSL_malloc(num_to_issue * sizeof(EC_JACOBIAN));
EC_JACOBIAN *Wsps = OPENSSL_malloc(num_to_issue * sizeof(EC_JACOBIAN));
EC_SCALAR *es = OPENSSL_malloc(num_to_issue * sizeof(EC_SCALAR));
CBB batch_cbb;
CBB_zero(&batch_cbb);
if (!Tps ||
!Sps ||
!Wps ||
!Wsps ||
!es ||
!CBB_init(&batch_cbb, 0) ||
!point_to_cbb(&batch_cbb, method->group, &key->pubs) ||
!point_to_cbb(&batch_cbb, method->group, &key->pub0) ||
!point_to_cbb(&batch_cbb, method->group, &key->pub1)) {
goto err;
}
for (size_t i = 0; i < num_to_issue; i++) {
EC_AFFINE Tp_affine;
EC_JACOBIAN Tp;
if (!cbs_get_prefixed_point(cbs, group, &Tp_affine, method->prefix_point)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE);
goto err;
}
ec_affine_to_jacobian(group, &Tp, &Tp_affine);
EC_SCALAR xb, yb;
BN_ULONG mask = ((BN_ULONG)0) - (private_metadata & 1);
ec_scalar_select(group, &xb, mask, &key->x1, &key->x0);
ec_scalar_select(group, &yb, mask, &key->y1, &key->y0);
uint8_t s[TRUST_TOKEN_NONCE_SIZE];
RAND_bytes(s, TRUST_TOKEN_NONCE_SIZE);
// The |jacobians| and |affines| contain Sp, Wp, and Wsp.
EC_JACOBIAN jacobians[3];
EC_AFFINE affines[3];
if (!method->hash_s(group, &jacobians[0], &Tp_affine, s) ||
!ec_point_mul_scalar_batch(group, &jacobians[1], &Tp, &xb,
&jacobians[0], &yb, NULL, NULL) ||
!ec_point_mul_scalar_batch(group, &jacobians[2], &Tp, &key->xs,
&jacobians[0], &key->ys, NULL, NULL) ||
!ec_jacobian_to_affine_batch(group, affines, jacobians, 3) ||
!CBB_add_bytes(cbb, s, TRUST_TOKEN_NONCE_SIZE) ||
!cbb_add_prefixed_point(cbb, group, &affines[1],
method->prefix_point) ||
!cbb_add_prefixed_point(cbb, group, &affines[2],
method->prefix_point)) {
goto err;
}
if (!point_to_cbb(&batch_cbb, group, &Tp_affine) ||
!point_to_cbb(&batch_cbb, group, &affines[0]) ||
!point_to_cbb(&batch_cbb, group, &affines[1]) ||
!point_to_cbb(&batch_cbb, group, &affines[2])) {
goto err;
}
Tps[i] = Tp;
Sps[i] = jacobians[0];
Wps[i] = jacobians[1];
Wsps[i] = jacobians[2];
if (!CBB_flush(cbb)) {
goto err;
}
}
// The DLEQ batching construction is described in appendix B of
// https://eprint.iacr.org/2020/072/20200324:214215. Note the additional
// computations all act on public inputs.
for (size_t i = 0; i < num_to_issue; i++) {
if (!hash_c_batch(method, &es[i], &batch_cbb, i)) {
goto err;
}
}
EC_JACOBIAN Tp_batch, Sp_batch, Wp_batch, Wsp_batch;
if (!ec_point_mul_scalar_public_batch(group, &Tp_batch,
/*g_scalar=*/NULL, Tps, es,
num_to_issue) ||
!ec_point_mul_scalar_public_batch(group, &Sp_batch,
/*g_scalar=*/NULL, Sps, es,
num_to_issue) ||
!ec_point_mul_scalar_public_batch(group, &Wp_batch,
/*g_scalar=*/NULL, Wps, es,
num_to_issue) ||
!ec_point_mul_scalar_public_batch(group, &Wsp_batch,
/*g_scalar=*/NULL, Wsps, es,
num_to_issue)) {
goto err;
}
CBB proof;
if (!CBB_add_u16_length_prefixed(cbb, &proof) ||
!dleq_generate(method, &proof, key, &Tp_batch, &Sp_batch, &Wp_batch,
&Wsp_batch, private_metadata) ||
!CBB_flush(cbb)) {
goto err;
}
// Skip over any unused requests.
size_t point_len = 1 + 2 * BN_num_bytes(&group->field);
size_t token_len = point_len;
if (method->prefix_point) {
token_len += 2;
}
if (!CBS_skip(cbs, token_len * (num_requested - num_to_issue))) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE);
goto err;
}
ret = 1;
err:
OPENSSL_free(Tps);
OPENSSL_free(Sps);
OPENSSL_free(Wps);
OPENSSL_free(Wsps);
OPENSSL_free(es);
CBB_cleanup(&batch_cbb);
return ret;
}
static STACK_OF(TRUST_TOKEN) *pmbtoken_unblind(
const PMBTOKEN_METHOD *method, const TRUST_TOKEN_CLIENT_KEY *key,
const STACK_OF(TRUST_TOKEN_PRETOKEN) *pretokens, CBS *cbs, size_t count,
uint32_t key_id) {
const EC_GROUP *group = method->group;
if (count > sk_TRUST_TOKEN_PRETOKEN_num(pretokens)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE);
return NULL;
}
if (count > ((size_t)-1) / sizeof(EC_JACOBIAN) ||
count > ((size_t)-1) / sizeof(EC_SCALAR)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, ERR_R_OVERFLOW);
return NULL;
}
int ok = 0;
STACK_OF(TRUST_TOKEN) *ret = sk_TRUST_TOKEN_new_null();
EC_JACOBIAN *Tps = OPENSSL_malloc(count * sizeof(EC_JACOBIAN));
EC_JACOBIAN *Sps = OPENSSL_malloc(count * sizeof(EC_JACOBIAN));
EC_JACOBIAN *Wps = OPENSSL_malloc(count * sizeof(EC_JACOBIAN));
EC_JACOBIAN *Wsps = OPENSSL_malloc(count * sizeof(EC_JACOBIAN));
EC_SCALAR *es = OPENSSL_malloc(count * sizeof(EC_SCALAR));
CBB batch_cbb;
CBB_zero(&batch_cbb);
if (ret == NULL ||
Tps == NULL ||
Sps == NULL ||
Wps == NULL ||
Wsps == NULL ||
es == NULL ||
!CBB_init(&batch_cbb, 0) ||
!point_to_cbb(&batch_cbb, method->group, &key->pubs) ||
!point_to_cbb(&batch_cbb, method->group, &key->pub0) ||
!point_to_cbb(&batch_cbb, method->group, &key->pub1)) {
goto err;
}
for (size_t i = 0; i < count; i++) {
const TRUST_TOKEN_PRETOKEN *pretoken =
sk_TRUST_TOKEN_PRETOKEN_value(pretokens, i);
uint8_t s[TRUST_TOKEN_NONCE_SIZE];
EC_AFFINE Wp_affine, Wsp_affine;
if (!CBS_copy_bytes(cbs, s, TRUST_TOKEN_NONCE_SIZE) ||
!cbs_get_prefixed_point(cbs, group, &Wp_affine, method->prefix_point) ||
!cbs_get_prefixed_point(cbs, group, &Wsp_affine,
method->prefix_point)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE);
goto err;
}
ec_affine_to_jacobian(group, &Tps[i], &pretoken->Tp);
ec_affine_to_jacobian(group, &Wps[i], &Wp_affine);
ec_affine_to_jacobian(group, &Wsps[i], &Wsp_affine);
if (!method->hash_s(group, &Sps[i], &pretoken->Tp, s)) {
goto err;
}
EC_AFFINE Sp_affine;
if (!point_to_cbb(&batch_cbb, group, &pretoken->Tp) ||
!ec_jacobian_to_affine(group, &Sp_affine, &Sps[i]) ||
!point_to_cbb(&batch_cbb, group, &Sp_affine) ||
!point_to_cbb(&batch_cbb, group, &Wp_affine) ||
!point_to_cbb(&batch_cbb, group, &Wsp_affine)) {
goto err;
}
// Unblind the token.
EC_JACOBIAN jacobians[3];
EC_AFFINE affines[3];
if (!ec_point_mul_scalar(group, &jacobians[0], &Sps[i], &pretoken->r) ||
!ec_point_mul_scalar(group, &jacobians[1], &Wps[i], &pretoken->r) ||
!ec_point_mul_scalar(group, &jacobians[2], &Wsps[i], &pretoken->r) ||
!ec_jacobian_to_affine_batch(group, affines, jacobians, 3)) {
goto err;
}
// Serialize the token. Include |key_id| to avoid an extra copy in the layer
// above.
CBB token_cbb;
size_t point_len = 1 + 2 * BN_num_bytes(&group->field);
if (!CBB_init(&token_cbb,
4 + TRUST_TOKEN_NONCE_SIZE + 3 * (2 + point_len)) ||
!CBB_add_u32(&token_cbb, key_id) ||
!CBB_add_bytes(&token_cbb, pretoken->salt, TRUST_TOKEN_NONCE_SIZE) ||
!cbb_add_prefixed_point(&token_cbb, group, &affines[0],
method->prefix_point) ||
!cbb_add_prefixed_point(&token_cbb, group, &affines[1],
method->prefix_point) ||
!cbb_add_prefixed_point(&token_cbb, group, &affines[2],
method->prefix_point) ||
!CBB_flush(&token_cbb)) {
CBB_cleanup(&token_cbb);
goto err;
}
TRUST_TOKEN *token =
TRUST_TOKEN_new(CBB_data(&token_cbb), CBB_len(&token_cbb));
CBB_cleanup(&token_cbb);
if (token == NULL ||
!sk_TRUST_TOKEN_push(ret, token)) {
TRUST_TOKEN_free(token);
goto err;
}
}
// The DLEQ batching construction is described in appendix B of
// https://eprint.iacr.org/2020/072/20200324:214215. Note the additional
// computations all act on public inputs.
for (size_t i = 0; i < count; i++) {
if (!hash_c_batch(method, &es[i], &batch_cbb, i)) {
goto err;
}
}
EC_JACOBIAN Tp_batch, Sp_batch, Wp_batch, Wsp_batch;
if (!ec_point_mul_scalar_public_batch(group, &Tp_batch,
/*g_scalar=*/NULL, Tps, es, count) ||
!ec_point_mul_scalar_public_batch(group, &Sp_batch,
/*g_scalar=*/NULL, Sps, es, count) ||
!ec_point_mul_scalar_public_batch(group, &Wp_batch,
/*g_scalar=*/NULL, Wps, es, count) ||
!ec_point_mul_scalar_public_batch(group, &Wsp_batch,
/*g_scalar=*/NULL, Wsps, es, count)) {
goto err;
}
CBS proof;
if (!CBS_get_u16_length_prefixed(cbs, &proof) ||
!dleq_verify(method, &proof, key, &Tp_batch, &Sp_batch, &Wp_batch,
&Wsp_batch) ||
CBS_len(&proof) != 0) {
goto err;
}
ok = 1;
err:
OPENSSL_free(Tps);
OPENSSL_free(Sps);
OPENSSL_free(Wps);
OPENSSL_free(Wsps);
OPENSSL_free(es);
CBB_cleanup(&batch_cbb);
if (!ok) {
sk_TRUST_TOKEN_pop_free(ret, TRUST_TOKEN_free);
ret = NULL;
}
return ret;
}
static int pmbtoken_read(const PMBTOKEN_METHOD *method,
const TRUST_TOKEN_ISSUER_KEY *key,
uint8_t out_nonce[TRUST_TOKEN_NONCE_SIZE],
uint8_t *out_private_metadata, const uint8_t *token,
size_t token_len, int include_message,
const uint8_t *msg, size_t msg_len) {
const EC_GROUP *group = method->group;
CBS cbs, salt;
CBS_init(&cbs, token, token_len);
EC_AFFINE S, W, Ws;
if (!CBS_get_bytes(&cbs, &salt, TRUST_TOKEN_NONCE_SIZE) ||
!cbs_get_prefixed_point(&cbs, group, &S, method->prefix_point) ||
!cbs_get_prefixed_point(&cbs, group, &W, method->prefix_point) ||
!cbs_get_prefixed_point(&cbs, group, &Ws, method->prefix_point) ||
CBS_len(&cbs) != 0) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_INVALID_TOKEN);
return 0;
}
if (include_message) {
SHA512_CTX hash_ctx;
assert(SHA512_DIGEST_LENGTH == TRUST_TOKEN_NONCE_SIZE);
SHA512_Init(&hash_ctx);
SHA512_Update(&hash_ctx, CBS_data(&salt), CBS_len(&salt));
SHA512_Update(&hash_ctx, msg, msg_len);
SHA512_Final(out_nonce, &hash_ctx);
} else {
OPENSSL_memcpy(out_nonce, CBS_data(&salt), CBS_len(&salt));
}
EC_JACOBIAN T;
if (!method->hash_t(group, &T, out_nonce)) {
return 0;
}
// We perform three multiplications with S and T. This is enough that it is
// worth using |ec_point_mul_scalar_precomp|.
EC_JACOBIAN S_jacobian;
EC_PRECOMP S_precomp, T_precomp;
ec_affine_to_jacobian(group, &S_jacobian, &S);
if (!ec_init_precomp(group, &S_precomp, &S_jacobian) ||
!ec_init_precomp(group, &T_precomp, &T)) {
return 0;
}
EC_JACOBIAN Ws_calculated;
// Check the validity of the token.
if (!ec_point_mul_scalar_precomp(group, &Ws_calculated, &T_precomp, &key->xs,
&S_precomp, &key->ys, NULL, NULL) ||
!ec_affine_jacobian_equal(group, &Ws, &Ws_calculated)) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_BAD_VALIDITY_CHECK);
return 0;
}
EC_JACOBIAN W0, W1;
if (!ec_point_mul_scalar_precomp(group, &W0, &T_precomp, &key->x0, &S_precomp,
&key->y0, NULL, NULL) ||
!ec_point_mul_scalar_precomp(group, &W1, &T_precomp, &key->x1, &S_precomp,
&key->y1, NULL, NULL)) {
return 0;
}
const int is_W0 = ec_affine_jacobian_equal(group, &W, &W0);
const int is_W1 = ec_affine_jacobian_equal(group, &W, &W1);
const int is_valid = is_W0 ^ is_W1;
if (!is_valid) {
// Invalid tokens will fail the validity check above.
OPENSSL_PUT_ERROR(TRUST_TOKEN, ERR_R_INTERNAL_ERROR);
return 0;
}
*out_private_metadata = is_W1;
return 1;
}
// PMBTokens experiment v1.
static int pmbtoken_exp1_hash_t(const EC_GROUP *group, EC_JACOBIAN *out,
const uint8_t t[TRUST_TOKEN_NONCE_SIZE]) {
const uint8_t kHashTLabel[] = "PMBTokens Experiment V1 HashT";
return ec_hash_to_curve_p384_xmd_sha512_sswu_draft07(
group, out, kHashTLabel, sizeof(kHashTLabel), t, TRUST_TOKEN_NONCE_SIZE);
}
static int pmbtoken_exp1_hash_s(const EC_GROUP *group, EC_JACOBIAN *out,
const EC_AFFINE *t,
const uint8_t s[TRUST_TOKEN_NONCE_SIZE]) {
const uint8_t kHashSLabel[] = "PMBTokens Experiment V1 HashS";
int ret = 0;
CBB cbb;
uint8_t *buf = NULL;
size_t len;
if (!CBB_init(&cbb, 0) ||
!point_to_cbb(&cbb, group, t) ||
!CBB_add_bytes(&cbb, s, TRUST_TOKEN_NONCE_SIZE) ||
!CBB_finish(&cbb, &buf, &len) ||
!ec_hash_to_curve_p384_xmd_sha512_sswu_draft07(
group, out, kHashSLabel, sizeof(kHashSLabel), buf, len)) {
goto err;
}
ret = 1;
err:
OPENSSL_free(buf);
CBB_cleanup(&cbb);
return ret;
}
static int pmbtoken_exp1_hash_c(const EC_GROUP *group, EC_SCALAR *out,
uint8_t *buf, size_t len) {
const uint8_t kHashCLabel[] = "PMBTokens Experiment V1 HashC";
return ec_hash_to_scalar_p384_xmd_sha512_draft07(
group, out, kHashCLabel, sizeof(kHashCLabel), buf, len);
}
static int pmbtoken_exp1_hash_to_scalar(const EC_GROUP *group, EC_SCALAR *out,
uint8_t *buf, size_t len) {
const uint8_t kHashLabel[] = "PMBTokens Experiment V1 HashToScalar";
return ec_hash_to_scalar_p384_xmd_sha512_draft07(
group, out, kHashLabel, sizeof(kHashLabel), buf, len);
}
static int pmbtoken_exp1_ok = 0;
static PMBTOKEN_METHOD pmbtoken_exp1_method;
static CRYPTO_once_t pmbtoken_exp1_method_once = CRYPTO_ONCE_INIT;
static void pmbtoken_exp1_init_method_impl(void) {
// This is the output of |ec_hash_to_scalar_p384_xmd_sha512_draft07| with DST
// "PMBTokens Experiment V1 HashH" and message "generator".
static const uint8_t kH[] = {
0x04, 0x82, 0xd5, 0x68, 0xf5, 0x39, 0xf6, 0x08, 0x19, 0xa1, 0x75,
0x9f, 0x98, 0xb5, 0x10, 0xf5, 0x0b, 0x9d, 0x2b, 0xe1, 0x64, 0x4d,
0x02, 0x76, 0x18, 0x11, 0xf8, 0x2f, 0xd3, 0x33, 0x25, 0x1f, 0x2c,
0xb8, 0xf6, 0xf1, 0x9e, 0x93, 0x85, 0x79, 0xb3, 0xb7, 0x81, 0xa3,
0xe6, 0x23, 0xc3, 0x1c, 0xff, 0x03, 0xd9, 0x40, 0x6c, 0xec, 0xe0,
0x4d, 0xea, 0xdf, 0x9d, 0x94, 0xd1, 0x87, 0xab, 0x27, 0xf7, 0x4f,
0x53, 0xea, 0xa3, 0x18, 0x72, 0xb9, 0xd1, 0x56, 0xa0, 0x4e, 0x81,
0xaa, 0xeb, 0x1c, 0x22, 0x6d, 0x39, 0x1c, 0x5e, 0xb1, 0x27, 0xfc,
0x87, 0xc3, 0x95, 0xd0, 0x13, 0xb7, 0x0b, 0x5c, 0xc7,
};
pmbtoken_exp1_ok = pmbtoken_init_method(
&pmbtoken_exp1_method, NID_secp384r1, kH, sizeof(kH),
pmbtoken_exp1_hash_t, pmbtoken_exp1_hash_s, pmbtoken_exp1_hash_c,
pmbtoken_exp1_hash_to_scalar, 1);
}
static int pmbtoken_exp1_init_method(void) {
CRYPTO_once(&pmbtoken_exp1_method_once, pmbtoken_exp1_init_method_impl);
if (!pmbtoken_exp1_ok) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, ERR_R_INTERNAL_ERROR);
return 0;
}
return 1;
}
int pmbtoken_exp1_generate_key(CBB *out_private, CBB *out_public) {
if (!pmbtoken_exp1_init_method()) {
return 0;
}
return pmbtoken_generate_key(&pmbtoken_exp1_method, out_private, out_public);
}
int pmbtoken_exp1_derive_key_from_secret(CBB *out_private, CBB *out_public,
const uint8_t *secret,
size_t secret_len) {
if (!pmbtoken_exp1_init_method()) {
return 0;
}
return pmbtoken_derive_key_from_secret(&pmbtoken_exp1_method, out_private,
out_public, secret, secret_len);
}
int pmbtoken_exp1_client_key_from_bytes(TRUST_TOKEN_CLIENT_KEY *key,
const uint8_t *in, size_t len) {
if (!pmbtoken_exp1_init_method()) {
return 0;
}
return pmbtoken_client_key_from_bytes(&pmbtoken_exp1_method, key, in, len);
}
int pmbtoken_exp1_issuer_key_from_bytes(TRUST_TOKEN_ISSUER_KEY *key,
const uint8_t *in, size_t len) {
if (!pmbtoken_exp1_init_method()) {
return 0;
}
return pmbtoken_issuer_key_from_bytes(&pmbtoken_exp1_method, key, in, len);
}
STACK_OF(TRUST_TOKEN_PRETOKEN) *pmbtoken_exp1_blind(CBB *cbb, size_t count,
int include_message,
const uint8_t *msg,
size_t msg_len) {
if (!pmbtoken_exp1_init_method()) {
return NULL;
}
return pmbtoken_blind(&pmbtoken_exp1_method, cbb, count, include_message, msg,
msg_len);
}
int pmbtoken_exp1_sign(const TRUST_TOKEN_ISSUER_KEY *key, CBB *cbb, CBS *cbs,
size_t num_requested, size_t num_to_issue,
uint8_t private_metadata) {
if (!pmbtoken_exp1_init_method()) {
return 0;
}
return pmbtoken_sign(&pmbtoken_exp1_method, key, cbb, cbs, num_requested,
num_to_issue, private_metadata);
}
STACK_OF(TRUST_TOKEN) *pmbtoken_exp1_unblind(
const TRUST_TOKEN_CLIENT_KEY *key,
const STACK_OF(TRUST_TOKEN_PRETOKEN) *pretokens, CBS *cbs, size_t count,
uint32_t key_id) {
if (!pmbtoken_exp1_init_method()) {
return NULL;
}
return pmbtoken_unblind(&pmbtoken_exp1_method, key, pretokens, cbs, count,
key_id);
}
int pmbtoken_exp1_read(const TRUST_TOKEN_ISSUER_KEY *key,
uint8_t out_nonce[TRUST_TOKEN_NONCE_SIZE],
uint8_t *out_private_metadata, const uint8_t *token,
size_t token_len, int include_message,
const uint8_t *msg, size_t msg_len) {
if (!pmbtoken_exp1_init_method()) {
return 0;
}
return pmbtoken_read(&pmbtoken_exp1_method, key, out_nonce,
out_private_metadata, token, token_len, include_message,
msg, msg_len);
}
int pmbtoken_exp1_get_h_for_testing(uint8_t out[97]) {
if (!pmbtoken_exp1_init_method()) {
return 0;
}
EC_AFFINE h;
return ec_jacobian_to_affine(pmbtoken_exp1_method.group, &h,
&pmbtoken_exp1_method.h) &&
ec_point_to_bytes(pmbtoken_exp1_method.group, &h,
POINT_CONVERSION_UNCOMPRESSED, out, 97) == 97;
}
// PMBTokens experiment v2.
static int pmbtoken_exp2_hash_t(const EC_GROUP *group, EC_JACOBIAN *out,
const uint8_t t[TRUST_TOKEN_NONCE_SIZE]) {
const uint8_t kHashTLabel[] = "PMBTokens Experiment V2 HashT";
return ec_hash_to_curve_p384_xmd_sha512_sswu_draft07(
group, out, kHashTLabel, sizeof(kHashTLabel), t, TRUST_TOKEN_NONCE_SIZE);
}
static int pmbtoken_exp2_hash_s(const EC_GROUP *group, EC_JACOBIAN *out,
const EC_AFFINE *t,
const uint8_t s[TRUST_TOKEN_NONCE_SIZE]) {
const uint8_t kHashSLabel[] = "PMBTokens Experiment V2 HashS";
int ret = 0;
CBB cbb;
uint8_t *buf = NULL;
size_t len;
if (!CBB_init(&cbb, 0) ||
!point_to_cbb(&cbb, group, t) ||
!CBB_add_bytes(&cbb, s, TRUST_TOKEN_NONCE_SIZE) ||
!CBB_finish(&cbb, &buf, &len) ||
!ec_hash_to_curve_p384_xmd_sha512_sswu_draft07(
group, out, kHashSLabel, sizeof(kHashSLabel), buf, len)) {
goto err;
}
ret = 1;
err:
OPENSSL_free(buf);
CBB_cleanup(&cbb);
return ret;
}
static int pmbtoken_exp2_hash_c(const EC_GROUP *group, EC_SCALAR *out,
uint8_t *buf, size_t len) {
const uint8_t kHashCLabel[] = "PMBTokens Experiment V2 HashC";
return ec_hash_to_scalar_p384_xmd_sha512_draft07(
group, out, kHashCLabel, sizeof(kHashCLabel), buf, len);
}
static int pmbtoken_exp2_hash_to_scalar(const EC_GROUP *group, EC_SCALAR *out,
uint8_t *buf, size_t len) {
const uint8_t kHashLabel[] = "PMBTokens Experiment V2 HashToScalar";
return ec_hash_to_scalar_p384_xmd_sha512_draft07(
group, out, kHashLabel, sizeof(kHashLabel), buf, len);
}
static int pmbtoken_exp2_ok = 0;
static PMBTOKEN_METHOD pmbtoken_exp2_method;
static CRYPTO_once_t pmbtoken_exp2_method_once = CRYPTO_ONCE_INIT;
static void pmbtoken_exp2_init_method_impl(void) {
// This is the output of |ec_hash_to_scalar_p384_xmd_sha512_draft07| with DST
// "PMBTokens Experiment V2 HashH" and message "generator".
static const uint8_t kH[] = {
0x04, 0xbc, 0x27, 0x24, 0x99, 0xfa, 0xc9, 0xa4, 0x74, 0x6f, 0xf9,
0x07, 0x81, 0x55, 0xf8, 0x1f, 0x6f, 0xda, 0x09, 0xe7, 0x8c, 0x5d,
0x9e, 0x4e, 0x14, 0x7c, 0x53, 0x14, 0xbc, 0x7e, 0x29, 0x57, 0x92,
0x17, 0x94, 0x6e, 0xd2, 0xdf, 0xa5, 0x31, 0x1b, 0x4e, 0xb7, 0xfc,
0x93, 0xe3, 0x6e, 0x14, 0x1f, 0x4f, 0x14, 0xf3, 0xe5, 0x47, 0x61,
0x1c, 0x2c, 0x72, 0x25, 0xf0, 0x4a, 0x45, 0x23, 0x2d, 0x57, 0x93,
0x0e, 0xb2, 0x55, 0xb8, 0x57, 0x25, 0x4c, 0x1e, 0xdb, 0xfd, 0x58,
0x70, 0x17, 0x9a, 0xbb, 0x9e, 0x5e, 0x93, 0x9e, 0x92, 0xd3, 0xe8,
0x25, 0x62, 0xbf, 0x59, 0xb2, 0xd2, 0x3d, 0x71, 0xff
};
pmbtoken_exp2_ok = pmbtoken_init_method(
&pmbtoken_exp2_method, NID_secp384r1, kH, sizeof(kH),
pmbtoken_exp2_hash_t, pmbtoken_exp2_hash_s, pmbtoken_exp2_hash_c,
pmbtoken_exp2_hash_to_scalar, 0);
}
static int pmbtoken_exp2_init_method(void) {
CRYPTO_once(&pmbtoken_exp2_method_once, pmbtoken_exp2_init_method_impl);
if (!pmbtoken_exp2_ok) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, ERR_R_INTERNAL_ERROR);
return 0;
}
return 1;
}
int pmbtoken_exp2_generate_key(CBB *out_private, CBB *out_public) {
if (!pmbtoken_exp2_init_method()) {
return 0;
}
return pmbtoken_generate_key(&pmbtoken_exp2_method, out_private, out_public);
}
int pmbtoken_exp2_derive_key_from_secret(CBB *out_private, CBB *out_public,
const uint8_t *secret,
size_t secret_len) {
if (!pmbtoken_exp2_init_method()) {
return 0;
}
return pmbtoken_derive_key_from_secret(&pmbtoken_exp2_method, out_private,
out_public, secret, secret_len);
}
int pmbtoken_exp2_client_key_from_bytes(TRUST_TOKEN_CLIENT_KEY *key,
const uint8_t *in, size_t len) {
if (!pmbtoken_exp2_init_method()) {
return 0;
}
return pmbtoken_client_key_from_bytes(&pmbtoken_exp2_method, key, in, len);
}
int pmbtoken_exp2_issuer_key_from_bytes(TRUST_TOKEN_ISSUER_KEY *key,
const uint8_t *in, size_t len) {
if (!pmbtoken_exp2_init_method()) {
return 0;
}
return pmbtoken_issuer_key_from_bytes(&pmbtoken_exp2_method, key, in, len);
}
STACK_OF(TRUST_TOKEN_PRETOKEN) *pmbtoken_exp2_blind(CBB *cbb, size_t count,
int include_message,
const uint8_t *msg,
size_t msg_len) {
if (!pmbtoken_exp2_init_method()) {
return NULL;
}
return pmbtoken_blind(&pmbtoken_exp2_method, cbb, count, include_message, msg,
msg_len);
}
int pmbtoken_exp2_sign(const TRUST_TOKEN_ISSUER_KEY *key, CBB *cbb, CBS *cbs,
size_t num_requested, size_t num_to_issue,
uint8_t private_metadata) {
if (!pmbtoken_exp2_init_method()) {
return 0;
}
return pmbtoken_sign(&pmbtoken_exp2_method, key, cbb, cbs, num_requested,
num_to_issue, private_metadata);
}
STACK_OF(TRUST_TOKEN) *pmbtoken_exp2_unblind(
const TRUST_TOKEN_CLIENT_KEY *key,
const STACK_OF(TRUST_TOKEN_PRETOKEN) *pretokens, CBS *cbs, size_t count,
uint32_t key_id) {
if (!pmbtoken_exp2_init_method()) {
return NULL;
}
return pmbtoken_unblind(&pmbtoken_exp2_method, key, pretokens, cbs, count,
key_id);
}
int pmbtoken_exp2_read(const TRUST_TOKEN_ISSUER_KEY *key,
uint8_t out_nonce[TRUST_TOKEN_NONCE_SIZE],
uint8_t *out_private_metadata, const uint8_t *token,
size_t token_len, int include_message,
const uint8_t *msg, size_t msg_len) {
if (!pmbtoken_exp2_init_method()) {
return 0;
}
return pmbtoken_read(&pmbtoken_exp2_method, key, out_nonce,
out_private_metadata, token, token_len, include_message,
msg, msg_len);
}
int pmbtoken_exp2_get_h_for_testing(uint8_t out[97]) {
if (!pmbtoken_exp2_init_method()) {
return 0;
}
EC_AFFINE h;
return ec_jacobian_to_affine(pmbtoken_exp2_method.group, &h,
&pmbtoken_exp2_method.h) &&
ec_point_to_bytes(pmbtoken_exp2_method.group, &h,
POINT_CONVERSION_UNCOMPRESSED, out, 97) == 97;
}
// PMBTokens PST v1.
static int pmbtoken_pst1_hash_t(const EC_GROUP *group, EC_JACOBIAN *out,
const uint8_t t[TRUST_TOKEN_NONCE_SIZE]) {
const uint8_t kHashTLabel[] = "PMBTokens PST V1 HashT";
return ec_hash_to_curve_p384_xmd_sha384_sswu(
group, out, kHashTLabel, sizeof(kHashTLabel), t, TRUST_TOKEN_NONCE_SIZE);
}
static int pmbtoken_pst1_hash_s(const EC_GROUP *group, EC_JACOBIAN *out,
const EC_AFFINE *t,
const uint8_t s[TRUST_TOKEN_NONCE_SIZE]) {
const uint8_t kHashSLabel[] = "PMBTokens PST V1 HashS";
int ret = 0;
CBB cbb;
uint8_t *buf = NULL;
size_t len;
if (!CBB_init(&cbb, 0) ||
!point_to_cbb(&cbb, group, t) ||
!CBB_add_bytes(&cbb, s, TRUST_TOKEN_NONCE_SIZE) ||
!CBB_finish(&cbb, &buf, &len) ||
!ec_hash_to_curve_p384_xmd_sha384_sswu(
group, out, kHashSLabel, sizeof(kHashSLabel), buf, len)) {
goto err;
}
ret = 1;
err:
OPENSSL_free(buf);
CBB_cleanup(&cbb);
return ret;
}
static int pmbtoken_pst1_hash_c(const EC_GROUP *group, EC_SCALAR *out,
uint8_t *buf, size_t len) {
const uint8_t kHashCLabel[] = "PMBTokens PST V1 HashC";
return ec_hash_to_scalar_p384_xmd_sha384(
group, out, kHashCLabel, sizeof(kHashCLabel), buf, len);
}
static int pmbtoken_pst1_hash_to_scalar(const EC_GROUP *group, EC_SCALAR *out,
uint8_t *buf, size_t len) {
const uint8_t kHashLabel[] = "PMBTokens PST V1 HashToScalar";
return ec_hash_to_scalar_p384_xmd_sha384(
group, out, kHashLabel, sizeof(kHashLabel), buf, len);
}
static int pmbtoken_pst1_ok = 0;
static PMBTOKEN_METHOD pmbtoken_pst1_method;
static CRYPTO_once_t pmbtoken_pst1_method_once = CRYPTO_ONCE_INIT;
static void pmbtoken_pst1_init_method_impl(void) {
// This is the output of |ec_hash_to_scalar_p384_xmd_sha384| with DST
// "PMBTokens PST V1 HashH" and message "generator".
static const uint8_t kH[] = {
0x04, 0x4c, 0xfa, 0xd4, 0x33, 0x6d, 0x8c, 0x4e, 0x18, 0xce, 0x1a,
0x82, 0x7b, 0x53, 0x8c, 0xf8, 0x63, 0x18, 0xe5, 0xa3, 0x96, 0x0d,
0x05, 0xde, 0xf4, 0x83, 0xa7, 0xd8, 0xde, 0x9c, 0x50, 0x81, 0x38,
0xc9, 0x38, 0x25, 0xa3, 0x70, 0x97, 0xc1, 0x1c, 0x33, 0x2e, 0x83,
0x68, 0x64, 0x9c, 0x53, 0x73, 0xc3, 0x03, 0xc1, 0xa9, 0xd8, 0x92,
0xa2, 0x32, 0xf4, 0x22, 0x40, 0x07, 0x2d, 0x9b, 0x6f, 0xab, 0xff,
0x2a, 0x92, 0x03, 0xb1, 0x73, 0x09, 0x1a, 0x6a, 0x4a, 0xc2, 0x4c,
0xac, 0x13, 0x59, 0xf4, 0x28, 0x0e, 0x78, 0x69, 0xa5, 0xdf, 0x0d,
0x74, 0xeb, 0x14, 0xca, 0x8a, 0x32, 0xbb, 0xd3, 0x91
};
pmbtoken_pst1_ok = pmbtoken_init_method(
&pmbtoken_pst1_method, NID_secp384r1, kH, sizeof(kH),
pmbtoken_pst1_hash_t, pmbtoken_pst1_hash_s, pmbtoken_pst1_hash_c,
pmbtoken_pst1_hash_to_scalar, 0);
}
static int pmbtoken_pst1_init_method(void) {
CRYPTO_once(&pmbtoken_pst1_method_once, pmbtoken_pst1_init_method_impl);
if (!pmbtoken_pst1_ok) {
OPENSSL_PUT_ERROR(TRUST_TOKEN, ERR_R_INTERNAL_ERROR);
return 0;
}
return 1;
}
int pmbtoken_pst1_generate_key(CBB *out_private, CBB *out_public) {
if (!pmbtoken_pst1_init_method()) {
return 0;
}
return pmbtoken_generate_key(&pmbtoken_pst1_method, out_private, out_public);
}
int pmbtoken_pst1_derive_key_from_secret(CBB *out_private, CBB *out_public,
const uint8_t *secret,
size_t secret_len) {
if (!pmbtoken_pst1_init_method()) {
return 0;
}
return pmbtoken_derive_key_from_secret(&pmbtoken_pst1_method, out_private,
out_public, secret, secret_len);
}
int pmbtoken_pst1_client_key_from_bytes(TRUST_TOKEN_CLIENT_KEY *key,
const uint8_t *in, size_t len) {
if (!pmbtoken_pst1_init_method()) {
return 0;
}
return pmbtoken_client_key_from_bytes(&pmbtoken_pst1_method, key, in, len);
}
int pmbtoken_pst1_issuer_key_from_bytes(TRUST_TOKEN_ISSUER_KEY *key,
const uint8_t *in, size_t len) {
if (!pmbtoken_pst1_init_method()) {
return 0;
}
return pmbtoken_issuer_key_from_bytes(&pmbtoken_pst1_method, key, in, len);
}
STACK_OF(TRUST_TOKEN_PRETOKEN) *pmbtoken_pst1_blind(CBB *cbb, size_t count,
int include_message,
const uint8_t *msg,
size_t msg_len) {
if (!pmbtoken_pst1_init_method()) {
return NULL;
}
return pmbtoken_blind(&pmbtoken_pst1_method, cbb, count, include_message, msg,
msg_len);
}
int pmbtoken_pst1_sign(const TRUST_TOKEN_ISSUER_KEY *key, CBB *cbb, CBS *cbs,
size_t num_requested, size_t num_to_issue,
uint8_t private_metadata) {
if (!pmbtoken_pst1_init_method()) {
return 0;
}
return pmbtoken_sign(&pmbtoken_pst1_method, key, cbb, cbs, num_requested,
num_to_issue, private_metadata);
}
STACK_OF(TRUST_TOKEN) *pmbtoken_pst1_unblind(
const TRUST_TOKEN_CLIENT_KEY *key,
const STACK_OF(TRUST_TOKEN_PRETOKEN) *pretokens, CBS *cbs, size_t count,
uint32_t key_id) {
if (!pmbtoken_pst1_init_method()) {
return NULL;
}
return pmbtoken_unblind(&pmbtoken_pst1_method, key, pretokens, cbs, count,
key_id);
}
int pmbtoken_pst1_read(const TRUST_TOKEN_ISSUER_KEY *key,
uint8_t out_nonce[TRUST_TOKEN_NONCE_SIZE],
uint8_t *out_private_metadata, const uint8_t *token,
size_t token_len, int include_message,
const uint8_t *msg, size_t msg_len) {
if (!pmbtoken_pst1_init_method()) {
return 0;
}
return pmbtoken_read(&pmbtoken_pst1_method, key, out_nonce,
out_private_metadata, token, token_len, include_message,
msg, msg_len);
}
int pmbtoken_pst1_get_h_for_testing(uint8_t out[97]) {
if (!pmbtoken_pst1_init_method()) {
return 0;
}
EC_AFFINE h;
return ec_jacobian_to_affine(pmbtoken_pst1_method.group, &h,
&pmbtoken_pst1_method.h) &&
ec_point_to_bytes(pmbtoken_pst1_method.group, &h,
POINT_CONVERSION_UNCOMPRESSED, out, 97) == 97;
}