| /* 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/ec/internal.h" | 
 |  | 
 | #include "internal.h" | 
 |  | 
 |  | 
 | typedef int (*hash_to_group_func_t)(const EC_GROUP *group, EC_JACOBIAN *out, | 
 |                                     const uint8_t t[TRUST_TOKEN_NONCE_SIZE]); | 
 | 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_func)(void); | 
 |  | 
 |   // hash_to_group implements the HashToGroup operation for VOPRFs. It returns | 
 |   // one on success and zero on error. | 
 |   hash_to_group_func_t hash_to_group; | 
 |   // hash_to_scalar implements the HashToScalar operation for VOPRFs. It returns | 
 |   // one on success and zero on error. | 
 |   hash_to_scalar_func_t hash_to_scalar; | 
 | } VOPRF_METHOD; | 
 |  | 
 | static const uint8_t kDefaultAdditionalData[32] = {0}; | 
 |  | 
 | static int cbb_add_point(CBB *out, const EC_GROUP *group, | 
 |                          const EC_AFFINE *point) { | 
 |   uint8_t *p; | 
 |   size_t len = ec_point_byte_len(group, POINT_CONVERSION_UNCOMPRESSED); | 
 |   return CBB_add_space(out, &p, len) && | 
 |          ec_point_to_bytes(group, point, POINT_CONVERSION_UNCOMPRESSED, p, | 
 |                            len) == len && | 
 |          CBB_flush(out); | 
 | } | 
 |  | 
 | static int cbb_serialize_point(CBB *out, const EC_GROUP *group, | 
 |                                const EC_AFFINE *point) { | 
 |   uint8_t *p; | 
 |   size_t len = ec_point_byte_len(group, POINT_CONVERSION_COMPRESSED); | 
 |   return CBB_add_u16(out, len) && CBB_add_space(out, &p, len) && | 
 |          ec_point_to_bytes(group, point, POINT_CONVERSION_COMPRESSED, p, len) == | 
 |              len && | 
 |          CBB_flush(out); | 
 | } | 
 |  | 
 | static int cbs_get_point(CBS *cbs, const EC_GROUP *group, EC_AFFINE *out) { | 
 |   CBS child; | 
 |   size_t plen = ec_point_byte_len(group, POINT_CONVERSION_UNCOMPRESSED); | 
 |   if (!CBS_get_bytes(cbs, &child, plen) || | 
 |       !ec_point_from_uncompressed(group, out, CBS_data(&child), | 
 |                                   CBS_len(&child))) { | 
 |     return 0; | 
 |   } | 
 |   return 1; | 
 | } | 
 |  | 
 | 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 voprf_calculate_key(const VOPRF_METHOD *method, CBB *out_private, | 
 |                                CBB *out_public, const EC_SCALAR *priv) { | 
 |   const EC_GROUP *group = method->group_func(); | 
 |   EC_JACOBIAN pub; | 
 |   EC_AFFINE pub_affine; | 
 |   if (!ec_point_mul_scalar_base(group, &pub, priv) || | 
 |       !ec_jacobian_to_affine(group, &pub_affine, &pub)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_KEYGEN_FAILURE); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   if (!scalar_to_cbb(out_private, group, priv) || | 
 |       !cbb_add_point(out_public, group, &pub_affine)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_BUFFER_TOO_SMALL); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 |  | 
 | static int voprf_generate_key(const VOPRF_METHOD *method, CBB *out_private, | 
 |                               CBB *out_public) { | 
 |   EC_SCALAR priv; | 
 |   if (!ec_random_nonzero_scalar(method->group_func(), &priv, | 
 |                                 kDefaultAdditionalData)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_KEYGEN_FAILURE); | 
 |     return 0; | 
 |   } | 
 |   return voprf_calculate_key(method, out_private, out_public, &priv); | 
 | } | 
 |  | 
 | static int voprf_derive_key_from_secret(const VOPRF_METHOD *method, | 
 |                                         CBB *out_private, CBB *out_public, | 
 |                                         const uint8_t *secret, | 
 |                                         size_t secret_len) { | 
 |   static const uint8_t kKeygenLabel[] = "TrustTokenVOPRFKeyGen"; | 
 |  | 
 |   EC_SCALAR priv; | 
 |   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_bytes(&cbb, secret, secret_len) || | 
 |       !CBB_finish(&cbb, &buf, &len) || | 
 |       !method->hash_to_scalar(method->group_func(), &priv, buf, len)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_KEYGEN_FAILURE); | 
 |     goto err; | 
 |   } | 
 |  | 
 |   ok = voprf_calculate_key(method, out_private, out_public, &priv); | 
 |  | 
 | err: | 
 |   CBB_cleanup(&cbb); | 
 |   OPENSSL_free(buf); | 
 |   return ok; | 
 | } | 
 |  | 
 | static int voprf_client_key_from_bytes(const VOPRF_METHOD *method, | 
 |                                        TRUST_TOKEN_CLIENT_KEY *key, | 
 |                                        const uint8_t *in, size_t len) { | 
 |   const EC_GROUP *group = method->group_func(); | 
 |   if (!ec_point_from_uncompressed(group, &key->pubs, in, len)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 | static int voprf_issuer_key_from_bytes(const VOPRF_METHOD *method, | 
 |                                        TRUST_TOKEN_ISSUER_KEY *key, | 
 |                                        const uint8_t *in, size_t len) { | 
 |   const EC_GROUP *group = method->group_func(); | 
 |   if (!ec_scalar_from_bytes(group, &key->xs, in, len)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   // Recompute the public key. | 
 |   EC_JACOBIAN pub; | 
 |   if (!ec_point_mul_scalar_base(group, &pub, &key->xs) || | 
 |       !ec_jacobian_to_affine(group, &key->pubs, &pub)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 | static STACK_OF(TRUST_TOKEN_PRETOKEN) *voprf_blind(const VOPRF_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_func(); | 
 |   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 r in Montgomery form to simplify inverting. | 
 |     EC_SCALAR r; | 
 |     if (!ec_random_nonzero_scalar(group, &r, | 
 |                                   kDefaultAdditionalData)) { | 
 |       goto err; | 
 |     } | 
 |  | 
 |     // pretoken->r is rinv. | 
 |     ec_scalar_inv0_montgomery(group, &pretoken->r, &r); | 
 |     // Convert both out of Montgomery form. | 
 |     ec_scalar_from_montgomery(group, &r, &r); | 
 |     ec_scalar_from_montgomery(group, &pretoken->r, &pretoken->r); | 
 |  | 
 |     // Tp is the blinded token in the VOPRF protocol. | 
 |     EC_JACOBIAN P, Tp; | 
 |     if (!method->hash_to_group(group, &P, pretoken->t) || | 
 |         !ec_point_mul_scalar(group, &Tp, &P, &r) || | 
 |         !ec_jacobian_to_affine(group, &pretoken->Tp, &Tp)) { | 
 |       goto err; | 
 |     } | 
 |  | 
 |     if (!cbb_add_point(cbb, group, &pretoken->Tp)) { | 
 |       goto err; | 
 |     } | 
 |   } | 
 |  | 
 |   return pretokens; | 
 |  | 
 | err: | 
 |   sk_TRUST_TOKEN_PRETOKEN_pop_free(pretokens, TRUST_TOKEN_PRETOKEN_free); | 
 |   return NULL; | 
 | } | 
 |  | 
 | static int hash_to_scalar_dleq(const VOPRF_METHOD *method, EC_SCALAR *out, | 
 |                                const EC_AFFINE *X, const EC_AFFINE *T, | 
 |                                const EC_AFFINE *W, const EC_AFFINE *K0, | 
 |                                const EC_AFFINE *K1) { | 
 |   static const uint8_t kDLEQLabel[] = "DLEQ"; | 
 |  | 
 |   const EC_GROUP *group = method->group_func(); | 
 |   int ok = 0; | 
 |   CBB cbb; | 
 |   CBB_zero(&cbb); | 
 |   uint8_t *buf = NULL; | 
 |   size_t len; | 
 |   if (!CBB_init(&cbb, 0) || | 
 |       !CBB_add_bytes(&cbb, kDLEQLabel, sizeof(kDLEQLabel)) || | 
 |       !cbb_add_point(&cbb, group, X) || | 
 |       !cbb_add_point(&cbb, group, T) || | 
 |       !cbb_add_point(&cbb, group, W) || | 
 |       !cbb_add_point(&cbb, group, K0) || | 
 |       !cbb_add_point(&cbb, group, K1) || | 
 |       !CBB_finish(&cbb, &buf, &len) || | 
 |       !method->hash_to_scalar(group, out, buf, len)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   ok = 1; | 
 |  | 
 | err: | 
 |   CBB_cleanup(&cbb); | 
 |   OPENSSL_free(buf); | 
 |   return ok; | 
 | } | 
 |  | 
 | static int hash_to_scalar_challenge(const VOPRF_METHOD *method, EC_SCALAR *out, | 
 |                                     const EC_AFFINE *Bm, const EC_AFFINE *a0, | 
 |                                     const EC_AFFINE *a1, const EC_AFFINE *a2, | 
 |                                     const EC_AFFINE *a3) { | 
 |   static const uint8_t kChallengeLabel[] = "Challenge"; | 
 |  | 
 |   const EC_GROUP *group = method->group_func(); | 
 |   CBB cbb; | 
 |   uint8_t transcript[5 * EC_MAX_COMPRESSED + 2 + sizeof(kChallengeLabel) - 1]; | 
 |   size_t len; | 
 |   if (!CBB_init_fixed(&cbb, transcript, sizeof(transcript)) || | 
 |       !cbb_serialize_point(&cbb, group, Bm) || | 
 |       !cbb_serialize_point(&cbb, group, a0) || | 
 |       !cbb_serialize_point(&cbb, group, a1) || | 
 |       !cbb_serialize_point(&cbb, group, a2) || | 
 |       !cbb_serialize_point(&cbb, group, a3) || | 
 |       !CBB_add_bytes(&cbb, kChallengeLabel, sizeof(kChallengeLabel) - 1) || | 
 |       !CBB_finish(&cbb, NULL, &len) || | 
 |       !method->hash_to_scalar(group, out, transcript, len)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 | static int hash_to_scalar_batch(const VOPRF_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_to_scalar(method->group_func(), out, buf, len)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   ok = 1; | 
 |  | 
 | err: | 
 |   CBB_cleanup(&cbb); | 
 |   OPENSSL_free(buf); | 
 |   return ok; | 
 | } | 
 |  | 
 | static int dleq_generate(const VOPRF_METHOD *method, CBB *cbb, | 
 |                          const TRUST_TOKEN_ISSUER_KEY *priv, | 
 |                          const EC_JACOBIAN *T, const EC_JACOBIAN *W) { | 
 |   const EC_GROUP *group = method->group_func(); | 
 |  | 
 |   enum { | 
 |     idx_T, | 
 |     idx_W, | 
 |     idx_k0, | 
 |     idx_k1, | 
 |     num_idx, | 
 |   }; | 
 |   EC_JACOBIAN jacobians[num_idx]; | 
 |  | 
 |   // Setup the DLEQ proof. | 
 |   EC_SCALAR r; | 
 |   if (// r <- Zp | 
 |       !ec_random_nonzero_scalar(group, &r, kDefaultAdditionalData) || | 
 |       // k0;k1 = r*(G;T) | 
 |       !ec_point_mul_scalar_base(group, &jacobians[idx_k0], &r) || | 
 |       !ec_point_mul_scalar(group, &jacobians[idx_k1], T, &r))  { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   EC_AFFINE affines[num_idx]; | 
 |   jacobians[idx_T] = *T; | 
 |   jacobians[idx_W] = *W; | 
 |   if (!ec_jacobian_to_affine_batch(group, affines, jacobians, num_idx)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   // Compute c = Hc(...). | 
 |   EC_SCALAR c; | 
 |   if (!hash_to_scalar_dleq(method, &c, &priv->pubs, &affines[idx_T], | 
 |                            &affines[idx_W], &affines[idx_k0], | 
 |                            &affines[idx_k1])) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |  | 
 |   EC_SCALAR c_mont; | 
 |   ec_scalar_to_montgomery(group, &c_mont, &c); | 
 |  | 
 |   // u = r + c*xs | 
 |   EC_SCALAR u; | 
 |   ec_scalar_mul_montgomery(group, &u, &priv->xs, &c_mont); | 
 |   ec_scalar_add(group, &u, &r, &u); | 
 |  | 
 |   // Store DLEQ proof in transcript. | 
 |   if (!scalar_to_cbb(cbb, group, &c) || | 
 |       !scalar_to_cbb(cbb, group, &u)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 | static int mul_public_2(const EC_GROUP *group, EC_JACOBIAN *out, | 
 |                         const EC_JACOBIAN *p0, const EC_SCALAR *scalar0, | 
 |                         const EC_JACOBIAN *p1, const EC_SCALAR *scalar1) { | 
 |   EC_JACOBIAN points[2] = {*p0, *p1}; | 
 |   EC_SCALAR scalars[2] = {*scalar0, *scalar1}; | 
 |   return ec_point_mul_scalar_public_batch(group, out, /*g_scalar=*/NULL, points, | 
 |                                           scalars, 2); | 
 | } | 
 |  | 
 | static int dleq_verify(const VOPRF_METHOD *method, CBS *cbs, | 
 |                        const TRUST_TOKEN_CLIENT_KEY *pub, const EC_JACOBIAN *T, | 
 |                        const EC_JACOBIAN *W) { | 
 |   const EC_GROUP *group = method->group_func(); | 
 |  | 
 |  | 
 |   enum { | 
 |     idx_T, | 
 |     idx_W, | 
 |     idx_k0, | 
 |     idx_k1, | 
 |     num_idx, | 
 |   }; | 
 |   EC_JACOBIAN jacobians[num_idx]; | 
 |  | 
 |   // Decode the DLEQ proof. | 
 |   EC_SCALAR c, u; | 
 |   if (!scalar_from_cbs(cbs, group, &c) || | 
 |       !scalar_from_cbs(cbs, group, &u)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   // k0;k1 = u*(G;T) - c*(pub;W) | 
 |   EC_JACOBIAN pubs; | 
 |   ec_affine_to_jacobian(group, &pubs, &pub->pubs); | 
 |   EC_SCALAR minus_c; | 
 |   ec_scalar_neg(group, &minus_c, &c); | 
 |   if (!ec_point_mul_scalar_public(group, &jacobians[idx_k0], &u, &pubs, | 
 |                                   &minus_c) || | 
 |       !mul_public_2(group, &jacobians[idx_k1], T, &u, W, &minus_c)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   // Check the DLEQ proof. | 
 |   EC_AFFINE affines[num_idx]; | 
 |   jacobians[idx_T] = *T; | 
 |   jacobians[idx_W] = *W; | 
 |   if (!ec_jacobian_to_affine_batch(group, affines, jacobians, num_idx)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   // Compute c = Hc(...). | 
 |   EC_SCALAR calculated; | 
 |   if (!hash_to_scalar_dleq(method, &calculated, &pub->pubs, &affines[idx_T], | 
 |                            &affines[idx_W], &affines[idx_k0], | 
 |                            &affines[idx_k1])) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   // c == calculated | 
 |   if (!ec_scalar_equal_vartime(group, &c, &calculated)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_INVALID_PROOF); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 | static int voprf_sign_tt(const VOPRF_METHOD *method, | 
 |                          const TRUST_TOKEN_ISSUER_KEY *key, CBB *cbb, CBS *cbs, | 
 |                          size_t num_requested, size_t num_to_issue) { | 
 |   const EC_GROUP *group = method->group_func(); | 
 |   if (num_requested < num_to_issue) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, ERR_R_INTERNAL_ERROR); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   int ret = 0; | 
 |   EC_JACOBIAN *BTs = OPENSSL_calloc(num_to_issue, sizeof(EC_JACOBIAN)); | 
 |   EC_JACOBIAN *Zs = OPENSSL_calloc(num_to_issue, sizeof(EC_JACOBIAN)); | 
 |   EC_SCALAR *es = OPENSSL_calloc(num_to_issue, sizeof(EC_SCALAR)); | 
 |   CBB batch_cbb; | 
 |   CBB_zero(&batch_cbb); | 
 |   if (!BTs || | 
 |       !Zs || | 
 |       !es || | 
 |       !CBB_init(&batch_cbb, 0) || | 
 |       !cbb_add_point(&batch_cbb, group, &key->pubs)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   for (size_t i = 0; i < num_to_issue; i++) { | 
 |     EC_AFFINE BT_affine, Z_affine; | 
 |     EC_JACOBIAN BT, Z; | 
 |     if (!cbs_get_point(cbs, group, &BT_affine)) { | 
 |       OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |       goto err; | 
 |     } | 
 |     ec_affine_to_jacobian(group, &BT, &BT_affine); | 
 |     if (!ec_point_mul_scalar(group, &Z, &BT, &key->xs) || | 
 |         !ec_jacobian_to_affine(group, &Z_affine, &Z) || | 
 |         !cbb_add_point(cbb, group, &Z_affine)) { | 
 |       goto err; | 
 |     } | 
 |  | 
 |     if (!cbb_add_point(&batch_cbb, group, &BT_affine) || | 
 |         !cbb_add_point(&batch_cbb, group, &Z_affine)) { | 
 |       goto err; | 
 |     } | 
 |     BTs[i] = BT; | 
 |     Zs[i] = Z; | 
 |  | 
 |     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_to_scalar_batch(method, &es[i], &batch_cbb, i)) { | 
 |       goto err; | 
 |     } | 
 |   } | 
 |  | 
 |   EC_JACOBIAN BT_batch, Z_batch; | 
 |   if (!ec_point_mul_scalar_public_batch(group, &BT_batch, | 
 |                                         /*g_scalar=*/NULL, BTs, es, | 
 |                                         num_to_issue) || | 
 |       !ec_point_mul_scalar_public_batch(group, &Z_batch, | 
 |                                         /*g_scalar=*/NULL, Zs, es, | 
 |                                         num_to_issue)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   CBB proof; | 
 |   if (!CBB_add_u16_length_prefixed(cbb, &proof) || | 
 |       !dleq_generate(method, &proof, key, &BT_batch, &Z_batch) || | 
 |       !CBB_flush(cbb)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   // Skip over any unused requests. | 
 |   size_t point_len = ec_point_byte_len(group, POINT_CONVERSION_UNCOMPRESSED); | 
 |   if (!CBS_skip(cbs, point_len * (num_requested - num_to_issue))) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |     goto err; | 
 |   } | 
 |  | 
 |   ret = 1; | 
 |  | 
 | err: | 
 |   OPENSSL_free(BTs); | 
 |   OPENSSL_free(Zs); | 
 |   OPENSSL_free(es); | 
 |   CBB_cleanup(&batch_cbb); | 
 |   return ret; | 
 | } | 
 |  | 
 | static STACK_OF(TRUST_TOKEN) *voprf_unblind_tt( | 
 |     const VOPRF_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_func(); | 
 |   if (count > sk_TRUST_TOKEN_PRETOKEN_num(pretokens)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |     return NULL; | 
 |   } | 
 |  | 
 |   int ok = 0; | 
 |   STACK_OF(TRUST_TOKEN) *ret = sk_TRUST_TOKEN_new_null(); | 
 |   EC_JACOBIAN *BTs = OPENSSL_calloc(count, sizeof(EC_JACOBIAN)); | 
 |   EC_JACOBIAN *Zs = OPENSSL_calloc(count, sizeof(EC_JACOBIAN)); | 
 |   EC_SCALAR *es = OPENSSL_calloc(count, sizeof(EC_SCALAR)); | 
 |   CBB batch_cbb; | 
 |   CBB_zero(&batch_cbb); | 
 |   if (ret == NULL || | 
 |       BTs == NULL || | 
 |       Zs == NULL || | 
 |       es == NULL || | 
 |       !CBB_init(&batch_cbb, 0) || | 
 |       !cbb_add_point(&batch_cbb, group, &key->pubs)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   for (size_t i = 0; i < count; i++) { | 
 |     const TRUST_TOKEN_PRETOKEN *pretoken = | 
 |         sk_TRUST_TOKEN_PRETOKEN_value(pretokens, i); | 
 |  | 
 |     EC_AFFINE Z_affine; | 
 |     if (!cbs_get_point(cbs, group, &Z_affine)) { | 
 |       OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |       goto err; | 
 |     } | 
 |  | 
 |     ec_affine_to_jacobian(group, &BTs[i], &pretoken->Tp); | 
 |     ec_affine_to_jacobian(group, &Zs[i], &Z_affine); | 
 |  | 
 |     if (!cbb_add_point(&batch_cbb, group, &pretoken->Tp) || | 
 |         !cbb_add_point(&batch_cbb, group, &Z_affine)) { | 
 |       goto err; | 
 |     } | 
 |  | 
 |     // Unblind the token. | 
 |     // pretoken->r is rinv. | 
 |     EC_JACOBIAN N; | 
 |     EC_AFFINE N_affine; | 
 |     if (!ec_point_mul_scalar(group, &N, &Zs[i], &pretoken->r) || | 
 |         !ec_jacobian_to_affine(group, &N_affine, &N)) { | 
 |       goto err; | 
 |     } | 
 |  | 
 |     // Serialize the token. Include |key_id| to avoid an extra copy in the layer | 
 |     // above. | 
 |     CBB token_cbb; | 
 |     size_t point_len = ec_point_byte_len(group, POINT_CONVERSION_UNCOMPRESSED); | 
 |     if (!CBB_init(&token_cbb, 4 + TRUST_TOKEN_NONCE_SIZE + (2 + point_len)) || | 
 |         !CBB_add_u32(&token_cbb, key_id) || | 
 |         !CBB_add_bytes(&token_cbb, pretoken->salt, TRUST_TOKEN_NONCE_SIZE) || | 
 |         !cbb_add_point(&token_cbb, group, &N_affine) || | 
 |         !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_to_scalar_batch(method, &es[i], &batch_cbb, i)) { | 
 |       goto err; | 
 |     } | 
 |   } | 
 |  | 
 |   EC_JACOBIAN BT_batch, Z_batch; | 
 |   if (!ec_point_mul_scalar_public_batch(group, &BT_batch, | 
 |                                         /*g_scalar=*/NULL, BTs, es, count) || | 
 |       !ec_point_mul_scalar_public_batch(group, &Z_batch, | 
 |                                         /*g_scalar=*/NULL, Zs, es, count)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   CBS proof; | 
 |   if (!CBS_get_u16_length_prefixed(cbs, &proof) || | 
 |       !dleq_verify(method, &proof, key, &BT_batch, &Z_batch) || | 
 |       CBS_len(&proof) != 0) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   ok = 1; | 
 |  | 
 | err: | 
 |   OPENSSL_free(BTs); | 
 |   OPENSSL_free(Zs); | 
 |   OPENSSL_free(es); | 
 |   CBB_cleanup(&batch_cbb); | 
 |   if (!ok) { | 
 |     sk_TRUST_TOKEN_pop_free(ret, TRUST_TOKEN_free); | 
 |     ret = NULL; | 
 |   } | 
 |   return ret; | 
 | } | 
 |  | 
 | static void sha384_update_u16(SHA512_CTX *ctx, uint16_t v) { | 
 |   uint8_t buf[2] = {v >> 8, v & 0xff}; | 
 |   SHA384_Update(ctx, buf, 2); | 
 | } | 
 |  | 
 | static void sha384_update_point_with_length( | 
 |      SHA512_CTX *ctx, const EC_GROUP *group, const EC_AFFINE *point) { | 
 |   uint8_t buf[EC_MAX_COMPRESSED]; | 
 |   size_t len = ec_point_to_bytes(group, point, POINT_CONVERSION_COMPRESSED, | 
 |                                  buf, sizeof(buf)); | 
 |   assert(len > 0); | 
 |   sha384_update_u16(ctx, (uint16_t)len); | 
 |   SHA384_Update(ctx, buf, len); | 
 | } | 
 |  | 
 | static int compute_composite_seed(const VOPRF_METHOD *method, | 
 |                                   uint8_t out[SHA384_DIGEST_LENGTH], | 
 |                                   const EC_AFFINE *pub) { | 
 |   const EC_GROUP *group = method->group_func(); | 
 |   static const uint8_t kSeedDST[] = "Seed-OPRFV1-\x01-P384-SHA384"; | 
 |  | 
 |   SHA512_CTX hash_ctx; | 
 |   SHA384_Init(&hash_ctx); | 
 |   sha384_update_point_with_length(&hash_ctx, group, pub); | 
 |   sha384_update_u16(&hash_ctx, sizeof(kSeedDST) - 1); | 
 |   SHA384_Update(&hash_ctx, kSeedDST, sizeof(kSeedDST) - 1); | 
 |   SHA384_Final(out, &hash_ctx); | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 | static int compute_composite_element(const VOPRF_METHOD *method, | 
 |                                      uint8_t seed[SHA384_DIGEST_LENGTH], | 
 |                                      EC_SCALAR *di, size_t index, | 
 |                                      const EC_AFFINE *C, const EC_AFFINE *D) { | 
 |   static const uint8_t kCompositeLabel[] = "Composite"; | 
 |   const EC_GROUP *group = method->group_func(); | 
 |  | 
 |   if (index > UINT16_MAX) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   CBB cbb; | 
 |   uint8_t transcript[2 + SHA384_DIGEST_LENGTH + 2 + 2 * EC_MAX_COMPRESSED + | 
 |                      sizeof(kCompositeLabel) - 1]; | 
 |   size_t len; | 
 |   if (!CBB_init_fixed(&cbb, transcript, sizeof(transcript)) || | 
 |       !CBB_add_u16(&cbb, SHA384_DIGEST_LENGTH) || | 
 |       !CBB_add_bytes(&cbb, seed, SHA384_DIGEST_LENGTH) || | 
 |       !CBB_add_u16(&cbb, index) || | 
 |       !cbb_serialize_point(&cbb, group, C) || | 
 |       !cbb_serialize_point(&cbb, group, D) || | 
 |       !CBB_add_bytes(&cbb, kCompositeLabel, | 
 |                      sizeof(kCompositeLabel) - 1) || | 
 |       !CBB_finish(&cbb, NULL, &len) || | 
 |       !method->hash_to_scalar(group, di, transcript, len)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 | static int generate_proof(const VOPRF_METHOD *method, CBB *cbb, | 
 |                           const TRUST_TOKEN_ISSUER_KEY *priv, | 
 |                           const EC_SCALAR *r, const EC_JACOBIAN *M, | 
 |                           const EC_JACOBIAN *Z) { | 
 |   const EC_GROUP *group = method->group_func(); | 
 |  | 
 |   enum { | 
 |     idx_M, | 
 |     idx_Z, | 
 |     idx_t2, | 
 |     idx_t3, | 
 |     num_idx, | 
 |   }; | 
 |   EC_JACOBIAN jacobians[num_idx]; | 
 |  | 
 |   if (!ec_point_mul_scalar_base(group, &jacobians[idx_t2], r) || | 
 |       !ec_point_mul_scalar(group, &jacobians[idx_t3], M, r)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |  | 
 |   EC_AFFINE affines[num_idx]; | 
 |   jacobians[idx_M] = *M; | 
 |   jacobians[idx_Z] = *Z; | 
 |   if (!ec_jacobian_to_affine_batch(group, affines, jacobians, num_idx)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   EC_SCALAR c; | 
 |   if (!hash_to_scalar_challenge(method, &c, &priv->pubs, &affines[idx_M], | 
 |                                 &affines[idx_Z], &affines[idx_t2], | 
 |                                 &affines[idx_t3])) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   EC_SCALAR c_mont; | 
 |   ec_scalar_to_montgomery(group, &c_mont, &c); | 
 |  | 
 |   // s = r - c*xs | 
 |   EC_SCALAR s; | 
 |   ec_scalar_mul_montgomery(group, &s, &priv->xs, &c_mont); | 
 |   ec_scalar_sub(group, &s, r, &s); | 
 |  | 
 |   // Store DLEQ proof in transcript. | 
 |   if (!scalar_to_cbb(cbb, group, &c) || | 
 |       !scalar_to_cbb(cbb, group, &s)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 | static int verify_proof(const VOPRF_METHOD *method, CBS *cbs, | 
 |                         const TRUST_TOKEN_CLIENT_KEY *pub, | 
 |                         const EC_JACOBIAN *M, const EC_JACOBIAN *Z) { | 
 |   const EC_GROUP *group = method->group_func(); | 
 |  | 
 |   enum { | 
 |     idx_M, | 
 |     idx_Z, | 
 |     idx_t2, | 
 |     idx_t3, | 
 |     num_idx, | 
 |   }; | 
 |   EC_JACOBIAN jacobians[num_idx]; | 
 |  | 
 |   EC_SCALAR c, s; | 
 |   if (!scalar_from_cbs(cbs, group, &c) || | 
 |       !scalar_from_cbs(cbs, group, &s)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   EC_JACOBIAN pubs; | 
 |   ec_affine_to_jacobian(group, &pubs, &pub->pubs); | 
 |   if (!ec_point_mul_scalar_public(group, &jacobians[idx_t2], &s, &pubs, | 
 |                                   &c) || | 
 |       !mul_public_2(group, &jacobians[idx_t3], M, &s, Z, &c)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   EC_AFFINE affines[num_idx]; | 
 |   jacobians[idx_M] = *M; | 
 |   jacobians[idx_Z] = *Z; | 
 |   if (!ec_jacobian_to_affine_batch(group, affines, jacobians, num_idx)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   EC_SCALAR expected_c; | 
 |   if (!hash_to_scalar_challenge(method, &expected_c, &pub->pubs, | 
 |                                 &affines[idx_M], &affines[idx_Z], | 
 |                                 &affines[idx_t2], &affines[idx_t3])) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   // c == expected_c | 
 |   if (!ec_scalar_equal_vartime(group, &c, &expected_c)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_INVALID_PROOF); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 | static int voprf_sign_impl(const VOPRF_METHOD *method, | 
 |                            const TRUST_TOKEN_ISSUER_KEY *key, CBB *cbb, | 
 |                            CBS *cbs, size_t num_requested, size_t num_to_issue, | 
 |                            const EC_SCALAR *proof_scalar) { | 
 |   const EC_GROUP *group = method->group_func(); | 
 |   if (num_requested < num_to_issue) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, ERR_R_INTERNAL_ERROR); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   int ret = 0; | 
 |   EC_JACOBIAN *BTs = OPENSSL_calloc(num_to_issue, sizeof(EC_JACOBIAN)); | 
 |   EC_JACOBIAN *Zs = OPENSSL_calloc(num_to_issue, sizeof(EC_JACOBIAN)); | 
 |   EC_SCALAR *dis = OPENSSL_calloc(num_to_issue, sizeof(EC_SCALAR)); | 
 |   if (!BTs || !Zs || !dis) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   uint8_t seed[SHA384_DIGEST_LENGTH]; | 
 |   if (!compute_composite_seed(method, seed, &key->pubs)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   // This implements the BlindEvaluateBatch as defined in section 4 of | 
 |   // draft-robert-privacypass-batched-tokens-01, based on the constructions | 
 |   // in draft-irtf-cfrg-voprf-21. To optimize the computation of the proof, | 
 |   // the computation of di is done during the token signing and passed into | 
 |   // the proof generation. | 
 |   for (size_t i = 0; i < num_to_issue; i++) { | 
 |     EC_AFFINE BT_affine, Z_affine; | 
 |     EC_JACOBIAN BT, Z; | 
 |     if (!cbs_get_point(cbs, group, &BT_affine)) { | 
 |       OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |       goto err; | 
 |     } | 
 |     ec_affine_to_jacobian(group, &BT, &BT_affine); | 
 |     if (!ec_point_mul_scalar(group, &Z, &BT, &key->xs) || | 
 |         !ec_jacobian_to_affine(group, &Z_affine, &Z) || | 
 |         !cbb_add_point(cbb, group, &Z_affine)) { | 
 |       goto err; | 
 |     } | 
 |     BTs[i] = BT; | 
 |     Zs[i] = Z; | 
 |     if (!compute_composite_element(method, seed, &dis[i], i, &BT_affine, | 
 |                                    &Z_affine)) { | 
 |       goto err; | 
 |     } | 
 |  | 
 |     if (!CBB_flush(cbb)) { | 
 |       goto err; | 
 |     } | 
 |   } | 
 |  | 
 |   EC_JACOBIAN M, Z; | 
 |   if (!ec_point_mul_scalar_public_batch(group, &M, | 
 |                                         /*g_scalar=*/NULL, BTs, dis, | 
 |                                         num_to_issue) || | 
 |       !ec_point_mul_scalar(group, &Z, &M, &key->xs)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   CBB proof; | 
 |   if (!CBB_add_u16_length_prefixed(cbb, &proof) || | 
 |       !generate_proof(method, &proof, key, proof_scalar, &M, &Z) || | 
 |       !CBB_flush(cbb)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   // Skip over any unused requests. | 
 |   size_t point_len = ec_point_byte_len(group, POINT_CONVERSION_UNCOMPRESSED); | 
 |   if (!CBS_skip(cbs, point_len * (num_requested - num_to_issue))) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |     goto err; | 
 |   } | 
 |  | 
 |   ret = 1; | 
 |  | 
 | err: | 
 |   OPENSSL_free(BTs); | 
 |   OPENSSL_free(Zs); | 
 |   OPENSSL_free(dis); | 
 |   return ret; | 
 | } | 
 |  | 
 | static int voprf_sign(const VOPRF_METHOD *method, | 
 |                       const TRUST_TOKEN_ISSUER_KEY *key, CBB *cbb, CBS *cbs, | 
 |                       size_t num_requested, size_t num_to_issue) { | 
 |   EC_SCALAR proof_scalar; | 
 |   if (!ec_random_nonzero_scalar(method->group_func(), &proof_scalar, | 
 |                                 kDefaultAdditionalData)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return voprf_sign_impl(method, key, cbb, cbs, num_requested, num_to_issue, | 
 |                          &proof_scalar); | 
 | } | 
 |  | 
 | static int voprf_sign_with_proof_scalar_for_testing( | 
 |     const VOPRF_METHOD *method, const TRUST_TOKEN_ISSUER_KEY *key, CBB *cbb, | 
 |     CBS *cbs, size_t num_requested, size_t num_to_issue, | 
 |     const uint8_t *proof_scalar_buf, size_t proof_scalar_len) { | 
 |   EC_SCALAR proof_scalar; | 
 |   if (!ec_scalar_from_bytes(method->group_func(), &proof_scalar, | 
 |                             proof_scalar_buf, proof_scalar_len)) { | 
 |     return 0; | 
 |   } | 
 |   return voprf_sign_impl(method, key, cbb, cbs, num_requested, num_to_issue, | 
 |                          &proof_scalar); | 
 | } | 
 |  | 
 | static STACK_OF(TRUST_TOKEN) *voprf_unblind( | 
 |     const VOPRF_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_func(); | 
 |   if (count > sk_TRUST_TOKEN_PRETOKEN_num(pretokens)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |     return NULL; | 
 |   } | 
 |  | 
 |   int ok = 0; | 
 |   STACK_OF(TRUST_TOKEN) *ret = sk_TRUST_TOKEN_new_null(); | 
 |   EC_JACOBIAN *BTs = OPENSSL_calloc(count, sizeof(EC_JACOBIAN)); | 
 |   EC_JACOBIAN *Zs = OPENSSL_calloc(count, sizeof(EC_JACOBIAN)); | 
 |   EC_SCALAR *dis = OPENSSL_calloc(count, sizeof(EC_SCALAR)); | 
 |   if (ret == NULL || !BTs || !Zs || !dis) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   uint8_t seed[SHA384_DIGEST_LENGTH]; | 
 |   if (!compute_composite_seed(method, seed, &key->pubs)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   for (size_t i = 0; i < count; i++) { | 
 |     const TRUST_TOKEN_PRETOKEN *pretoken = | 
 |         sk_TRUST_TOKEN_PRETOKEN_value(pretokens, i); | 
 |  | 
 |     EC_AFFINE Z_affine; | 
 |     if (!cbs_get_point(cbs, group, &Z_affine)) { | 
 |       OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_DECODE_FAILURE); | 
 |       goto err; | 
 |     } | 
 |  | 
 |     ec_affine_to_jacobian(group, &BTs[i], &pretoken->Tp); | 
 |     ec_affine_to_jacobian(group, &Zs[i], &Z_affine); | 
 |     if (!compute_composite_element(method, seed, &dis[i], i, &pretoken->Tp, | 
 |                                    &Z_affine)) { | 
 |       goto err; | 
 |     } | 
 |  | 
 |     // Unblind the token. | 
 |     // pretoken->r is rinv. | 
 |     EC_JACOBIAN N; | 
 |     EC_AFFINE N_affine; | 
 |     if (!ec_point_mul_scalar(group, &N, &Zs[i], &pretoken->r) || | 
 |         !ec_jacobian_to_affine(group, &N_affine, &N)) { | 
 |       goto err; | 
 |     } | 
 |  | 
 |     // Serialize the token. Include |key_id| to avoid an extra copy in the layer | 
 |     // above. | 
 |     CBB token_cbb; | 
 |     size_t point_len = ec_point_byte_len(group, POINT_CONVERSION_UNCOMPRESSED); | 
 |     if (!CBB_init(&token_cbb, 4 + TRUST_TOKEN_NONCE_SIZE + (2 + point_len)) || | 
 |         !CBB_add_u32(&token_cbb, key_id) || | 
 |         !CBB_add_bytes(&token_cbb, pretoken->salt, TRUST_TOKEN_NONCE_SIZE) || | 
 |         !cbb_add_point(&token_cbb, group, &N_affine) || | 
 |         !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; | 
 |     } | 
 |   } | 
 |  | 
 |   EC_JACOBIAN M, Z; | 
 |   if (!ec_point_mul_scalar_public_batch(group, &M, | 
 |                                         /*g_scalar=*/NULL, BTs, dis, | 
 |                                         count) || | 
 |       !ec_point_mul_scalar_public_batch(group, &Z, | 
 |                                         /*g_scalar=*/NULL, Zs, dis, | 
 |                                         count)) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   CBS proof; | 
 |   if (!CBS_get_u16_length_prefixed(cbs, &proof) || | 
 |       !verify_proof(method, &proof, key, &M, &Z) || | 
 |       CBS_len(&proof) != 0) { | 
 |     goto err; | 
 |   } | 
 |  | 
 |   ok = 1; | 
 |  | 
 | err: | 
 |   OPENSSL_free(BTs); | 
 |   OPENSSL_free(Zs); | 
 |   OPENSSL_free(dis); | 
 |   if (!ok) { | 
 |     sk_TRUST_TOKEN_pop_free(ret, TRUST_TOKEN_free); | 
 |     ret = NULL; | 
 |   } | 
 |   return ret; | 
 | } | 
 |  | 
 | static int voprf_read(const VOPRF_METHOD *method, | 
 |                       const TRUST_TOKEN_ISSUER_KEY *key, | 
 |                       uint8_t out_nonce[TRUST_TOKEN_NONCE_SIZE], | 
 |                       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_func(); | 
 |   CBS cbs, salt; | 
 |   CBS_init(&cbs, token, token_len); | 
 |   EC_AFFINE Ws; | 
 |   if (!CBS_get_bytes(&cbs, &salt, TRUST_TOKEN_NONCE_SIZE) || | 
 |       !cbs_get_point(&cbs, group, &Ws) || | 
 |       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_to_group(group, &T, out_nonce)) { | 
 |     return 0; | 
 |   } | 
 |  | 
 |   EC_JACOBIAN Ws_calculated; | 
 |   if (!ec_point_mul_scalar(group, &Ws_calculated, &T, &key->xs) || | 
 |       !ec_affine_jacobian_equal(group, &Ws, &Ws_calculated)) { | 
 |     OPENSSL_PUT_ERROR(TRUST_TOKEN, TRUST_TOKEN_R_BAD_VALIDITY_CHECK); | 
 |     return 0; | 
 |   } | 
 |  | 
 |   return 1; | 
 | } | 
 |  | 
 |  | 
 | // VOPRF experiment v2. | 
 |  | 
 | static int voprf_exp2_hash_to_group(const EC_GROUP *group, EC_JACOBIAN *out, | 
 |                                     const uint8_t t[TRUST_TOKEN_NONCE_SIZE]) { | 
 |   const uint8_t kHashTLabel[] = "TrustToken VOPRF Experiment V2 HashToGroup"; | 
 |   return ec_hash_to_curve_p384_xmd_sha512_sswu_draft07( | 
 |       group, out, kHashTLabel, sizeof(kHashTLabel), t, TRUST_TOKEN_NONCE_SIZE); | 
 | } | 
 |  | 
 | static int voprf_exp2_hash_to_scalar(const EC_GROUP *group, EC_SCALAR *out, | 
 |                              uint8_t *buf, size_t len) { | 
 |   const uint8_t kHashCLabel[] = "TrustToken VOPRF Experiment V2 HashToScalar"; | 
 |   return ec_hash_to_scalar_p384_xmd_sha512_draft07( | 
 |       group, out, kHashCLabel, sizeof(kHashCLabel), buf, len); | 
 | } | 
 |  | 
 | static VOPRF_METHOD voprf_exp2_method = { | 
 |     EC_group_p384, voprf_exp2_hash_to_group, voprf_exp2_hash_to_scalar}; | 
 |  | 
 | int voprf_exp2_generate_key(CBB *out_private, CBB *out_public) { | 
 |   return voprf_generate_key(&voprf_exp2_method, out_private, out_public); | 
 | } | 
 |  | 
 | int voprf_exp2_derive_key_from_secret(CBB *out_private, CBB *out_public, | 
 |                                       const uint8_t *secret, | 
 |                                       size_t secret_len) { | 
 |   return voprf_derive_key_from_secret(&voprf_exp2_method, out_private, | 
 |                                       out_public, secret, secret_len); | 
 | } | 
 |  | 
 | int voprf_exp2_client_key_from_bytes(TRUST_TOKEN_CLIENT_KEY *key, | 
 |                                      const uint8_t *in, size_t len) { | 
 |   return voprf_client_key_from_bytes(&voprf_exp2_method, key, in, len); | 
 | } | 
 |  | 
 | int voprf_exp2_issuer_key_from_bytes(TRUST_TOKEN_ISSUER_KEY *key, | 
 |                                      const uint8_t *in, size_t len) { | 
 |   return voprf_issuer_key_from_bytes(&voprf_exp2_method, key, in, len); | 
 | } | 
 |  | 
 | STACK_OF(TRUST_TOKEN_PRETOKEN) *voprf_exp2_blind(CBB *cbb, size_t count, | 
 |                                                  int include_message, | 
 |                                                  const uint8_t *msg, | 
 |                                                  size_t msg_len) { | 
 |   return voprf_blind(&voprf_exp2_method, cbb, count, include_message, msg, | 
 |                      msg_len); | 
 | } | 
 |  | 
 | int voprf_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 (private_metadata != 0) { | 
 |     return 0; | 
 |   } | 
 |   return voprf_sign_tt(&voprf_exp2_method, key, cbb, cbs, num_requested, | 
 |                        num_to_issue); | 
 | } | 
 |  | 
 | STACK_OF(TRUST_TOKEN) *voprf_exp2_unblind( | 
 |     const TRUST_TOKEN_CLIENT_KEY *key, | 
 |     const STACK_OF(TRUST_TOKEN_PRETOKEN) *pretokens, CBS *cbs, size_t count, | 
 |     uint32_t key_id) { | 
 |   return voprf_unblind_tt(&voprf_exp2_method, key, pretokens, cbs, count, | 
 |                           key_id); | 
 | } | 
 |  | 
 | int voprf_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) { | 
 |   return voprf_read(&voprf_exp2_method, key, out_nonce, token, token_len, | 
 |                     include_message, msg, msg_len); | 
 | } | 
 |  | 
 | // VOPRF PST v1. | 
 |  | 
 | static int voprf_pst1_hash_to_group(const EC_GROUP *group, EC_JACOBIAN *out, | 
 |                                     const uint8_t t[TRUST_TOKEN_NONCE_SIZE]) { | 
 |   const uint8_t kHashTLabel[] = "HashToGroup-OPRFV1-\x01-P384-SHA384"; | 
 |   return ec_hash_to_curve_p384_xmd_sha384_sswu(group, out, kHashTLabel, | 
 |                                                sizeof(kHashTLabel) - 1, t, | 
 |                                                TRUST_TOKEN_NONCE_SIZE); | 
 | } | 
 |  | 
 | static int voprf_pst1_hash_to_scalar(const EC_GROUP *group, EC_SCALAR *out, | 
 |                              uint8_t *buf, size_t len) { | 
 |   const uint8_t kHashCLabel[] = "HashToScalar-OPRFV1-\x01-P384-SHA384"; | 
 |   return ec_hash_to_scalar_p384_xmd_sha384(group, out, kHashCLabel, | 
 |                                            sizeof(kHashCLabel) - 1, buf, len); | 
 | } | 
 |  | 
 | static VOPRF_METHOD voprf_pst1_method = { | 
 |     EC_group_p384, voprf_pst1_hash_to_group, voprf_pst1_hash_to_scalar}; | 
 |  | 
 | int voprf_pst1_generate_key(CBB *out_private, CBB *out_public) { | 
 |   return voprf_generate_key(&voprf_pst1_method, out_private, out_public); | 
 | } | 
 |  | 
 | int voprf_pst1_derive_key_from_secret(CBB *out_private, CBB *out_public, | 
 |                                       const uint8_t *secret, | 
 |                                       size_t secret_len) { | 
 |   return voprf_derive_key_from_secret(&voprf_pst1_method, out_private, | 
 |                                       out_public, secret, secret_len); | 
 | } | 
 |  | 
 | int voprf_pst1_client_key_from_bytes(TRUST_TOKEN_CLIENT_KEY *key, | 
 |                                      const uint8_t *in, size_t len) { | 
 |   return voprf_client_key_from_bytes(&voprf_pst1_method, key, in, len); | 
 | } | 
 |  | 
 | int voprf_pst1_issuer_key_from_bytes(TRUST_TOKEN_ISSUER_KEY *key, | 
 |                                      const uint8_t *in, size_t len) { | 
 |   return voprf_issuer_key_from_bytes(&voprf_pst1_method, key, in, len); | 
 | } | 
 |  | 
 | STACK_OF(TRUST_TOKEN_PRETOKEN) *voprf_pst1_blind(CBB *cbb, size_t count, | 
 |                                                  int include_message, | 
 |                                                  const uint8_t *msg, | 
 |                                                  size_t msg_len) { | 
 |   return voprf_blind(&voprf_pst1_method, cbb, count, include_message, msg, | 
 |                      msg_len); | 
 | } | 
 |  | 
 | int voprf_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 (private_metadata != 0) { | 
 |     return 0; | 
 |   } | 
 |   return voprf_sign(&voprf_pst1_method, key, cbb, cbs, num_requested, | 
 |                     num_to_issue); | 
 | } | 
 |  | 
 |  | 
 | int voprf_pst1_sign_with_proof_scalar_for_testing( | 
 |     const TRUST_TOKEN_ISSUER_KEY *key, CBB *cbb, CBS *cbs, size_t num_requested, | 
 |     size_t num_to_issue, uint8_t private_metadata, | 
 |     const uint8_t *proof_scalar_buf, size_t proof_scalar_len) { | 
 |   if (private_metadata != 0) { | 
 |     return 0; | 
 |   } | 
 |   return voprf_sign_with_proof_scalar_for_testing( | 
 |       &voprf_pst1_method, key, cbb, cbs, num_requested, num_to_issue, | 
 |       proof_scalar_buf, proof_scalar_len); | 
 | } | 
 |  | 
 | STACK_OF(TRUST_TOKEN) *voprf_pst1_unblind( | 
 |     const TRUST_TOKEN_CLIENT_KEY *key, | 
 |     const STACK_OF(TRUST_TOKEN_PRETOKEN) *pretokens, CBS *cbs, size_t count, | 
 |     uint32_t key_id) { | 
 |   return voprf_unblind(&voprf_pst1_method, key, pretokens, cbs, count, key_id); | 
 | } | 
 |  | 
 | int voprf_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) { | 
 |   return voprf_read(&voprf_pst1_method, key, out_nonce, token, token_len, | 
 |                     include_message, msg, msg_len); | 
 | } |