frost: signature generation and aggregation

jesseposner · jesseposner · commit ef15156ffb37 · 2024-07-16T23:36:51.000-07:00
This commit adds signature generation and aggregation, as well as
partial signature serialization and parsing.
diff --git a/include/secp256k1_frost.h b/include/secp256k1_frost.h
@@ -14,7 +14,8 @@ extern "C" {
  *
  * This module implements a variant of Flexible Round-Optimized Schnorr
  * Threshold Signatures (FROST) by Chelsea Komlo and Ian Goldberg
- * (https://crysp.uwaterloo.ca/software/frost/).
+ * (https://crysp.uwaterloo.ca/software/frost/). Signatures are compatible with
+ * BIP-340 ("Schnorr").
  *
  * The module also supports BIP-341 ("Taproot") and BIP-32 ("ordinary") public
  * key tweaking, and adaptor signatures.
@@ -88,6 +89,15 @@ typedef struct {
     unsigned char data[133];
 } secp256k1_frost_session;
 
+/** Opaque data structure that holds a partial FROST signature.
+ *
+ *  Guaranteed to be 36 bytes in size. Serialized and parsed with
+ *  `frost_partial_sig_serialize` and `frost_partial_sig_parse`.
+ */
+typedef struct {
+    unsigned char data[36];
+} secp256k1_frost_partial_sig;
+
 /** Parse a signer's public nonce.
  *
  *  Returns: 1 when the nonce could be parsed, 0 otherwise.
@@ -114,6 +124,36 @@ SECP256K1_API int secp256k1_frost_pubnonce_serialize(
     const secp256k1_frost_pubnonce *nonce
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
+/** Serialize a FROST partial signature
+ *
+ *  Returns: 1 when the signature could be serialized, 0 otherwise
+ *  Args:    ctx: pointer to a context object
+ *  Out:   out32: pointer to a 32-byte array to store the serialized signature
+ *  In:      sig: pointer to the signature
+ */
+SECP256K1_API int secp256k1_frost_partial_sig_serialize(
+    const secp256k1_context *ctx,
+    unsigned char *out32,
+    const secp256k1_frost_partial_sig *sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Parse a FROST partial signature.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args:    ctx: pointer to a context object
+ *  Out:     sig: pointer to a signature object
+ *  In:     in32: pointer to the 32-byte signature to be parsed
+ *
+ *  After the call, sig will always be initialized. If parsing failed or the
+ *  encoded numbers are out of range, signature verification with it is
+ *  guaranteed to fail for every message and public key.
+ */
+SECP256K1_API int secp256k1_frost_partial_sig_parse(
+    const secp256k1_context *ctx,
+    secp256k1_frost_partial_sig *sig,
+    const unsigned char *in32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
 /** Serialize a FROST share
  *
  *  Returns: 1 when the share could be serialized, 0 otherwise
@@ -467,6 +507,90 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_frost_nonce_process(
     const secp256k1_pubkey *adaptor
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(6) SECP256K1_ARG_NONNULL(7) SECP256K1_ARG_NONNULL(8);
 
+/** Produces a partial signature
+ *
+ *  This function overwrites the given secnonce with zeros and will abort if given a
+ *  secnonce that is all zeros. This is a best effort attempt to protect against nonce
+ *  reuse. However, this is of course easily defeated if the secnonce has been
+ *  copied (or serialized). Remember that nonce reuse will leak the secret key!
+ *
+ *  Returns: 0 if the arguments are invalid or the provided secnonce has already
+ *           been used for signing, 1 otherwise
+ *  Args:         ctx: pointer to a context object
+ *  Out:  partial_sig: pointer to struct to store the partial signature
+ *  In/Out:  secnonce: pointer to the secnonce struct created in
+ *                     frost_nonce_gen that has been never used in a
+ *                     partial_sign call before
+ *  In:     agg_share: the aggregated share
+ *            session: pointer to the session that was created with
+ *                     frost_nonce_process
+ *        tweak_cache: pointer to frost_tweak_cache struct (can be NULL)
+ */
+SECP256K1_API int secp256k1_frost_partial_sign(
+    const secp256k1_context *ctx,
+    secp256k1_frost_partial_sig *partial_sig,
+    secp256k1_frost_secnonce *secnonce,
+    const secp256k1_frost_share *agg_share,
+    const secp256k1_frost_session *session,
+    const secp256k1_frost_tweak_cache *tweak_cache
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
+/** Verifies an individual signer's partial signature
+ *
+ *  The signature is verified for a specific signing session. In order to avoid
+ *  accidentally verifying a signature from a different or non-existing signing
+ *  session, you must ensure the following:
+ *    1. The `tweak_cache` argument is identical to the one used to create the
+ *       `session` with `frost_nonce_process`.
+ *    2. The `pubshare` argument must be the output of
+ *       `secp256k1_frost_compute_pubshare` for the signer's ID.
+ *    3. The `pubnonce` argument must be identical to the one sent by the
+ *       signer and used to create the `session` with `frost_nonce_process`.
+ *
+ *  This function can be used to assign blame for a failed signature.
+ *
+ *  Returns: 0 if the arguments are invalid or the partial signature does not
+ *           verify, 1 otherwise
+ *  Args         ctx: pointer to a context object
+ *  In:  partial_sig: pointer to partial signature to verify, sent by
+ *                    the signer associated with `pubnonce` and `pubkey`
+ *          pubnonce: public nonce of the signer in the signing session
+ *          pubshare: public verification share of the signer in the signing
+ *                    session that is the output of
+ *                    `secp256k1_frost_compute_pubshare`
+ *           session: pointer to the session that was created with
+ *                    `frost_nonce_process`
+ *       tweak_cache: pointer to frost_tweak_cache struct (can be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_frost_partial_sig_verify(
+    const secp256k1_context *ctx,
+    const secp256k1_frost_partial_sig *partial_sig,
+    const secp256k1_frost_pubnonce *pubnonce,
+    const secp256k1_pubkey *pubshare,
+    const secp256k1_frost_session *session,
+    const secp256k1_frost_tweak_cache *tweak_cache
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
+/** Aggregates partial signatures
+ *
+ *  Returns: 0 if the arguments are invalid, 1 otherwise (which does NOT mean
+ *           the resulting signature verifies).
+ *  Args:         ctx: pointer to a context object
+ *  Out:        sig64: complete (but possibly invalid) Schnorr signature
+ *  In:       session: pointer to the session that was created with
+ *                     frost_nonce_process
+ *       partial_sigs: array of pointers to partial signatures to aggregate
+ *             n_sigs: number of elements in the partial_sigs array. Must be
+ *                     greater than 0.
+ */
+SECP256K1_API int secp256k1_frost_partial_sig_agg(
+    const secp256k1_context *ctx,
+    unsigned char *sig64,
+    const secp256k1_frost_session *session,
+    const secp256k1_frost_partial_sig * const *partial_sigs,
+    size_t n_sigs
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
 /** Extracts the nonce_parity bit from a session
  *
  *  This is used for adaptor signatures.
diff --git a/src/modules/frost/session_impl.h b/src/modules/frost/session_impl.h
@@ -117,6 +117,23 @@ static int secp256k1_frost_session_load(const secp256k1_context* ctx, secp256k1_
     return 1;
 }
 
+static const unsigned char secp256k1_frost_partial_sig_magic[4] = { 0x8d, 0xd8, 0x31, 0x6e };
+
+static void secp256k1_frost_partial_sig_save(secp256k1_frost_partial_sig* sig, secp256k1_scalar *s) {
+    memcpy(&sig->data[0], secp256k1_frost_partial_sig_magic, 4);
+    secp256k1_scalar_get_b32(&sig->data[4], s);
+}
+
+static int secp256k1_frost_partial_sig_load(const secp256k1_context* ctx, secp256k1_scalar *s, const secp256k1_frost_partial_sig* sig) {
+    int overflow;
+
+    ARG_CHECK(secp256k1_memcmp_var(&sig->data[0], secp256k1_frost_partial_sig_magic, 4) == 0);
+    secp256k1_scalar_set_b32(s, &sig->data[4], &overflow);
+    /* Parsed signatures can not overflow */
+    VERIFY_CHECK(!overflow);
+    return 1;
+}
+
 int secp256k1_frost_pubnonce_serialize(const secp256k1_context* ctx, unsigned char *out66, const secp256k1_frost_pubnonce* nonce) {
     secp256k1_ge ge[2];
     int i;
@@ -163,6 +180,29 @@ int secp256k1_frost_pubnonce_parse(const secp256k1_context* ctx, secp256k1_frost
     return 1;
 }
 
+int secp256k1_frost_partial_sig_serialize(const secp256k1_context* ctx, unsigned char *out32, const secp256k1_frost_partial_sig* sig) {
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(out32 != NULL);
+    ARG_CHECK(sig != NULL);
+    memcpy(out32, &sig->data[4], 32);
+    return 1;
+}
+
+int secp256k1_frost_partial_sig_parse(const secp256k1_context* ctx, secp256k1_frost_partial_sig* sig, const unsigned char *in32) {
+    secp256k1_scalar tmp;
+    int overflow;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(in32 != NULL);
+
+    secp256k1_scalar_set_b32(&tmp, in32, &overflow);
+    if (overflow) {
+        return 0;
+    }
+    secp256k1_frost_partial_sig_save(sig, &tmp);
+    return 1;
+}
+
 static void secp256k1_nonce_function_frost(secp256k1_scalar *k, const unsigned char *session_id, const unsigned char *msg32, const unsigned char *key32, const unsigned char *pk32, const unsigned char *extra_input32) {
     secp256k1_sha256 sha;
     unsigned char seed[32];
@@ -469,4 +509,154 @@ int secp256k1_frost_nonce_process(const secp256k1_context* ctx, secp256k1_frost_
     return 1;
 }
 
+void secp256k1_frost_partial_sign_clear(secp256k1_scalar *sk, secp256k1_scalar *k) {
+    secp256k1_scalar_clear(sk);
+    secp256k1_scalar_clear(&k[0]);
+    secp256k1_scalar_clear(&k[1]);
+}
+
+int secp256k1_frost_partial_sign(const secp256k1_context* ctx, secp256k1_frost_partial_sig *partial_sig, secp256k1_frost_secnonce *secnonce, const secp256k1_frost_share *share, const secp256k1_frost_session *session, const secp256k1_frost_tweak_cache *tweak_cache) {
+    secp256k1_scalar sk;
+    secp256k1_scalar k[2];
+    secp256k1_scalar s;
+    secp256k1_frost_session_internal session_i;
+    int ret;
+
+    VERIFY_CHECK(ctx != NULL);
+
+    ARG_CHECK(secnonce != NULL);
+    /* Fails if the magic doesn't match */
+    ret = secp256k1_frost_secnonce_load(ctx, k, secnonce);
+    /* Set nonce to zero to avoid nonce reuse. This will cause subsequent calls
+     * of this function to fail */
+    memset(secnonce, 0, sizeof(*secnonce));
+    if (!ret) {
+        secp256k1_frost_partial_sign_clear(&sk, k);
+        return 0;
+    }
+
+    ARG_CHECK(partial_sig != NULL);
+    ARG_CHECK(share != NULL);
+    ARG_CHECK(session != NULL);
+
+    if (!secp256k1_frost_share_load(ctx, &sk, share)) {
+        secp256k1_frost_partial_sign_clear(&sk, k);
+        return 0;
+    }
+    if (!secp256k1_frost_session_load(ctx, &session_i, session)) {
+        secp256k1_frost_partial_sign_clear(&sk, k);
+        return 0;
+    }
+
+    if (tweak_cache != NULL) {
+        secp256k1_tweak_cache_internal cache_i;
+        if (!secp256k1_tweak_cache_load(ctx, &cache_i, tweak_cache)) {
+            secp256k1_frost_partial_sign_clear(&sk, k);
+            return 0;
+        }
+        if (secp256k1_fe_is_odd(&cache_i.pk.y) != cache_i.parity_acc) {
+            secp256k1_scalar_negate(&sk, &sk);
+        }
+    }
+
+    if (session_i.fin_nonce_parity) {
+        secp256k1_scalar_negate(&k[0], &k[0]);
+        secp256k1_scalar_negate(&k[1], &k[1]);
+    }
+
+    /* Sign */
+    secp256k1_scalar_mul(&s, &session_i.challenge, &sk);
+    secp256k1_scalar_mul(&k[1], &session_i.noncecoef, &k[1]);
+    secp256k1_scalar_add(&k[0], &k[0], &k[1]);
+    secp256k1_scalar_add(&s, &s, &k[0]);
+    secp256k1_frost_partial_sig_save(partial_sig, &s);
+    secp256k1_frost_partial_sign_clear(&sk, k);
+    return 1;
+}
+
+int secp256k1_frost_partial_sig_verify(const secp256k1_context* ctx, const secp256k1_frost_partial_sig *partial_sig, const secp256k1_frost_pubnonce *pubnonce, const secp256k1_pubkey *pubshare, const secp256k1_frost_session *session, const secp256k1_frost_tweak_cache *tweak_cache) {
+    secp256k1_frost_session_internal session_i;
+    secp256k1_scalar e, s;
+    secp256k1_gej pkj;
+    secp256k1_ge nonce_pt[2];
+    secp256k1_gej rj;
+    secp256k1_gej tmp;
+    secp256k1_ge pkp;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(partial_sig != NULL);
+    ARG_CHECK(pubnonce != NULL);
+    ARG_CHECK(pubshare != NULL);
+    ARG_CHECK(session != NULL);
+
+    if (!secp256k1_frost_session_load(ctx, &session_i, session)) {
+        return 0;
+    }
+
+    /* Compute "effective" nonce rj = aggnonce[0] + b*aggnonce[1] */
+    /* TODO: use multiexp to compute -s*G + e*pubshare + aggnonce[0] + b*aggnonce[1] */
+    if (!secp256k1_frost_pubnonce_load(ctx, nonce_pt, pubnonce)) {
+        return 0;
+    }
+    secp256k1_gej_set_ge(&rj, &nonce_pt[1]);
+    secp256k1_ecmult(&rj, &rj, &session_i.noncecoef, NULL);
+    secp256k1_gej_add_ge_var(&rj, &rj, &nonce_pt[0], NULL);
+
+    if (!secp256k1_pubkey_load(ctx, &pkp, pubshare)) {
+        return 0;
+    }
+
+    secp256k1_scalar_set_int(&e, 1);
+    if (tweak_cache != NULL) {
+        secp256k1_tweak_cache_internal cache_i;
+        if (!secp256k1_tweak_cache_load(ctx, &cache_i, tweak_cache)) {
+            return 0;
+        }
+        if (secp256k1_fe_is_odd(&cache_i.pk.y)
+                != cache_i.parity_acc) {
+            secp256k1_scalar_negate(&e, &e);
+        }
+    }
+    secp256k1_scalar_mul(&e, &e, &session_i.challenge);
+
+    if (!secp256k1_frost_partial_sig_load(ctx, &s, partial_sig)) {
+        return 0;
+    }
+    /* Compute -s*G + e*pkj + rj (e already includes the lagrange coefficient l) */
+    secp256k1_scalar_negate(&s, &s);
+    secp256k1_gej_set_ge(&pkj, &pkp);
+    secp256k1_ecmult(&tmp, &pkj, &e, &s);
+    if (session_i.fin_nonce_parity) {
+        secp256k1_gej_neg(&rj, &rj);
+    }
+    secp256k1_gej_add_var(&tmp, &tmp, &rj, NULL);
+
+    return secp256k1_gej_is_infinity(&tmp);
+}
+
+int secp256k1_frost_partial_sig_agg(const secp256k1_context* ctx, unsigned char *sig64, const secp256k1_frost_session *session, const secp256k1_frost_partial_sig * const* partial_sigs, size_t n_sigs) {
+    size_t i;
+    secp256k1_frost_session_internal session_i;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sig64 != NULL);
+    ARG_CHECK(session != NULL);
+    ARG_CHECK(partial_sigs != NULL);
+    ARG_CHECK(n_sigs > 0);
+
+    if (!secp256k1_frost_session_load(ctx, &session_i, session)) {
+        return 0;
+    }
+    for (i = 0; i < n_sigs; i++) {
+        secp256k1_scalar term;
+        if (!secp256k1_frost_partial_sig_load(ctx, &term, partial_sigs[i])) {
+            return 0;
+        }
+        secp256k1_scalar_add(&session_i.s_part, &session_i.s_part, &term);
+    }
+    secp256k1_scalar_get_b32(&sig64[32], &session_i.s_part);
+    memcpy(&sig64[0], session_i.fin_nonce, 32);
+    return 1;
+}
+
 #endif
