frost trusted dealer: key tweaking

This commits add BIP-341 ("Taproot") and BIP-32 ("ordinary") public key
tweaking.

include/secp256k1_frost.h

@@ -16,6 +16,9 @@ extern "C" {
  * Threshold Signatures (FROST) by Chelsea Komlo and Ian Goldberg
  * (https://crysp.uwaterloo.ca/software/frost/).
  *
+ * The module also supports BIP-341 ("Taproot") and BIP-32 ("ordinary") public
+ * key tweaking, and adaptor signatures.
+ *
  * Following the convention used in the MuSig module, the API uses the singular
  * term "nonce" to refer to the two "nonces" used by the FROST scheme.
  */
@@ -28,6 +31,15 @@ extern "C" {
  *  comparison, use the corresponding serialization and parsing functions.
  */
 
+/** Opaque data structure that caches information about key tweaking.
+ *
+ *  Guaranteed to be 101 bytes in size. It can be safely copied/moved. No
+ *  serialization and parsing functions.
+ */
+typedef struct {
+    unsigned char data[101];
+} secp256k1_frost_tweak_cache;
+
 /** Opaque data structure that holds a signer's _secret_ share.
  *
  *  Guaranteed to be 36 bytes in size. Serialized and parsed with
@@ -153,6 +165,123 @@ SECP256K1_API int secp256k1_frost_shares_trusted_gen(
     size_t n_participants
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
 
+/** Obtain the aggregate public key from a FROST x-only aggregate public key.
+ *
+ *  This is only useful if you need the non-xonly public key, in particular for
+ *  ordinary (non-xonly) tweaking or batch-verifying multiple key aggregations
+ *  (not implemented).
+ *
+ *  Returns: 0 if the arguments are invalid, 1 otherwise
+ *  Args:        ctx: pointer to a context object
+ *  Out:   ec_agg_pk: the FROST-aggregated public key.
+ *  In: xonly_agg_pk: the aggregated x-only public key that is the output of
+ *                    `secp256k1_frost_shares_gen`
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_frost_pubkey_get(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *ec_agg_pk,
+    const secp256k1_xonly_pubkey *xonly_agg_pk
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Initializes a tweak cache used for applying tweaks to a FROST key
+ *
+ *  Returns: 0 if the arguments are invalid, 1 otherwise
+ *  Args:        ctx: pointer to a context object
+ *  Out: tweak_cache: pointer to a frost_tweak_cache struct that is required
+ *                    for key tweaking
+ *  In:       agg_pk: the aggregated x-only public key that is the output of
+ *                    `secp256k1_frost_shares_gen`
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_frost_pubkey_tweak(
+    const secp256k1_context *ctx,
+    secp256k1_frost_tweak_cache *tweak_cache,
+    const secp256k1_xonly_pubkey *agg_pk
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Apply ordinary "EC" tweaking to a public key in a given tweak_cache by
+ *  adding the generator multiplied with `tweak32` to it. This is useful for
+ *  deriving child keys from an aggregate public key via BIP32.
+ *
+ *  The tweaking method is the same as `secp256k1_ec_pubkey_tweak_add`. So after
+ *  the following pseudocode buf and buf2 have identical contents (absent
+ *  earlier failures).
+ *
+ *  secp256k1_frost_shares_gen(..., xonly_agg_pk, ...)
+ *  secp256k1_frost_pubkey_tweak(..., tweak_cache, xonly_agg_pk)
+ *  secp256k1_frost_pubkey_ec_tweak_add(..., output_pk, tweak_cache, tweak32)
+ *  secp256k1_ec_pubkey_serialize(..., buf, output_pk)
+ *  secp256k1_frost_pubkey_get(..., ec_agg_pk, xonly_agg_pk)
+ *  secp256k1_ec_pubkey_tweak_add(..., ec_agg_pk, tweak32)
+ *  secp256k1_ec_pubkey_serialize(..., buf2, ec_agg_pk)
+ *
+ *  This function is required if you want to _sign_ for a tweaked aggregate key.
+ *  On the other hand, if you are only computing a public key, but not intending
+ *  to create a signature for it, you can just use
+ *  `secp256k1_ec_pubkey_tweak_add`.
+ *
+ *  Returns: 0 if the arguments are invalid or the resulting public key would be
+ *           invalid (only when the tweak is the negation of the corresponding
+ *           secret key). 1 otherwise.
+ *  Args:            ctx: pointer to a context object
+ *  Out:   output_pubkey: pointer to a public key to store the result. Will be set
+ *                        to an invalid value if this function returns 0. If you
+ *                        do not need it, this arg can be NULL.
+ *  In/Out:  tweak_cache: pointer to a `frost_tweak_cache` struct initialized by
+ *                       `frost_pubkey_tweak`
+ *  In:          tweak32: pointer to a 32-byte tweak. If the tweak is invalid
+ *                        according to `secp256k1_ec_seckey_verify`, this function
+ *                        returns 0. For uniformly random 32-byte arrays the
+ *                        chance of being invalid is negligible (around 1 in
+ *                        2^128).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_frost_pubkey_ec_tweak_add(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *output_pubkey,
+    secp256k1_frost_tweak_cache *tweak_cache,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Apply x-only tweaking to a public key in a given tweak_cache by adding the
+ *  generator multiplied with `tweak32` to it. This is useful for creating
+ *  Taproot outputs.
+ *
+ *  The tweaking method is the same as `secp256k1_xonly_pubkey_tweak_add`. So in
+ *  the following pseudocode xonly_pubkey_tweak_add_check (absent earlier
+ *  failures) returns 1.
+ *
+ *  secp256k1_frost_shares_gen(..., agg_pk, ...)
+ *  secp256k1_frost_pubkey_tweak(..., tweak_cache, agg_pk)
+ *  secp256k1_frost_pubkey_xonly_tweak_add(..., output_pk, tweak_cache, tweak32)
+ *  secp256k1_xonly_pubkey_serialize(..., buf, output_pk)
+ *  secp256k1_xonly_pubkey_tweak_add_check(..., buf, ..., agg_pk, tweak32)
+ *
+ *  This function is required if you want to _sign_ for a tweaked aggregate key.
+ *  On the other hand, if you are only computing a public key, but not intending
+ *  to create a signature for it, you can just use
+ *  `secp256k1_xonly_pubkey_tweak_add`.
+ *
+ *  Returns: 0 if the arguments are invalid or the resulting public key would be
+ *           invalid (only when the tweak is the negation of the corresponding
+ *           secret key). 1 otherwise.
+ *  Args:            ctx: pointer to a context object
+ *  Out:   output_pubkey: pointer to a public key to store the result. Will be set
+ *                        to an invalid value if this function returns 0. If you
+ *                        do not need it, this arg can be NULL.
+ *  In/Out:  tweak_cache: pointer to a `frost_tweak_cache` struct initialized by
+ *                       `frost_pubkey_tweak`
+ *  In:          tweak32: pointer to a 32-byte tweak. If the tweak is invalid
+ *                        according to secp256k1_ec_seckey_verify, this function
+ *                        returns 0. For uniformly random 32-byte arrays the
+ *                        chance of being invalid is negligible (around 1 in
+ *                        2^128).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_frost_pubkey_xonly_tweak_add(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *output_pubkey,
+    secp256k1_frost_tweak_cache *tweak_cache,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
 /** Starts a signing session by generating a nonce
  *
  *  This function outputs a secret nonce that will be required for signing and a

src/modules/frost/keygen.h

@@ -10,8 +10,15 @@
 #include "../../../include/secp256k1.h"
 #include "../../../include/secp256k1_frost.h"
 
+#include "../../group.h"
 #include "../../scalar.h"
 
+typedef struct {
+    secp256k1_ge pk;
+    secp256k1_scalar tweak;
+    int parity_acc;
+} secp256k1_tweak_cache_internal;
+
 static int secp256k1_frost_share_load(const secp256k1_context* ctx, secp256k1_scalar *s, const secp256k1_frost_share* share);
 
 #endif

src/modules/frost/keygen_impl.h

@@ -20,6 +20,39 @@
 #include "../../hash.h"
 #include "../../scalar.h"
 
+static const unsigned char secp256k1_frost_tweak_cache_magic[4] = { 0x40, 0x25, 0x2e, 0x41 };
+
+/* A tweak cache consists of
+ * - 4 byte magic set during initialization to allow detecting an uninitialized
+ *   object.
+ * - 64 byte aggregate (and potentially tweaked) public key
+ * - 1 byte the parity of the internal key (if tweaked, otherwise 0)
+ * - 32 byte tweak
+ */
+/* Requires that cache_i->pk is not infinity. */
+static void secp256k1_tweak_cache_save(secp256k1_frost_tweak_cache *cache, secp256k1_tweak_cache_internal *cache_i) {
+    unsigned char *ptr = cache->data;
+    memcpy(ptr, secp256k1_frost_tweak_cache_magic, 4);
+    ptr += 4;
+    secp256k1_point_save_ext(ptr, &cache_i->pk);
+    ptr += 64;
+    *ptr = cache_i->parity_acc;
+    ptr += 1;
+    secp256k1_scalar_get_b32(ptr, &cache_i->tweak);
+}
+
+static int secp256k1_tweak_cache_load(const secp256k1_context* ctx, secp256k1_tweak_cache_internal *cache_i, const secp256k1_frost_tweak_cache *cache) {
+    const unsigned char *ptr = cache->data;
+    ARG_CHECK(secp256k1_memcmp_var(ptr, secp256k1_frost_tweak_cache_magic, 4) == 0);
+    ptr += 4;
+    secp256k1_point_load_ext(&cache_i->pk, ptr);
+    ptr += 64;
+    cache_i->parity_acc = *ptr & 1;
+    ptr += 1;
+    secp256k1_scalar_set_b32(&cache_i->tweak, ptr, NULL);
+    return 1;
+}
+
 static const unsigned char secp256k1_frost_share_magic[4] = { 0xa1, 0x6a, 0x42, 0x03 };
 
 static void secp256k1_frost_share_save(secp256k1_frost_share* share, secp256k1_scalar *s) {
@@ -143,4 +176,82 @@ int secp256k1_frost_shares_trusted_gen(const secp256k1_context *ctx, secp256k1_f
     return ret;
 }
 
+int secp256k1_frost_pubkey_get(const secp256k1_context* ctx, secp256k1_pubkey *ec_pk, const secp256k1_xonly_pubkey *xonly_pk) {
+    secp256k1_ge pk;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(ec_pk != NULL);
+    memset(ec_pk, 0, sizeof(*ec_pk));
+    ARG_CHECK(xonly_pk != NULL);
+
+    /* The output of keygen is an aggregated public key that *always* has an
+     * even Y coordinate. */
+    if (!secp256k1_xonly_pubkey_load(ctx, &pk, xonly_pk)) {
+        return 0;
+    }
+    secp256k1_pubkey_save(ec_pk, &pk);
+    return 1;
+}
+
+int secp256k1_frost_pubkey_tweak(const secp256k1_context* ctx, secp256k1_frost_tweak_cache *tweak_cache, const secp256k1_xonly_pubkey *pk) {
+    secp256k1_tweak_cache_internal cache_i = { 0 };
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(tweak_cache != NULL);
+    ARG_CHECK(pk != NULL);
+
+    /* The output of keygen is an aggregated public key that *always* has an
+     * even Y coordinate. */
+    if (!secp256k1_xonly_pubkey_load(ctx, &cache_i.pk, pk)) {
+        return 0;
+    }
+    secp256k1_tweak_cache_save(tweak_cache, &cache_i);
+
+    return 1;
+}
+
+static int secp256k1_frost_pubkey_tweak_add_internal(const secp256k1_context* ctx, secp256k1_pubkey *output_pubkey, secp256k1_frost_tweak_cache *tweak_cache, const unsigned char *tweak32, int xonly) {
+    secp256k1_tweak_cache_internal cache_i;
+    int overflow = 0;
+    secp256k1_scalar tweak;
+
+    VERIFY_CHECK(ctx != NULL);
+    if (output_pubkey != NULL) {
+        memset(output_pubkey, 0, sizeof(*output_pubkey));
+    }
+    ARG_CHECK(tweak_cache != NULL);
+    ARG_CHECK(tweak32 != NULL);
+
+    if (!secp256k1_tweak_cache_load(ctx, &cache_i, tweak_cache)) {
+        return 0;
+    }
+    secp256k1_scalar_set_b32(&tweak, tweak32, &overflow);
+    if (overflow) {
+        return 0;
+    }
+    if (xonly && secp256k1_extrakeys_ge_even_y(&cache_i.pk)) {
+        cache_i.parity_acc ^= 1;
+        secp256k1_scalar_negate(&cache_i.tweak, &cache_i.tweak);
+    }
+    secp256k1_scalar_add(&cache_i.tweak, &cache_i.tweak, &tweak);
+    if (!secp256k1_eckey_pubkey_tweak_add(&cache_i.pk, &tweak)) {
+        return 0;
+    }
+    /* eckey_pubkey_tweak_add fails if cache_i.pk is infinity */
+    VERIFY_CHECK(!secp256k1_ge_is_infinity(&cache_i.pk));
+    secp256k1_tweak_cache_save(tweak_cache, &cache_i);
+    if (output_pubkey != NULL) {
+        secp256k1_pubkey_save(output_pubkey, &cache_i.pk);
+    }
+    return 1;
+}
+
+int secp256k1_frost_pubkey_ec_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *output_pubkey, secp256k1_frost_tweak_cache *tweak_cache, const unsigned char *tweak32) {
+    return secp256k1_frost_pubkey_tweak_add_internal(ctx, output_pubkey, tweak_cache, tweak32, 0);
+}
+
+int secp256k1_frost_pubkey_xonly_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *output_pubkey, secp256k1_frost_tweak_cache *tweak_cache, const unsigned char *tweak32) {
+    return secp256k1_frost_pubkey_tweak_add_internal(ctx, output_pubkey, tweak_cache, tweak32, 1);
+}
+
 #endif