ecdsa_adaptor: add ECDSA adaptor signature APIs

This commit adds the ECDSA adaptor signature APIs:

- Encrypted Signing

  Creates an adaptor signature, which includes a proof to verify the adaptor
  signature.

- Encryption Verification

  Verifies that the adaptor decryption key can be extracted from the adaptor
  signature and the completed ECDSA signature.

- Signature Decryption

  Derives an ECDSA signature from an adaptor signature and an adaptor decryption
  key.

- Key Recovery

  Extracts the adaptor decryption key from the complete signature and the adaptor
  signature.

include/secp256k1_ecdsa_adaptor.h

@@ -10,7 +10,22 @@ extern "C" {
  *  Lloyd Fournier
  *  (https://lists.linuxfoundation.org/pipermail/lightning-dev/2019-November/002316.html
  *  and https://github.com/LLFourn/one-time-VES/blob/master/main.pdf).
-*/
+ *
+ *  WARNING! DANGER AHEAD!
+ *  As mentioned in Lloyd Fournier's paper, the adaptor signature leaks the
+ *  Elliptic-curve Diffie–Hellman (ECDH) key between the signing key and the
+ *  encryption key. This is not a problem for ECDSA adaptor signatures
+ *  themselves, but may result in a complete loss of security when they are
+ *  composed with other schemes. More specifically, let us refer to the
+ *  signer's public key as X = x*G, and to the encryption key as Y = y*G.
+ *  Given X, Y and the adaptor signature, it is trivial to compute Y^x = X^y.
+ *
+ *  A defense is to not reuse the signing key of ECDSA adaptor signatures in
+ *  protocols that rely on the hardness of the CDH problem, e.g., Diffie-Hellman
+ *  key exchange and ElGamal encryption. In general, it is a well-established
+ *  cryptographic practice to seperate keys for different purposes whenever
+ *  possible.
+ */
 
 /** A pointer to a function to deterministically generate a nonce.
  *
@@ -46,6 +61,100 @@ typedef int (*secp256k1_nonce_function_hardened_ecdsa_adaptor)(
  */
 SECP256K1_API extern const secp256k1_nonce_function_hardened_ecdsa_adaptor secp256k1_nonce_function_ecdsa_adaptor;
 
+/** Encrypted Signing
+ *
+ *  Creates an adaptor signature, which includes a proof to verify the adaptor
+ *  signature.
+ *  WARNING: Make sure you have read and understood the WARNING at the top of
+ *  this file and applied the suggested countermeasures.
+ *
+ *  Returns: 1 on success, 0 on failure
+ *  Args:             ctx: a secp256k1 context object, initialized for signing
+ *  Out:   adaptor_sig162: pointer to 162 byte to store the returned signature
+ *  In:          seckey32: pointer to 32 byte secret key that will be used for
+ *                         signing
+ *                 enckey: pointer to the encryption public key
+ *                  msg32: pointer to the 32-byte message hash to sign
+ *                noncefp: pointer to a nonce generation function. If NULL,
+ *                         secp256k1_nonce_function_ecdsa_adaptor is used
+ *                  ndata: pointer to arbitrary data used by the nonce generation
+ *                         function (can be NULL). If it is non-NULL and
+ *                         secp256k1_nonce_function_ecdsa_adaptor is used, then
+ *                         ndata must be a pointer to 32-byte auxiliary randomness
+ *                         as per BIP-340.
+ */
+SECP256K1_API int secp256k1_ecdsa_adaptor_encrypt(
+    const secp256k1_context* ctx,
+    unsigned char *adaptor_sig162,
+    unsigned char *seckey32,
+    const secp256k1_pubkey *enckey,
+    const unsigned char *msg32,
+    secp256k1_nonce_function_hardened_ecdsa_adaptor noncefp,
+    void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
+/** Encryption Verification
+ *
+ *  Verifies that the adaptor decryption key can be extracted from the adaptor signature
+ *  and the completed ECDSA signature.
+ *
+ *  Returns: 1 on success, 0 on failure
+ *  Args:            ctx: a secp256k1 context object, initialized for verification
+ *  In:   adaptor_sig162: pointer to 162-byte signature to verify
+ *                pubkey: pointer to the public key corresponding to the secret key
+ *                        used for signing
+ *                 msg32: pointer to the 32-byte message hash being verified
+ *                enckey: pointer to the adaptor encryption public key
+ */
+SECP256K1_API int secp256k1_ecdsa_adaptor_verify(
+    const secp256k1_context* ctx,
+    const unsigned char *adaptor_sig162,
+    const secp256k1_pubkey *pubkey,
+    const unsigned char *msg32,
+    const secp256k1_pubkey *enckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
+/** Signature Decryption
+ *
+ *  Derives an ECDSA signature from an adaptor signature and an adaptor decryption key.
+ *
+ *  Returns: 1 on success, 0 on failure
+ *  Args:              ctx: a secp256k1 context object
+ *  Out:               sig: pointer to the ECDSA signature to create
+ *  In:           deckey32: pointer to 32-byte decryption secret key for the adaptor
+ *                          encryption public key
+ *          adaptor_sig162: pointer to 162-byte adaptor sig
+ */
+SECP256K1_API int secp256k1_ecdsa_adaptor_decrypt(
+    const secp256k1_context* ctx,
+    secp256k1_ecdsa_signature *sig,
+    const unsigned char *deckey32,
+    const unsigned char *adaptor_sig162
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Decryption Key Recovery
+ *
+ *  Extracts the adaptor decryption key from the complete signature and the adaptor
+ *  signature.
+ *
+ *  Returns: 1 on success, 0 on failure
+ *  Args:             ctx: a secp256k1 context object, initialized for signing
+ *  Out:         deckey32: pointer to 32-byte adaptor decryption key for the adaptor
+ *                         encryption public key
+ *  In:               sig: pointer to ECDSA signature to recover the adaptor decryption
+ *                         key from
+ *         adaptor_sig162: pointer to adaptor signature to recover the adaptor
+ *                         decryption key from
+ *                 enckey: pointer to the adaptor encryption public key
+ */
+SECP256K1_API int secp256k1_ecdsa_adaptor_recover(
+    const secp256k1_context* ctx,
+    unsigned char *deckey32,
+    const secp256k1_ecdsa_signature *sig,
+    const unsigned char *adaptor_sig162,
+    const secp256k1_pubkey *enckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
 #ifdef __cplusplus
 }
 #endif

src/modules/ecdsa_adaptor/main_impl.h

@@ -10,6 +10,61 @@
 #include "include/secp256k1_ecdsa_adaptor.h"
 #include "modules/ecdsa_adaptor/dleq_impl.h"
 
+/* (R, R', s', dleq_proof) */
+static int secp256k1_ecdsa_adaptor_sig_serialize(unsigned char *adaptor_sig162, secp256k1_ge *r, secp256k1_ge *rp, const secp256k1_scalar *sp, const secp256k1_scalar *dleq_proof_e, const secp256k1_scalar *dleq_proof_s) {
+    size_t size = 33;
+
+    if (!secp256k1_eckey_pubkey_serialize(r, adaptor_sig162, &size, 1)) {
+        return 0;
+    }
+    if (!secp256k1_eckey_pubkey_serialize(rp, &adaptor_sig162[33], &size, 1)) {
+        return 0;
+    }
+    secp256k1_scalar_get_b32(&adaptor_sig162[66], sp);
+    secp256k1_scalar_get_b32(&adaptor_sig162[98], dleq_proof_e);
+    secp256k1_scalar_get_b32(&adaptor_sig162[130], dleq_proof_s);
+
+    return 1;
+}
+
+static int secp256k1_ecdsa_adaptor_sig_deserialize(secp256k1_ge *r, secp256k1_scalar *sigr, secp256k1_ge *rp, secp256k1_scalar *sp, secp256k1_scalar *dleq_proof_e, secp256k1_scalar *dleq_proof_s, const unsigned char *adaptor_sig162) {
+    /* If r is deserialized, require that a sigr is provided to receive
+     * the X-coordinate */
+    VERIFY_CHECK((r == NULL) || (r != NULL && sigr != NULL));
+    if (r != NULL) {
+        if (!secp256k1_eckey_pubkey_parse(r, &adaptor_sig162[0], 33)) {
+            return 0;
+        }
+    }
+    if (sigr != NULL) {
+        secp256k1_scalar_set_b32(sigr, &adaptor_sig162[1], NULL);
+        if (secp256k1_scalar_is_zero(sigr)) {
+            return 0;
+        }
+    }
+    if (rp != NULL) {
+        if (!secp256k1_eckey_pubkey_parse(rp, &adaptor_sig162[33], 33)) {
+            return 0;
+        }
+    }
+    if (sp != NULL) {
+        if (!secp256k1_scalar_set_b32_seckey(sp, &adaptor_sig162[66])) {
+            return 0;
+        }
+    }
+    if (dleq_proof_e != NULL) {
+        secp256k1_scalar_set_b32(dleq_proof_e, &adaptor_sig162[98], NULL);
+    }
+    if (dleq_proof_s != NULL) {
+        int overflow;
+        secp256k1_scalar_set_b32(dleq_proof_s, &adaptor_sig162[130], &overflow);
+        if (overflow) {
+            return 0;
+        }
+    }
+    return 1;
+}
+
 /* Initializes SHA256 with fixed midstate. This midstate was computed by applying
  * SHA256 to SHA256("ECDSAadaptor/non")||SHA256("ECDSAadaptor/non"). */
 static void secp256k1_nonce_function_ecdsa_adaptor_sha256_tagged(secp256k1_sha256 *sha) {
@@ -91,4 +146,220 @@ static int nonce_function_ecdsa_adaptor(unsigned char *nonce32, const unsigned c
 
 const secp256k1_nonce_function_hardened_ecdsa_adaptor secp256k1_nonce_function_ecdsa_adaptor = nonce_function_ecdsa_adaptor;
 
+int secp256k1_ecdsa_adaptor_encrypt(const secp256k1_context* ctx, unsigned char *adaptor_sig162, unsigned char *seckey32, const secp256k1_pubkey *enckey, const unsigned char *msg32, secp256k1_nonce_function_hardened_ecdsa_adaptor noncefp, void *ndata) {
+    secp256k1_scalar k;
+    secp256k1_gej rj, rpj;
+    secp256k1_ge r, rp;
+    secp256k1_ge enckey_ge;
+    secp256k1_scalar dleq_proof_s;
+    secp256k1_scalar dleq_proof_e;
+    secp256k1_scalar sk;
+    secp256k1_scalar msg;
+    secp256k1_scalar sp;
+    secp256k1_scalar sigr;
+    secp256k1_scalar n;
+    unsigned char nonce32[32] = { 0 };
+    unsigned char buf33[33];
+    size_t size = 33;
+    int ret = 1;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(adaptor_sig162 != NULL);
+    ARG_CHECK(seckey32 != NULL);
+    ARG_CHECK(enckey != NULL);
+    ARG_CHECK(msg32 != NULL);
+
+    secp256k1_scalar_clear(&dleq_proof_e);
+    secp256k1_scalar_clear(&dleq_proof_s);
+
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_ecdsa_adaptor;
+    }
+
+    ret &= secp256k1_pubkey_load(ctx, &enckey_ge, enckey);
+    ret &= secp256k1_eckey_pubkey_serialize(&enckey_ge, buf33, &size, 1);
+    ret &= !!noncefp(nonce32, msg32, seckey32, buf33, ecdsa_adaptor_algo, sizeof(ecdsa_adaptor_algo), ndata);
+    secp256k1_scalar_set_b32(&k, nonce32, NULL);
+    ret &= !secp256k1_scalar_is_zero(&k);
+    secp256k1_scalar_cmov(&k, &secp256k1_scalar_one, !ret);
+
+    /* R' := k*G */
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &rpj, &k);
+    secp256k1_ge_set_gej(&rp, &rpj);
+    /* R = k*Y; */
+    secp256k1_ecmult_const(&rj, &enckey_ge, &k, 256);
+    secp256k1_ge_set_gej(&r, &rj);
+    /* We declassify the non-secret values rp and r to allow using them
+     * as branch points. */
+    secp256k1_declassify(ctx, &rp, sizeof(rp));
+    secp256k1_declassify(ctx, &r, sizeof(r));
+
+    /* dleq_proof = DLEQ_prove(k, (R', Y, R)) */
+    ret &= secp256k1_dleq_prove(ctx, &dleq_proof_s, &dleq_proof_e, &k, &enckey_ge, &rp, &r, noncefp, ndata);
+
+    ret &= secp256k1_scalar_set_b32_seckey(&sk, seckey32);
+    secp256k1_scalar_cmov(&sk, &secp256k1_scalar_one, !ret);
+    secp256k1_scalar_set_b32(&msg, msg32, NULL);
+    secp256k1_fe_normalize(&r.x);
+    secp256k1_fe_get_b32(buf33, &r.x);
+    secp256k1_scalar_set_b32(&sigr, buf33, NULL);
+    ret &= !secp256k1_scalar_is_zero(&sigr);
+    /* s' = k⁻¹(m + R.x * x) */
+    secp256k1_scalar_mul(&n, &sigr, &sk);
+    secp256k1_scalar_add(&n, &n, &msg);
+    secp256k1_scalar_inverse(&sp, &k);
+    secp256k1_scalar_mul(&sp, &sp, &n);
+    ret &= !secp256k1_scalar_is_zero(&sp);
+
+    /* return (R, R', s', dleq_proof) */
+    ret &= secp256k1_ecdsa_adaptor_sig_serialize(adaptor_sig162, &r, &rp, &sp, &dleq_proof_e, &dleq_proof_s);
+
+    secp256k1_memczero(adaptor_sig162, 162, !ret);
+    secp256k1_scalar_clear(&n);
+    secp256k1_scalar_clear(&k);
+    secp256k1_scalar_clear(&sk);
+
+    return ret;
+}
+
+int secp256k1_ecdsa_adaptor_verify(const secp256k1_context* ctx, const unsigned char *adaptor_sig162, const secp256k1_pubkey *pubkey, const unsigned char *msg32, const secp256k1_pubkey *enckey) {
+    secp256k1_scalar dleq_proof_s, dleq_proof_e;
+    secp256k1_scalar msg;
+    secp256k1_ge pubkey_ge;
+    secp256k1_ge r, rp;
+    secp256k1_scalar sp;
+    secp256k1_scalar sigr;
+    secp256k1_ge enckey_ge;
+    secp256k1_gej derived_rp;
+    secp256k1_scalar sn, u1, u2;
+    secp256k1_gej pubkeyj;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(adaptor_sig162 != NULL);
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(enckey != NULL);
+
+    if (!secp256k1_ecdsa_adaptor_sig_deserialize(&r, &sigr, &rp, &sp, &dleq_proof_e, &dleq_proof_s, adaptor_sig162)) {
+        return 0;
+    }
+    if (!secp256k1_pubkey_load(ctx, &enckey_ge, enckey)) {
+        return 0;
+    }
+    /* DLEQ_verify((R', Y, R), dleq_proof) */
+    if(!secp256k1_dleq_verify(&ctx->ecmult_ctx, &dleq_proof_s, &dleq_proof_e, &rp, &enckey_ge, &r)) {
+        return 0;
+    }
+    secp256k1_scalar_set_b32(&msg, msg32, NULL);
+    if (!secp256k1_pubkey_load(ctx, &pubkey_ge, pubkey)) {
+        return 0;
+    }
+
+    /* return R' == s'⁻¹(m * G + R.x * X) */
+    secp256k1_scalar_inverse_var(&sn, &sp);
+    secp256k1_scalar_mul(&u1, &sn, &msg);
+    secp256k1_scalar_mul(&u2, &sn, &sigr);
+    secp256k1_gej_set_ge(&pubkeyj, &pubkey_ge);
+    secp256k1_ecmult(&ctx->ecmult_ctx, &derived_rp, &pubkeyj, &u2, &u1);
+    if (secp256k1_gej_is_infinity(&derived_rp)) {
+        return 0;
+    }
+    secp256k1_gej_neg(&derived_rp, &derived_rp);
+    secp256k1_gej_add_ge_var(&derived_rp, &derived_rp, &rp, NULL);
+    return secp256k1_gej_is_infinity(&derived_rp);
+}
+
+int secp256k1_ecdsa_adaptor_decrypt(const secp256k1_context* ctx, secp256k1_ecdsa_signature *sig, const unsigned char *deckey32, const unsigned char *adaptor_sig162) {
+    secp256k1_scalar deckey;
+    secp256k1_scalar sp;
+    secp256k1_scalar s;
+    secp256k1_scalar sigr;
+    int overflow;
+    int high;
+    int ret = 1;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(deckey32 != NULL);
+    ARG_CHECK(adaptor_sig162 != NULL);
+
+    secp256k1_scalar_clear(&sp);
+    secp256k1_scalar_set_b32(&deckey, deckey32, &overflow);
+    ret &= !overflow;
+    ret &= secp256k1_ecdsa_adaptor_sig_deserialize(NULL, &sigr, NULL, &sp, NULL, NULL, adaptor_sig162);
+    ret &= !secp256k1_scalar_is_zero(&deckey);
+    secp256k1_scalar_inverse(&s, &deckey);
+    /* s = s' * y⁻¹ */
+    secp256k1_scalar_mul(&s, &s, &sp);
+    high = secp256k1_scalar_is_high(&s);
+    secp256k1_scalar_cond_negate(&s, high);
+    secp256k1_ecdsa_signature_save(sig, &sigr, &s);
+
+    secp256k1_memczero(&sig->data[0], 64, !ret);
+    secp256k1_scalar_clear(&deckey);
+    secp256k1_scalar_clear(&sp);
+    secp256k1_scalar_clear(&s);
+
+    return ret;
+}
+
+int secp256k1_ecdsa_adaptor_recover(const secp256k1_context* ctx, unsigned char *deckey32, const secp256k1_ecdsa_signature *sig, const unsigned char *adaptor_sig162, const secp256k1_pubkey *enckey) {
+    secp256k1_scalar sp, adaptor_sigr;
+    secp256k1_scalar s, r;
+    secp256k1_scalar deckey;
+    secp256k1_ge enckey_expected_ge;
+    secp256k1_gej enckey_expected_gej;
+    unsigned char enckey33[33];
+    unsigned char enckey_expected33[33];
+    size_t size = 33;
+    int ret = 1;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(deckey32 != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(adaptor_sig162 != NULL);
+    ARG_CHECK(enckey != NULL);
+
+    if (!secp256k1_ecdsa_adaptor_sig_deserialize(NULL, &adaptor_sigr, NULL, &sp, NULL, NULL, adaptor_sig162)) {
+        return 0;
+    }
+    secp256k1_ecdsa_signature_load(ctx, &r, &s, sig);
+    /* Check that we're not looking at some unrelated signature */
+    ret &= secp256k1_scalar_eq(&adaptor_sigr, &r);
+    /* y = s⁻¹ * s' */
+    ret &= !secp256k1_scalar_is_zero(&s);
+    secp256k1_scalar_inverse(&deckey, &s);
+    secp256k1_scalar_mul(&deckey, &deckey, &sp);
+
+    /* Deal with ECDSA malleability */
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &enckey_expected_gej, &deckey);
+    secp256k1_ge_set_gej(&enckey_expected_ge, &enckey_expected_gej);
+    /* We declassify non-secret enckey_expected_ge to allow using it as a
+     * branch point. */
+    secp256k1_declassify(ctx, &enckey_expected_ge, sizeof(enckey_expected_ge));
+    if (!secp256k1_eckey_pubkey_serialize(&enckey_expected_ge, enckey_expected33, &size, SECP256K1_EC_COMPRESSED)) {
+        return 0;
+    }
+    if (!secp256k1_ec_pubkey_serialize(ctx, enckey33, &size, enckey, SECP256K1_EC_COMPRESSED)) {
+        return 0;
+    }
+    if (secp256k1_memcmp_var(&enckey_expected33[1], &enckey33[1], 32) != 0) {
+        return 0;
+    }
+    if (enckey_expected33[0] != enckey33[0]) {
+        /* try Y_implied == -Y */
+        secp256k1_scalar_negate(&deckey, &deckey);
+    }
+    secp256k1_scalar_get_b32(deckey32, &deckey);
+
+    secp256k1_scalar_clear(&deckey);
+    secp256k1_scalar_clear(&sp);
+    secp256k1_scalar_clear(&s);
+
+    return ret;
+}
+
 #endif