Compact signatures and key recovery

Introduce a new type of signatures that are only 65 bytes long, and allow
reconstruction of the public key that was used to create the signature.

src/key.h

@@ -75,6 +75,76 @@ err:
     return(ok);
 }
 
+int static inline ECDSA_SIG_recover_key_GFp(EC_KEY *eckey, ECDSA_SIG *ecsig, const unsigned char *msg, int msglen, int recid, int check)
+{
+    if (!eckey) return 0;
+
+    int ret = 0;
+    BN_CTX *ctx = NULL;
+
+    BIGNUM *x = NULL;
+    BIGNUM *e = NULL;
+    BIGNUM *order = NULL;
+    BIGNUM *sor = NULL;
+    BIGNUM *eor = NULL;
+    BIGNUM *field = NULL;
+    EC_POINT *R = NULL;
+    EC_POINT *O = NULL;
+    EC_POINT *Q = NULL;
+    BIGNUM *rr = NULL;
+    BIGNUM *zero = NULL;
+    int n = 0;
+    int i = recid / 2;
+
+    const EC_GROUP *group = EC_KEY_get0_group(eckey);
+    if ((ctx = BN_CTX_new()) == NULL) { ret = -1; goto err; }
+    BN_CTX_start(ctx);
+    order = BN_CTX_get(ctx);
+    if (!EC_GROUP_get_order(group, order, ctx)) { ret = -2; goto err; }
+    x = BN_CTX_get(ctx);
+    if (!BN_copy(x, order)) { ret=-1; goto err; }
+    if (!BN_mul_word(x, i)) { ret=-1; goto err; }
+    if (!BN_add(x, x, ecsig->r)) { ret=-1; goto err; }
+    field = BN_CTX_get(ctx);
+    if (!EC_GROUP_get_curve_GFp(group, field, NULL, NULL, ctx)) { ret=-2; goto err; }
+    if (BN_cmp(x, field) >= 0) { ret=0; goto err; }
+    if ((R = EC_POINT_new(group)) == NULL) { ret = -2; goto err; }
+    if (!EC_POINT_set_compressed_coordinates_GFp(group, R, x, recid % 2, ctx)) { ret=0; goto err; }
+    if (check)
+    {
+        if ((O = EC_POINT_new(group)) == NULL) { ret = -2; goto err; }
+        if (!EC_POINT_mul(group, O, NULL, R, order, ctx)) { ret=-2; goto err; }
+        if (!EC_POINT_is_at_infinity(group, O)) { ret = 0; goto err; }
+    }
+    if ((Q = EC_POINT_new(group)) == NULL) { ret = -2; goto err; }
+    n = EC_GROUP_get_degree(group);
+    e = BN_CTX_get(ctx);
+    if (!BN_bin2bn(msg, msglen, e)) { ret=-1; goto err; }
+    if (8*msglen > n) BN_rshift(e, e, 8-(n & 7));
+    zero = BN_CTX_get(ctx);
+    if (!BN_zero(zero)) { ret=-1; goto err; }
+    if (!BN_mod_sub(e, zero, e, order, ctx)) { ret=-1; goto err; }
+    rr = BN_CTX_get(ctx);
+    if (!BN_mod_inverse(rr, ecsig->r, order, ctx)) { ret=-1; goto err; }
+    sor = BN_CTX_get(ctx);
+    if (!BN_mod_mul(sor, ecsig->s, rr, order, ctx)) { ret=-1; goto err; }
+    eor = BN_CTX_get(ctx);
+    if (!BN_mod_mul(eor, e, rr, order, ctx)) { ret=-1; goto err; }
+    if (!EC_POINT_mul(group, Q, eor, R, sor, ctx)) { ret=-2; goto err; }
+    if (!EC_KEY_set_public_key(eckey, Q)) { ret=-2; goto err; }
+
+    ret = 1;
+
+err:
+    if (ctx) {
+        BN_CTX_end(ctx);
+        BN_CTX_free(ctx);
+    }
+    if (R != NULL) EC_POINT_free(R);
+    if (O != NULL) EC_POINT_free(O);
+    if (Q != NULL) EC_POINT_free(Q);
+    return ret;
+}
 
 class key_error : public std::runtime_error
 {
@@ -221,6 +291,66 @@ public:
         return true;
     }
 
+    // create a compact signature (65 bytes), which allows reconstructing the used public key
+    bool SignCompact(uint256 hash, std::vector<unsigned char>& vchSig)
+    {
+        bool fOk = false;
+        ECDSA_SIG *sig = ECDSA_do_sign((unsigned char*)&hash, sizeof(hash), pkey);
+        if (sig==NULL)
+            return false;
+        vchSig.clear();
+        vchSig.resize(65,0);
+        int nBitsR = BN_num_bits(sig->r);
+        int nBitsS = BN_num_bits(sig->s);
+        if (nBitsR <= 256 && nBitsS <= 256)
+        {
+            int nRecId = -1;
+            for (int i=0; i<4; i++)
+            {
+                CKey keyRec;
+                keyRec.fSet = true;
+                if (ECDSA_SIG_recover_key_GFp(keyRec.pkey, sig, (unsigned char*)&hash, sizeof(hash), i, 1) == 1)
+                    if (keyRec.GetPubKey() == this->GetPubKey())
+                    {
+                        nRecId = i;
+                        break;
+                    }
+            }
+
+            if (nRecId == -1)
+                throw key_error("CKEy::SignCompact() : unable to construct recoverable key");
+
+            vchSig[0] = nRecId+27;
+            BN_bn2bin(sig->r,&vchSig[33-(nBitsR+7)/8]);
+            BN_bn2bin(sig->s,&vchSig[65-(nBitsS+7)/8]);
+            fOk = true;
+        }
+        ECDSA_SIG_free(sig);
+        return fOk;
+    }
+
+    // reconstruct public key from a compact signature
+    bool SetCompactSignature(uint256 hash, const std::vector<unsigned char>& vchSig)
+    {
+        if (vchSig.size() != 65)
+            return false;
+        if (vchSig[0]<27 || vchSig[0]>=31)
+            return false;
+        ECDSA_SIG *sig = ECDSA_SIG_new();
+        BN_bin2bn(&vchSig[1],32,sig->r);
+        BN_bin2bn(&vchSig[33],32,sig->s);
+
+        EC_KEY_free(pkey);
+        pkey = EC_KEY_new_by_curve_name(NID_secp256k1);
+        if (ECDSA_SIG_recover_key_GFp(pkey, sig, (unsigned char*)&hash, sizeof(hash), vchSig[0] - 27, 0) == 1)
+        {
+            fSet = true;
+            ECDSA_SIG_free(sig);
+            return true;
+        }
+        return false;
+    }
+
     bool Verify(uint256 hash, const std::vector<unsigned char>& vchSig)
     {
         // -1 = error, 0 = bad sig, 1 = good
@@ -229,6 +359,16 @@ public:
         return true;
     }
 
+    bool VerifyCompact(uint256 hash, const std::vector<unsigned char>& vchSig)
+    {
+        CKey key;
+        if (!key.SetCompactSignature(hash, vchSig))
+            return false;
+        if (GetPubKey() != key.GetPubKey())
+            return false;
+        return true;
+    }
+
     CBitcoinAddress GetAddress() const
     {
         return CBitcoinAddress(GetPubKey());