text: // Copyright (c) 2009-2014 The Bitcoin developers
  // Distributed under the MIT/X11 software license, see the accompanying
  // file COPYING or http://www.opensource.org/licenses/mit-license.php.
  
  #include <openssl/ecdsa.h>
  #include <openssl/rand.h>
  #include <openssl/obj_mac.h>
  
  #include "key.h"
  
  
  // anonymous namespace with local implementation code (OpenSSL interaction)
  namespace {
  
  // Generate a private key from just the secret parameter
  int EC_KEY_regenerate_key(EC_KEY *eckey, BIGNUM *priv_key)
  {
      int ok = 0;
      BN_CTX *ctx = NULL;
      EC_POINT *pub_key = NULL;
  
      if (!eckey) return 0;
  
      const EC_GROUP *group = EC_KEY_get0_group(eckey);
  
      if ((ctx = BN_CTX_new()) == NULL)
          goto err;
  
      pub_key = EC_POINT_new(group);
  
      if (pub_key == NULL)
          goto err;
  
      if (!EC_POINT_mul(group, pub_key, priv_key, NULL, NULL, ctx))
          goto err;
  
      EC_KEY_set_private_key(eckey,priv_key);
      EC_KEY_set_public_key(eckey,pub_key);
  
      ok = 1;
  
  err:
  
      if (pub_key)
          EC_POINT_free(pub_key);
      if (ctx != NULL)
          BN_CTX_free(ctx);
  
      return(ok);
  }
  
  // Perform ECDSA key recovery (see SEC1 4.1.6) for curves over (mod p)-fields
  // recid selects which key is recovered
  // if check is non-zero, additional checks are performed
  int 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;
  }
  
  // RAII Wrapper around OpenSSL's EC_KEY
  class CECKey {
  private:
      EC_KEY *pkey;
  
  public:
      CECKey() {
          pkey = EC_KEY_new_by_curve_name(NID_secp256k1);
          assert(pkey != NULL);
      }
  
      ~CECKey() {
          EC_KEY_free(pkey);
      }
  
      void GetSecretBytes(unsigned char vch[32]) const {
          const BIGNUM *bn = EC_KEY_get0_private_key(pkey);
          assert(bn);
          int nBytes = BN_num_bytes(bn);
          int n=BN_bn2bin(bn,&vch[32 - nBytes]);
          assert(n == nBytes);
          memset(vch, 0, 32 - nBytes);
      }
  
      void SetSecretBytes(const unsigned char vch[32]) {
          BIGNUM bn;
          BN_init(&bn);
          assert(BN_bin2bn(vch, 32, &bn));
          assert(EC_KEY_regenerate_key(pkey, &bn));
          BN_clear_free(&bn);
      }
  
      void GetPrivKey(CPrivKey &privkey, bool fCompressed) {
          EC_KEY_set_conv_form(pkey, fCompressed ? POINT_CONVERSION_COMPRESSED : POINT_CONVERSION_UNCOMPRESSED);
          int nSize = i2d_ECPrivateKey(pkey, NULL);
          assert(nSize);
          privkey.resize(nSize);
          unsigned char* pbegin = &privkey[0];
          int nSize2 = i2d_ECPrivateKey(pkey, &pbegin);
          assert(nSize == nSize2);
      }
  
      bool SetPrivKey(const CPrivKey &privkey) {
          const unsigned char* pbegin = &privkey[0];
          if (d2i_ECPrivateKey(&pkey, &pbegin, privkey.size())) {
              // d2i_ECPrivateKey returns true if parsing succeeds.
              // This doesn't necessarily mean the key is valid.
              if (EC_KEY_check_key(pkey))
                  return true;
          }
          return false;
      }
  
      void GetPubKey(CPubKey &pubkey, bool fCompressed) {
          EC_KEY_set_conv_form(pkey, fCompressed ? POINT_CONVERSION_COMPRESSED : POINT_CONVERSION_UNCOMPRESSED);
          int nSize = i2o_ECPublicKey(pkey, NULL);
          assert(nSize);
          assert(nSize <= 65);
          unsigned char c[65];
          unsigned char *pbegin = c;
          int nSize2 = i2o_ECPublicKey(pkey, &pbegin);
          assert(nSize == nSize2);
          pubkey.Set(&c[0], &c[nSize]);
      }
  
      bool SetPubKey(const CPubKey &pubkey) {
          const unsigned char* pbegin = pubkey.begin();
          return o2i_ECPublicKey(&pkey, &pbegin, pubkey.size());
      }
  
      bool Sign(const uint256 &hash, std::vector<unsigned char>& vchSig) {
          unsigned int nSize = ECDSA_size(pkey);
          vchSig.resize(nSize); // Make sure it is big enough
          assert(ECDSA_sign(0, (unsigned char*)&hash, sizeof(hash), &vchSig[0], &nSize, pkey));
          vchSig.resize(nSize); // Shrink to fit actual size
          return true;
      }
  
      bool Verify(const uint256 &hash, const std::vector<unsigned char>& vchSig) {
          if (vchSig.empty())
              return false;
          
          // New versions of OpenSSL will reject non-canonical DER signatures. de/re-serialize first.
          unsigned char *norm_der = NULL;
          ECDSA_SIG *norm_sig = ECDSA_SIG_new();
          const unsigned char* sigptr = &vchSig[0];
          d2i_ECDSA_SIG(&norm_sig, &sigptr, vchSig.size());
          int derlen = i2d_ECDSA_SIG(norm_sig, &norm_der);
          ECDSA_SIG_free(norm_sig);
          if (derlen <= 0)
              return false;
  
          // -1 = error, 0 = bad sig, 1 = good
          bool ret = ECDSA_verify(0, (unsigned char*)&hash, sizeof(hash), norm_der, derlen, pkey) == 1;
          OPENSSL_free(norm_der);
          return ret;
      }
  
      bool SignCompact(const uint256 &hash, unsigned char *p64, int &rec) {
          bool fOk = false;
          ECDSA_SIG *sig = ECDSA_do_sign((unsigned char*)&hash, sizeof(hash), pkey);
          if (sig==NULL)
              return false;
          memset(p64, 0, 64);
          int nBitsR = BN_num_bits(sig->r);
          int nBitsS = BN_num_bits(sig->s);
          if (nBitsR <= 256 && nBitsS <= 256) {
              CPubKey pubkey;
              GetPubKey(pubkey, true);
              for (int i=0; i<4; i++) {
                  CECKey keyRec;
                  if (ECDSA_SIG_recover_key_GFp(keyRec.pkey, sig, (unsigned char*)&hash, sizeof(hash), i, 1) == 1) {
                      CPubKey pubkeyRec;
                      keyRec.GetPubKey(pubkeyRec, true);
                      if (pubkeyRec == pubkey) {
                          rec = i;
                          fOk = true;
                          break;
                      }
                  }
              }
              assert(fOk);
              BN_bn2bin(sig->r,&p64[32-(nBitsR+7)/8]);
              BN_bn2bin(sig->s,&p64[64-(nBitsS+7)/8]);
          }
          ECDSA_SIG_free(sig);
          return fOk;
      }
  
      // reconstruct public key from a compact signature
      // This is only slightly more CPU intensive than just verifying it.
      // If this function succeeds, the recovered public key is guaranteed to be valid
      // (the signature is a valid signature of the given data for that key)
      bool Recover(const uint256 &hash, const unsigned char *p64, int rec)
      {
          if (rec<0 || rec>=3)
              return false;
          ECDSA_SIG *sig = ECDSA_SIG_new();
          BN_bin2bn(&p64[0],  32, sig->r);
          BN_bin2bn(&p64[32], 32, sig->s);
          bool ret = ECDSA_SIG_recover_key_GFp(pkey, sig, (unsigned char*)&hash, sizeof(hash), rec, 0) == 1;
          ECDSA_SIG_free(sig);
          return ret;
      }
  };
  
  }; // end of anonymous namespace
  
  bool CKey::Check(const unsigned char *vch) {
      // Do not convert to OpenSSL's data structures for range-checking keys,
      // it's easy enough to do directly.
      static const unsigned char vchMax[32] = {
          0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
          0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
          0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
          0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40
      };
      bool fIsZero = true;
      for (int i=0; i<32 && fIsZero; i++)
          if (vch[i] != 0)
              fIsZero = false;
      if (fIsZero)
          return false;
      for (int i=0; i<32; i++) {
          if (vch[i] < vchMax[i])
              return true;
          if (vch[i] > vchMax[i])
              return false;
      }
      return true;
  }
  
  void CKey::MakeNewKey(bool fCompressedIn) {
      do {
          RAND_bytes(vch, sizeof(vch));
      } while (!Check(vch));
      fValid = true;
      fCompressed = fCompressedIn;
  }
  
  bool CKey::SetPrivKey(const CPrivKey &privkey, bool fCompressedIn) {
      CECKey key;
      if (!key.SetPrivKey(privkey))
          return false;
      key.GetSecretBytes(vch);
      fCompressed = fCompressedIn;
      fValid = true;
      return true;
  }
  
  CPrivKey CKey::GetPrivKey() const {
      assert(fValid);
      CECKey key;
      key.SetSecretBytes(vch);
      CPrivKey privkey;
      key.GetPrivKey(privkey, fCompressed);
      return privkey;
  }
  
  CPubKey CKey::GetPubKey() const {
      assert(fValid);
      CECKey key;
      key.SetSecretBytes(vch);
      CPubKey pubkey;
      key.GetPubKey(pubkey, fCompressed);
      return pubkey;
  }
  
  bool CKey::Sign(const uint256 &hash, std::vector<unsigned char>& vchSig) const {
      if (!fValid)
          return false;
      CECKey key;
      key.SetSecretBytes(vch);
      return key.Sign(hash, vchSig);
  }
  
  bool CKey::SignCompact(const uint256 &hash, std::vector<unsigned char>& vchSig) const {
      if (!fValid)
          return false;
      CECKey key;
      key.SetSecretBytes(vch);
      vchSig.resize(65);
      int rec = -1;
      if (!key.SignCompact(hash, &vchSig[1], rec))
          return false;
      assert(rec != -1);
      vchSig[0] = 27 + rec + (fCompressed ? 4 : 0);
      return true;
  }
  
  bool CPubKey::Verify(const uint256 &hash, const std::vector<unsigned char>& vchSig) const {
      if (!IsValid())
          return false;
      CECKey key;
      if (!key.SetPubKey(*this))
          return false;
      if (!key.Verify(hash, vchSig))
          return false;
      return true;
  }
  
  bool CPubKey::RecoverCompact(const uint256 &hash, const std::vector<unsigned char>& vchSig) {
      if (vchSig.size() != 65)
          return false;
      CECKey key;
      if (!key.Recover(hash, &vchSig[1], (vchSig[0] - 27) & ~4))
          return false;
      key.GetPubKey(*this, (vchSig[0] - 27) & 4);
      return true;
  }
  
  bool CPubKey::VerifyCompact(const uint256 &hash, const std::vector<unsigned char>& vchSig) const {
      if (!IsValid())
          return false;
      if (vchSig.size() != 65)
          return false;
      CECKey key;
      if (!key.Recover(hash, &vchSig[1], (vchSig[0] - 27) & ~4))
          return false;
      CPubKey pubkeyRec;
      key.GetPubKey(pubkeyRec, IsCompressed());
      if (*this != pubkeyRec)
          return false;
      return true;
  }
  
  bool CPubKey::IsFullyValid() const {
      if (!IsValid())
          return false;
      CECKey key;
      if (!key.SetPubKey(*this))
          return false;
      return true;
  }
  
  bool CPubKey::Decompress() {
      if (!IsValid())
          return false;
      CECKey key;
      if (!key.SetPubKey(*this))
          return false;
      key.GetPubKey(*this, false);
      return true;
  }
  