text: // Copyright (c) 2009-2012 The Bitcoin developers
  	// Copyright (c) 2011-2012 Litecoin Developers
  	// Distributed under the MIT/X11 software license, see the accompanying
  	// file COPYING or http://www.opensource.org/licenses/mit-license.php.
  	
  	#include <map>
  	
  	#include <openssl/ecdsa.h>
  	#include <openssl/obj_mac.h>
  	
  	#include "key.h"
  	
  	// 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 nonzero, 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;
  	}
  	
  	void CKey::SetCompressedPubKey()
  	{
  	    EC_KEY_set_conv_form(pkey, POINT_CONVERSION_COMPRESSED);
  	    fCompressedPubKey = true;
  	}
  	
  	void CKey::Reset()
  	{
  	    fCompressedPubKey = false;
  	    if (pkey != NULL)
  	        EC_KEY_free(pkey);
  	    pkey = EC_KEY_new_by_curve_name(NID_secp256k1);
  	    if (pkey == NULL)
  	        throw key_error("CKey::CKey() : EC_KEY_new_by_curve_name failed");
  	    fSet = false;
  	}
  	
  	CKey::CKey()
  	{
  	    pkey = NULL;
  	    Reset();
  	}
  	
  	CKey::CKey(const CKey& b)
  	{
  	    pkey = EC_KEY_dup(b.pkey);
  	    if (pkey == NULL)
  	        throw key_error("CKey::CKey(const CKey&) : EC_KEY_dup failed");
  	    fSet = b.fSet;
  	}
  	
  	CKey& CKey::operator=(const CKey& b)
  	{
  	    if (!EC_KEY_copy(pkey, b.pkey))
  	        throw key_error("CKey::operator=(const CKey&) : EC_KEY_copy failed");
  	    fSet = b.fSet;
  	    return (*this);
  	}
  	
  	CKey::~CKey()
  	{
  	    EC_KEY_free(pkey);
  	}
  	
  	bool CKey::IsNull() const
  	{
  	    return !fSet;
  	}
  	
  	bool CKey::IsCompressed() const
  	{
  	    return fCompressedPubKey;
  	}
  	
  	void CKey::MakeNewKey(bool fCompressed)
  	{
  	    if (!EC_KEY_generate_key(pkey))
  	        throw key_error("CKey::MakeNewKey() : EC_KEY_generate_key failed");
  	    if (fCompressed)
  	        SetCompressedPubKey();
  	    fSet = true;
  	}
  	
  	bool CKey::SetPrivKey(const CPrivKey& vchPrivKey)
  	{
  	    const unsigned char* pbegin = &vchPrivKey[0];
  	    if (!d2i_ECPrivateKey(&pkey, &pbegin, vchPrivKey.size()))
  	        return false;
  	    fSet = true;
  	    return true;
  	}
  	
  	bool CKey::SetSecret(const CSecret& vchSecret, bool fCompressed)
  	{
  	    EC_KEY_free(pkey);
  	    pkey = EC_KEY_new_by_curve_name(NID_secp256k1);
  	    if (pkey == NULL)
  	        throw key_error("CKey::SetSecret() : EC_KEY_new_by_curve_name failed");
  	    if (vchSecret.size() != 32)
  	        throw key_error("CKey::SetSecret() : secret must be 32 bytes");
  	    BIGNUM *bn = BN_bin2bn(&vchSecret[0],32,BN_new());
  	    if (bn == NULL)
  	        throw key_error("CKey::SetSecret() : BN_bin2bn failed");
  	    if (!EC_KEY_regenerate_key(pkey,bn))
  	    {
  	        BN_clear_free(bn);
  	        throw key_error("CKey::SetSecret() : EC_KEY_regenerate_key failed");
  	    }
  	    BN_clear_free(bn);
  	    fSet = true;
  	    if (fCompressed || fCompressedPubKey)
  	        SetCompressedPubKey();
  	    return true;
  	}
  	
  	CSecret CKey::GetSecret(bool &fCompressed) const
  	{
  	    CSecret vchRet;
  	    vchRet.resize(32);
  	    const BIGNUM *bn = EC_KEY_get0_private_key(pkey);
  	    int nBytes = BN_num_bytes(bn);
  	    if (bn == NULL)
  	        throw key_error("CKey::GetSecret() : EC_KEY_get0_private_key failed");
  	    int n=BN_bn2bin(bn,&vchRet[32 - nBytes]);
  	    if (n != nBytes)
  	        throw key_error("CKey::GetSecret(): BN_bn2bin failed");
  	    fCompressed = fCompressedPubKey;
  	    return vchRet;
  	}
  	
  	CPrivKey CKey::GetPrivKey() const
  	{
  	    int nSize = i2d_ECPrivateKey(pkey, NULL);
  	    if (!nSize)
  	        throw key_error("CKey::GetPrivKey() : i2d_ECPrivateKey failed");
  	    CPrivKey vchPrivKey(nSize, 0);
  	    unsigned char* pbegin = &vchPrivKey[0];
  	    if (i2d_ECPrivateKey(pkey, &pbegin) != nSize)
  	        throw key_error("CKey::GetPrivKey() : i2d_ECPrivateKey returned unexpected size");
  	    return vchPrivKey;
  	}
  	
  	bool CKey::SetPubKey(const CPubKey& vchPubKey)
  	{
  	    const unsigned char* pbegin = &vchPubKey.vchPubKey[0];
  	    if (!o2i_ECPublicKey(&pkey, &pbegin, vchPubKey.vchPubKey.size()))
  	        return false;
  	    fSet = true;
  	    if (vchPubKey.vchPubKey.size() == 33)
  	        SetCompressedPubKey();
  	    return true;
  	}
  	
  	CPubKey CKey::GetPubKey() const
  	{
  	    int nSize = i2o_ECPublicKey(pkey, NULL);
  	    if (!nSize)
  	        throw key_error("CKey::GetPubKey() : i2o_ECPublicKey failed");
  	    std::vector<unsigned char> vchPubKey(nSize, 0);
  	    unsigned char* pbegin = &vchPubKey[0];
  	    if (i2o_ECPublicKey(pkey, &pbegin) != nSize)
  	        throw key_error("CKey::GetPubKey() : i2o_ECPublicKey returned unexpected size");
  	    return CPubKey(vchPubKey);
  	}
  	
  	bool CKey::Sign(uint256 hash, std::vector<unsigned char>& vchSig)
  	{
  	    unsigned int nSize = ECDSA_size(pkey);
  	    vchSig.resize(nSize); // Make sure it is big enough
  	    if (!ECDSA_sign(0, (unsigned char*)&hash, sizeof(hash), &vchSig[0], &nSize, pkey))
  	    {
  	        vchSig.clear();
  	        return false;
  	    }
  	    vchSig.resize(nSize); // Shrink to fit actual size
  	    return true;
  	}
  	
  	// create a compact signature (65 bytes), which allows reconstructing the used public key
  	// The format is one header byte, followed by two times 32 bytes for the serialized r and s values.
  	// The header byte: 0x1B = first key with even y, 0x1C = first key with odd y,
  	//                  0x1D = second key with even y, 0x1E = second key with odd y
  	bool CKey::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 (fCompressedPubKey)
  	                keyRec.SetCompressedPubKey();
  	            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+(fCompressedPubKey ? 4 : 0);
  	        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
  	// 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 CKey::SetCompactSignature(uint256 hash, const std::vector<unsigned char>& vchSig)
  	{
  	    if (vchSig.size() != 65)
  	        return false;
  	    int nV = vchSig[0];
  	    if (nV<27 || nV>=35)
  	        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 (nV >= 31)
  	    {
  	        SetCompressedPubKey();
  	        nV -= 4;
  	    }
  	    if (ECDSA_SIG_recover_key_GFp(pkey, sig, (unsigned char*)&hash, sizeof(hash), nV - 27, 0) == 1)
  	    {
  	        fSet = true;
  	        ECDSA_SIG_free(sig);
  	        return true;
  	    }
  	    return false;
  	}
  	
  	bool CKey::Verify(uint256 hash, const std::vector<unsigned char>& vchSig)
  	{
  	    // -1 = error, 0 = bad sig, 1 = good
  	    if (ECDSA_verify(0, (unsigned char*)&hash, sizeof(hash), &vchSig[0], vchSig.size(), pkey) != 1)
  	        return false;
  	
  	    return true;
  	}
  	
  	bool CKey::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;
  	}
  	
  	bool CKey::IsValid()
  	{
  	    if (!fSet)
  	        return false;
  	
  	    bool fCompr;
  	    CSecret secret = GetSecret(fCompr);
  	    CKey key2;
  	    key2.SetSecret(secret, fCompr);
  	    return GetPubKey() == key2.GetPubKey();
  	}
  