Made all bip32 primitives testnet compatible.
[electrum-nvc.git] / lib / bitcoin.py
index 9cdb25b..af0a6ed 100644 (file)
@@ -1,3 +1,4 @@
+# -*- coding: utf-8 -*-
 #!/usr/bin/env python
 #
 # Electrum - lightweight Bitcoin client
 # You should have received a copy of the GNU General Public License
 # along with this program. If not, see <http://www.gnu.org/licenses/>.
 
+import hashlib
+import base64
+import re
+import sys
+import hmac
 
-import hashlib, base64, ecdsa, re
+from util import print_error
+from version import SEED_PREFIX
+
+try:
+    import ecdsa
+except ImportError:
+    sys.exit("Error: python-ecdsa does not seem to be installed. Try 'sudo pip install ecdsa'")
+
+try:
+    import aes
+except ImportError:
+    sys.exit("Error: AES does not seem to be installed. Try 'sudo pip install slowaes'")
+
+################################## transactions
+
+MIN_RELAY_TX_FEE = 1000
+
+
+# AES encryption
+EncodeAES = lambda secret, s: base64.b64encode(aes.encryptData(secret,s))
+DecodeAES = lambda secret, e: aes.decryptData(secret, base64.b64decode(e))
+
+
+def pw_encode(s, password):
+    if password:
+        secret = Hash(password)
+        return EncodeAES(secret, s.encode("utf8"))
+    else:
+        return s
+
+
+def pw_decode(s, password):
+    if password is not None:
+        secret = Hash(password)
+        try:
+            d = DecodeAES(secret, s).decode("utf8")
+        except Exception:
+            raise Exception('Invalid password')
+        return d
+    else:
+        return s
 
 
 def rev_hex(s):
     return s.decode('hex')[::-1].encode('hex')
 
+
 def int_to_hex(i, length=1):
     s = hex(i)[2:].rstrip('L')
     s = "0"*(2*length - len(s)) + s
     return rev_hex(s)
 
 
-def Hash(data):
-    return hashlib.sha256(hashlib.sha256(data).digest()).digest()
+def var_int(i):
+    # https://en.bitcoin.it/wiki/Protocol_specification#Variable_length_integer
+    if i<0xfd:
+        return int_to_hex(i)
+    elif i<=0xffff:
+        return "fd"+int_to_hex(i,2)
+    elif i<=0xffffffff:
+        return "fe"+int_to_hex(i,4)
+    else:
+        return "ff"+int_to_hex(i,8)
+
+
+def op_push(i):
+    if i<0x4c:
+        return int_to_hex(i)
+    elif i<0xff:
+        return '4c' + int_to_hex(i)
+    elif i<0xffff:
+        return '4d' + int_to_hex(i,2)
+    else:
+        return '4e' + int_to_hex(i,4)
+
 
+def sha256(x):
+    return hashlib.sha256(x).digest()
 
-############ functions from pywallet ##################### 
 
-addrtype = 0
+def Hash(x):
+    if type(x) is unicode: x=x.encode('utf-8')
+    return sha256(sha256(x))
+
+
+hash_encode = lambda x: x[::-1].encode('hex')
+hash_decode = lambda x: x.decode('hex')[::-1]
+hmac_sha_512 = lambda x,y: hmac.new(x, y, hashlib.sha512).digest()
+
+
+def mnemonic_to_seed(mnemonic, passphrase):
+    from pbkdf2 import PBKDF2
+    import hmac
+    PBKDF2_ROUNDS = 2048
+    return PBKDF2(mnemonic, 'mnemonic' + passphrase, iterations = PBKDF2_ROUNDS, macmodule = hmac, digestmodule = hashlib.sha512).read(64)
+
+
+is_new_seed = lambda x: hmac_sha_512("Seed version", x.encode('utf8')).encode('hex')[0:2].startswith(SEED_PREFIX)
+
+def is_old_seed(seed):
+    import mnemonic
+    words = seed.strip().split()
+    try:
+        mnemonic.mn_decode(words)
+        uses_electrum_words = True
+    except Exception:
+        uses_electrum_words = False
+
+    try:
+        seed.decode('hex')
+        is_hex = (len(seed) == 32)
+    except Exception:
+        is_hex = False
+
+    return is_hex or (uses_electrum_words and len(words) == 12)
+
+
+# pywallet openssl private key implementation
+
+def i2d_ECPrivateKey(pkey, compressed=False):
+    if compressed:
+        key = '3081d30201010420' + \
+              '%064x' % pkey.secret + \
+              'a081a53081a2020101302c06072a8648ce3d0101022100' + \
+              '%064x' % _p + \
+              '3006040100040107042102' + \
+              '%064x' % _Gx + \
+              '022100' + \
+              '%064x' % _r + \
+              '020101a124032200'
+    else:
+        key = '308201130201010420' + \
+              '%064x' % pkey.secret + \
+              'a081a53081a2020101302c06072a8648ce3d0101022100' + \
+              '%064x' % _p + \
+              '3006040100040107044104' + \
+              '%064x' % _Gx + \
+              '%064x' % _Gy + \
+              '022100' + \
+              '%064x' % _r + \
+              '020101a144034200'
+
+    return key.decode('hex') + i2o_ECPublicKey(pkey.pubkey, compressed)
+
+def i2o_ECPublicKey(pubkey, compressed=False):
+    # public keys are 65 bytes long (520 bits)
+    # 0x04 + 32-byte X-coordinate + 32-byte Y-coordinate
+    # 0x00 = point at infinity, 0x02 and 0x03 = compressed, 0x04 = uncompressed
+    # compressed keys: <sign> <x> where <sign> is 0x02 if y is even and 0x03 if y is odd
+    if compressed:
+        if pubkey.point.y() & 1:
+            key = '03' + '%064x' % pubkey.point.x()
+        else:
+            key = '02' + '%064x' % pubkey.point.x()
+    else:
+        key = '04' + \
+              '%064x' % pubkey.point.x() + \
+              '%064x' % pubkey.point.y()
+
+    return key.decode('hex')
+
+# end pywallet openssl private key implementation
+
+
+
+############ functions from pywallet #####################
 
 def hash_160(public_key):
     try:
         md = hashlib.new('ripemd160')
-        md.update(hashlib.sha256(public_key).digest())
+        md.update(sha256(public_key))
         return md.digest()
-    except:
+    except Exception:
         import ripemd
-        md = ripemd.new(hashlib.sha256(public_key).digest())
+        md = ripemd.new(sha256(public_key))
         return md.digest()
 
 
@@ -52,7 +205,7 @@ def public_key_to_bc_address(public_key):
     h160 = hash_160(public_key)
     return hash_160_to_bc_address(h160)
 
-def hash_160_to_bc_address(h160):
+def hash_160_to_bc_address(h160, addrtype = 0):
     vh160 = chr(addrtype) + h160
     h = Hash(vh160)
     addr = vh160 + h[0:4]
@@ -60,21 +213,13 @@ def hash_160_to_bc_address(h160):
 
 def bc_address_to_hash_160(addr):
     bytes = b58decode(addr, 25)
-    return bytes[1:21]
+    return ord(bytes[0]), bytes[1:21]
 
-def encode_point(pubkey, compressed=False):
-    order = generator_secp256k1.order()
-    p = pubkey.pubkey.point
-    x_str = ecdsa.util.number_to_string(p.x(), order)
-    y_str = ecdsa.util.number_to_string(p.y(), order)
-    if compressed:
-        return chr(2 + (p.y() & 1)) + x_str
-    else:
-        return chr(4) + pubkey.to_string() #x_str + y_str
 
 __b58chars = '123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz'
 __b58base = len(__b58chars)
 
+
 def b58encode(v):
     """ encode v, which is a string of bytes, to base58."""
 
@@ -98,6 +243,7 @@ def b58encode(v):
 
     return (__b58chars[0]*nPad) + result
 
+
 def b58decode(v, length):
     """ decode v into a string of len bytes."""
     long_value = 0L
@@ -127,6 +273,7 @@ def EncodeBase58Check(vchIn):
     hash = Hash(vchIn)
     return b58encode(vchIn + hash[0:4])
 
+
 def DecodeBase58Check(psz):
     vchRet = b58decode(psz, None)
     key = vchRet[0:-4]
@@ -138,74 +285,484 @@ def DecodeBase58Check(psz):
     else:
         return key
 
+
 def PrivKeyToSecret(privkey):
     return privkey[9:9+32]
 
-def SecretToASecret(secret):
-    vchIn = chr(addrtype+128) + secret
+
+def SecretToASecret(secret, compressed=False, addrtype=0):
+    vchIn = chr((addrtype+128)&255) + secret
+    if compressed: vchIn += '\01'
     return EncodeBase58Check(vchIn)
 
-def ASecretToSecret(key):
+def ASecretToSecret(key, addrtype=0):
     vch = DecodeBase58Check(key)
-    if vch and vch[0] == chr(addrtype+128):
+    if vch and vch[0] == chr((addrtype+128)&255):
         return vch[1:]
     else:
         return False
 
+def regenerate_key(sec):
+    b = ASecretToSecret(sec)
+    if not b:
+        return False
+    b = b[0:32]
+    return EC_KEY(b)
+
+
+def GetPubKey(pubkey, compressed=False):
+    return i2o_ECPublicKey(pubkey, compressed)
+
+
+def GetPrivKey(pkey, compressed=False):
+    return i2d_ECPrivateKey(pkey, compressed)
+
+
+def GetSecret(pkey):
+    return ('%064x' % pkey.secret).decode('hex')
+
+
+def is_compressed(sec):
+    b = ASecretToSecret(sec)
+    return len(b) == 33
+
+
+def public_key_from_private_key(sec):
+    # rebuild public key from private key, compressed or uncompressed
+    pkey = regenerate_key(sec)
+    assert pkey
+    compressed = is_compressed(sec)
+    public_key = GetPubKey(pkey.pubkey, compressed)
+    return public_key.encode('hex')
+
+
+def address_from_private_key(sec):
+    public_key = public_key_from_private_key(sec)
+    address = public_key_to_bc_address(public_key.decode('hex'))
+    return address
+
+
+def is_valid(addr):
+    return is_address(addr)
+
+
+def is_address(addr):
+    ADDRESS_RE = re.compile('[1-9A-HJ-NP-Za-km-z]{26,}\\Z')
+    if not ADDRESS_RE.match(addr): return False
+    try:
+        addrtype, h = bc_address_to_hash_160(addr)
+    except Exception:
+        return False
+    return addr == hash_160_to_bc_address(h, addrtype)
+
+
+def is_private_key(key):
+    try:
+        k = ASecretToSecret(key)
+        return k is not False
+    except:
+        return False
+
+
 ########### end pywallet functions #######################
 
-# secp256k1, http://www.oid-info.com/get/1.3.132.0.10
-_p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2FL
-_r = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141L
-_b = 0x0000000000000000000000000000000000000000000000000000000000000007L
-_a = 0x0000000000000000000000000000000000000000000000000000000000000000L
-_Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798L
-_Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8L
-curve_secp256k1 = ecdsa.ellipticcurve.CurveFp( _p, _a, _b )
-generator_secp256k1 = ecdsa.ellipticcurve.Point( curve_secp256k1, _Gx, _Gy, _r )
-oid_secp256k1 = (1,3,132,0,10)
-SECP256k1 = ecdsa.curves.Curve("SECP256k1", curve_secp256k1, generator_secp256k1, oid_secp256k1 ) 
-
-
-def filter(s): 
-    out = re.sub('( [^\n]*|)\n','',s)
-    out = out.replace(' ','')
-    out = out.replace('\n','')
-    return out
-
-def raw_tx( inputs, outputs, for_sig = None ):
-    s  = int_to_hex(1,4)                                     +   '     version\n' 
-    s += int_to_hex( len(inputs) )                           +   '     number of inputs\n'
-    for i in range(len(inputs)):
-        _, _, p_hash, p_index, p_script, pubkey, sig = inputs[i]
-        s += p_hash.decode('hex')[::-1].encode('hex')        +  '     prev hash\n'
-        s += int_to_hex(p_index,4)                           +  '     prev index\n'
-        if for_sig is None:
-            sig = sig + chr(1)                               # hashtype
-            script  = int_to_hex( len(sig))                  +  '     push %d bytes\n'%len(sig)
-            script += sig.encode('hex')                      +  '     sig\n'
-            pubkey = chr(4) + pubkey
-            script += int_to_hex( len(pubkey))               +  '     push %d bytes\n'%len(pubkey)
-            script += pubkey.encode('hex')                   +  '     pubkey\n'
-        elif for_sig==i:
-            script = p_script                                +  '     scriptsig \n'
+try:
+    from ecdsa.ecdsa import curve_secp256k1, generator_secp256k1
+except Exception:
+    print "cannot import ecdsa.curve_secp256k1. You probably need to upgrade ecdsa.\nTry: sudo pip install --upgrade ecdsa"
+    exit()
+
+from ecdsa.curves import SECP256k1
+from ecdsa.ellipticcurve import Point
+from ecdsa.util import string_to_number, number_to_string
+
+def msg_magic(message):
+    varint = var_int(len(message))
+    encoded_varint = "".join([chr(int(varint[i:i+2], 16)) for i in xrange(0, len(varint), 2)])
+    return "\x18Bitcoin Signed Message:\n" + encoded_varint + message
+
+
+def verify_message(address, signature, message):
+    try:
+        EC_KEY.verify_message(address, signature, message)
+        return True
+    except Exception as e:
+        print_error("Verification error: {0}".format(e))
+        return False
+
+
+def encrypt_message(message, pubkey):
+    return EC_KEY.encrypt_message(message, pubkey.decode('hex'))
+
+
+def chunks(l, n):
+    return [l[i:i+n] for i in xrange(0, len(l), n)]
+
+
+def ECC_YfromX(x,curved=curve_secp256k1, odd=True):
+    _p = curved.p()
+    _a = curved.a()
+    _b = curved.b()
+    for offset in range(128):
+        Mx = x + offset
+        My2 = pow(Mx, 3, _p) + _a * pow(Mx, 2, _p) + _b % _p
+        My = pow(My2, (_p+1)/4, _p )
+
+        if curved.contains_point(Mx,My):
+            if odd == bool(My&1):
+                return [My,offset]
+            return [_p-My,offset]
+    raise Exception('ECC_YfromX: No Y found')
+
+
+def negative_point(P):
+    return Point( P.curve(), P.x(), -P.y(), P.order() )
+
+
+def point_to_ser(P, comp=True ):
+    if comp:
+        return ( ('%02x'%(2+(P.y()&1)))+('%064x'%P.x()) ).decode('hex')
+    return ( '04'+('%064x'%P.x())+('%064x'%P.y()) ).decode('hex')
+
+
+def ser_to_point(Aser):
+    curve = curve_secp256k1
+    generator = generator_secp256k1
+    _r  = generator.order()
+    assert Aser[0] in ['\x02','\x03','\x04']
+    if Aser[0] == '\x04':
+        return Point( curve, string_to_number(Aser[1:33]), string_to_number(Aser[33:]), _r )
+    Mx = string_to_number(Aser[1:])
+    return Point( curve, Mx, ECC_YfromX(Mx, curve, Aser[0]=='\x03')[0], _r )
+
+
+
+class MyVerifyingKey(ecdsa.VerifyingKey):
+    @classmethod
+    def from_signature(klass, sig, recid, h, curve):
+        """ See http://www.secg.org/download/aid-780/sec1-v2.pdf, chapter 4.1.6 """
+        from ecdsa import util, numbertheory
+        import msqr
+        curveFp = curve.curve
+        G = curve.generator
+        order = G.order()
+        # extract r,s from signature
+        r, s = util.sigdecode_string(sig, order)
+        # 1.1
+        x = r + (recid/2) * order
+        # 1.3
+        alpha = ( x * x * x  + curveFp.a() * x + curveFp.b() ) % curveFp.p()
+        beta = msqr.modular_sqrt(alpha, curveFp.p())
+        y = beta if (beta - recid) % 2 == 0 else curveFp.p() - beta
+        # 1.4 the constructor checks that nR is at infinity
+        R = Point(curveFp, x, y, order)
+        # 1.5 compute e from message:
+        e = string_to_number(h)
+        minus_e = -e % order
+        # 1.6 compute Q = r^-1 (sR - eG)
+        inv_r = numbertheory.inverse_mod(r,order)
+        Q = inv_r * ( s * R + minus_e * G )
+        return klass.from_public_point( Q, curve )
+
+
+class EC_KEY(object):
+    def __init__( self, k ):
+        secret = string_to_number(k)
+        self.pubkey = ecdsa.ecdsa.Public_key( generator_secp256k1, generator_secp256k1 * secret )
+        self.privkey = ecdsa.ecdsa.Private_key( self.pubkey, secret )
+        self.secret = secret
+
+    def get_public_key(self, compressed=True):
+        return point_to_ser(self.pubkey.point, compressed).encode('hex')
+
+    def sign_message(self, message, compressed, address):
+        private_key = ecdsa.SigningKey.from_secret_exponent( self.secret, curve = SECP256k1 )
+        public_key = private_key.get_verifying_key()
+        signature = private_key.sign_digest_deterministic( Hash( msg_magic(message) ), hashfunc=hashlib.sha256, sigencode = ecdsa.util.sigencode_string )
+        assert public_key.verify_digest( signature, Hash( msg_magic(message) ), sigdecode = ecdsa.util.sigdecode_string)
+        for i in range(4):
+            sig = base64.b64encode( chr(27 + i + (4 if compressed else 0)) + signature )
+            try:
+                self.verify_message( address, sig, message)
+                return sig
+            except Exception:
+                continue
+        else:
+            raise Exception("error: cannot sign message")
+
+
+    @classmethod
+    def verify_message(self, address, signature, message):
+        sig = base64.b64decode(signature)
+        if len(sig) != 65: raise Exception("Wrong encoding")
+
+        nV = ord(sig[0])
+        if nV < 27 or nV >= 35:
+            raise Exception("Bad encoding")
+        if nV >= 31:
+            compressed = True
+            nV -= 4
         else:
-            script=''
-        s += int_to_hex( len(filter(script))/2 )             +  '     script length \n'
-        s += script
-        s += "ffffffff"                                      +  '     sequence\n'
-    s += int_to_hex( len(outputs) )                          +  '     number of outputs\n'
-    for output in outputs:
-        addr, amount = output
-        s += int_to_hex( amount, 8)                          +  '     amount: %d\n'%amount 
-        script = '76a9'                                      # op_dup, op_hash_160
-        script += '14'                                       # push 0x14 bytes
-        script += bc_address_to_hash_160(addr).encode('hex')
-        script += '88ac'                                     # op_equalverify, op_checksig
-        s += int_to_hex( len(filter(script))/2 )             +  '     script length \n'
-        s += script                                          +  '     script \n'
-    s += int_to_hex(0,4)                                     # lock time
-    if for_sig is not None: s += int_to_hex(1, 4)            # hash type
-    return s
+            compressed = False
+
+        recid = nV - 27
+        h = Hash( msg_magic(message) )
+        public_key = MyVerifyingKey.from_signature( sig[1:], recid, h, curve = SECP256k1 )
+
+        # check public key
+        public_key.verify_digest( sig[1:], h, sigdecode = ecdsa.util.sigdecode_string)
+
+        # check that we get the original signing address
+        addr = public_key_to_bc_address( point_to_ser(public_key.pubkey.point, compressed) )
+        if address != addr:
+            raise Exception("Bad signature")
+
+
+    # ecies encryption/decryption methods; aes-256-cbc is used as the cipher; hmac-sha256 is used as the mac
+
+    @classmethod
+    def encrypt_message(self, message, pubkey):
+
+        pk = ser_to_point(pubkey)
+        if not ecdsa.ecdsa.point_is_valid(generator_secp256k1, pk.x(), pk.y()):
+            raise Exception('invalid pubkey')
+
+        ephemeral_exponent = number_to_string(ecdsa.util.randrange(pow(2,256)), generator_secp256k1.order())
+        ephemeral = EC_KEY(ephemeral_exponent)
+
+        ecdh_key = (pk * ephemeral.privkey.secret_multiplier).x()
+        ecdh_key = ('%064x' % ecdh_key).decode('hex')
+        key = hashlib.sha512(ecdh_key).digest()
+        key_e, key_m = key[:32], key[32:]
+
+        iv_ciphertext = aes.encryptData(key_e, message)
+
+        ephemeral_pubkey = ephemeral.get_public_key(compressed=True).decode('hex')
+        encrypted = 'BIE1' + ephemeral_pubkey + iv_ciphertext
+        mac = hmac.new(key_m, encrypted, hashlib.sha256).digest()
+
+        return base64.b64encode(encrypted + mac)
+
+
+    def decrypt_message(self, encrypted):
 
+        encrypted = base64.b64decode(encrypted)
 
+        if len(encrypted) < 85:
+            raise Exception('invalid ciphertext: length')
+
+        magic = encrypted[:4]
+        ephemeral_pubkey = encrypted[4:37]
+        iv_ciphertext = encrypted[37:-32]
+        mac = encrypted[-32:]
+
+        if magic != 'BIE1':
+            raise Exception('invalid ciphertext: invalid magic bytes')
+
+        try:
+            ephemeral_pubkey = ser_to_point(ephemeral_pubkey)
+        except AssertionError, e:
+            raise Exception('invalid ciphertext: invalid ephemeral pubkey')
+
+        if not ecdsa.ecdsa.point_is_valid(generator_secp256k1, ephemeral_pubkey.x(), ephemeral_pubkey.y()):
+            raise Exception('invalid ciphertext: invalid ephemeral pubkey')
+
+        ecdh_key = (ephemeral_pubkey * self.privkey.secret_multiplier).x()
+        ecdh_key = ('%064x' % ecdh_key).decode('hex')
+        key = hashlib.sha512(ecdh_key).digest()
+        key_e, key_m = key[:32], key[32:]
+        if mac != hmac.new(key_m, encrypted[:-32], hashlib.sha256).digest():
+            raise Exception('invalid ciphertext: invalid mac')
+
+        return aes.decryptData(key_e, iv_ciphertext)
+
+
+###################################### BIP32 ##############################
+
+random_seed = lambda n: "%032x"%ecdsa.util.randrange( pow(2,n) )
+BIP32_PRIME = 0x80000000
+
+
+def get_pubkeys_from_secret(secret):
+    # public key
+    private_key = ecdsa.SigningKey.from_string( secret, curve = SECP256k1 )
+    public_key = private_key.get_verifying_key()
+    K = public_key.to_string()
+    K_compressed = GetPubKey(public_key.pubkey,True)
+    return K, K_compressed
+
+
+# Child private key derivation function (from master private key)
+# k = master private key (32 bytes)
+# c = master chain code (extra entropy for key derivation) (32 bytes)
+# n = the index of the key we want to derive. (only 32 bits will be used)
+# If n is negative (i.e. the 32nd bit is set), the resulting private key's
+#  corresponding public key can NOT be determined without the master private key.
+# However, if n is positive, the resulting private key's corresponding
+#  public key can be determined without the master private key.
+def CKD_priv(k, c, n):
+    is_prime = n & BIP32_PRIME
+    return _CKD_priv(k, c, rev_hex(int_to_hex(n,4)).decode('hex'), is_prime)
+
+def _CKD_priv(k, c, s, is_prime):
+    import hmac
+    from ecdsa.util import string_to_number, number_to_string
+    order = generator_secp256k1.order()
+    keypair = EC_KEY(k)
+    cK = GetPubKey(keypair.pubkey,True)
+    data = chr(0) + k + s if is_prime else cK + s
+    I = hmac.new(c, data, hashlib.sha512).digest()
+    k_n = number_to_string( (string_to_number(I[0:32]) + string_to_number(k)) % order , order )
+    c_n = I[32:]
+    return k_n, c_n
+
+# Child public key derivation function (from public key only)
+# K = master public key
+# c = master chain code
+# n = index of key we want to derive
+# This function allows us to find the nth public key, as long as n is
+#  non-negative. If n is negative, we need the master private key to find it.
+def CKD_pub(cK, c, n):
+    if n & BIP32_PRIME: raise
+    return _CKD_pub(cK, c, rev_hex(int_to_hex(n,4)).decode('hex'))
+
+# helper function, callable with arbitrary string
+def _CKD_pub(cK, c, s):
+    import hmac
+    from ecdsa.util import string_to_number, number_to_string
+    order = generator_secp256k1.order()
+    I = hmac.new(c, cK + s, hashlib.sha512).digest()
+    curve = SECP256k1
+    pubkey_point = string_to_number(I[0:32])*curve.generator + ser_to_point(cK)
+    public_key = ecdsa.VerifyingKey.from_public_point( pubkey_point, curve = SECP256k1 )
+    c_n = I[32:]
+    cK_n = GetPubKey(public_key.pubkey,True)
+    return cK_n, c_n
+
+
+BITCOIN_HEADERS = ["0488ade4", "0488b21e"]
+TESTNET_HEADERS = ["043587cf", "04358394"]
+
+BITCOIN_HEAD = "0488ade4"
+TESTNET_HEAD = "04358394"
+
+BITCOIN_HEADER_PRIV = "0488ADE4"
+BITCOIN_HEADER_PUB = "0488B21E"
+
+TESTNET_HEADER_PRIV = "04358394"
+TESTNET_HEADER_PUB = "043587CF"
+
+
+def _get_headers(testnet):
+    """Returns the correct headers for either testnet or bitcoin, in the form
+    of a 2-tuple, like (public, private)."""
+    if testnet:
+        return (TESTNET_HEADER_PUB, TESTNET_HEADER_PRIV)
+    else:
+        return (BITCOIN_HEADER_PUB, BITCOIN_HEADER_PRIV)
+
+
+def deserialize_xkey(xkey):
+
+    xkey = DecodeBase58Check(xkey)
+    assert len(xkey) == 78
+
+    xkey_header = xkey[0:4].encode('hex')
+    # Determine if the key is a bitcoin key or a testnet key.
+    if xkey_header in TESTNET_HEADERS:
+        head = TESTNET_HEAD
+    elif xkey_header in BITCOIN_HEADERS:
+        head = BITCOIN_HEAD
+    else:
+        raise Exception("Unknown xkey header: '%s'" % xkey_header)
+
+    depth = ord(xkey[4])
+    fingerprint = xkey[5:9]
+    child_number = xkey[9:13]
+    c = xkey[13:13+32]
+    if xkey[0:4].encode('hex') == head:
+        K_or_k = xkey[13+33:]
+    else:
+        K_or_k = xkey[13+32:]
+    return depth, fingerprint, child_number, c, K_or_k
+
+
+def get_xkey_name(xkey, testnet=False):
+    depth, fingerprint, child_number, c, K = deserialize_xkey(xkey)
+    n = int(child_number.encode('hex'), 16)
+    if n & BIP32_PRIME:
+        child_id = "%d'"%(n - BIP32_PRIME)
+    else:
+        child_id = "%d"%n
+    if depth == 0:
+        return ''
+    elif depth == 1:
+        return child_id
+    else:
+        raise BaseException("xpub depth error")
+
+
+def xpub_from_xprv(xprv, testnet=False):
+    depth, fingerprint, child_number, c, k = deserialize_xkey(xprv)
+    K, cK = get_pubkeys_from_secret(k)
+    header_pub, _  = _get_headers(testnet)
+    xpub = header_pub.decode('hex') + chr(depth) + fingerprint + child_number + c + cK
+    return EncodeBase58Check(xpub)
+
+
+def bip32_root(seed, testnet=False):
+    import hmac
+    header_pub, header_priv = _get_headers(testnet)
+    seed = seed.decode('hex')
+    I = hmac.new("Bitcoin seed", seed, hashlib.sha512).digest()
+    master_k = I[0:32]
+    master_c = I[32:]
+    K, cK = get_pubkeys_from_secret(master_k)
+    xprv = (header_priv + "00" + "00000000" + "00000000").decode("hex") + master_c + chr(0) + master_k
+    xpub = (header_pub + "00" + "00000000" + "00000000").decode("hex") + master_c + cK
+    return EncodeBase58Check(xprv), EncodeBase58Check(xpub)
+
+
+def bip32_private_derivation(xprv, branch, sequence, testnet=False):
+    header_pub, header_priv = _get_headers(testnet)
+    depth, fingerprint, child_number, c, k = deserialize_xkey(xprv)
+    assert sequence.startswith(branch)
+    sequence = sequence[len(branch):]
+    for n in sequence.split('/'):
+        if n == '': continue
+        i = int(n[:-1]) + BIP32_PRIME if n[-1] == "'" else int(n)
+        parent_k = k
+        k, c = CKD_priv(k, c, i)
+        depth += 1
+
+    _, parent_cK = get_pubkeys_from_secret(parent_k)
+    fingerprint = hash_160(parent_cK)[0:4]
+    child_number = ("%08X"%i).decode('hex')
+    K, cK = get_pubkeys_from_secret(k)
+    xprv = header_priv.decode('hex') + chr(depth) + fingerprint + child_number + c + chr(0) + k
+    xpub = header_pub.decode('hex') + chr(depth) + fingerprint + child_number + c + cK
+    return EncodeBase58Check(xprv), EncodeBase58Check(xpub)
+
+
+def bip32_public_derivation(xpub, branch, sequence, testnet=False):
+    header_pub, _ = _get_headers(testnet)
+    depth, fingerprint, child_number, c, cK = deserialize_xkey(xpub)
+    assert sequence.startswith(branch)
+    sequence = sequence[len(branch):]
+    for n in sequence.split('/'):
+        if n == '': continue
+        i = int(n)
+        parent_cK = cK
+        cK, c = CKD_pub(cK, c, i)
+        depth += 1
+
+    fingerprint = hash_160(parent_cK)[0:4]
+    child_number = ("%08X"%i).decode('hex')
+    xpub = header_pub.decode('hex') + chr(depth) + fingerprint + child_number + c + cK
+    return EncodeBase58Check(xpub)
+
+
+def bip32_private_key(sequence, k, chain):
+    for i in sequence:
+        k, chain = CKD_priv(k, chain, i)
+    return SecretToASecret(k, True)