text: # -*- coding: utf-8 -*-
  #
  # Electrum - lightweight Bitcoin client
  # Copyright (C) 2011 thomasv@gitorious
  #
  # Permission is hereby granted, free of charge, to any person
  # obtaining a copy of this software and associated documentation files
  # (the "Software"), to deal in the Software without restriction,
  # including without limitation the rights to use, copy, modify, merge,
  # publish, distribute, sublicense, and/or sell copies of the Software,
  # and to permit persons to whom the Software is furnished to do so,
  # subject to the following conditions:
  #
  # The above copyright notice and this permission notice shall be
  # included in all copies or substantial portions of the Software.
  #
  # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  # EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  # MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
  # NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
  # BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
  # ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
  # CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  # SOFTWARE.
  
  import hashlib
  import base64
  import hmac
  import os
  import json
  
  import ecdsa
  import pyaes
  
  from .util import bfh, bh2u, to_string
  from . import version
  from .util import print_error, InvalidPassword, assert_bytes, to_bytes, inv_dict
  from . import segwit_addr
  
  def read_json_dict(filename):
      path = os.path.join(os.path.dirname(__file__), filename)
      try:
          with open(path, 'r') as f:
              r = json.loads(f.read())
      except:
          r = {}
      return r
  
  
  
  
  # Version numbers for BIP32 extended keys
  # standard: xprv, xpub
  XPRV_HEADERS = {
      'standard': 0x0488ade4,
  }
  XPUB_HEADERS = {
      'standard': 0x0488b21e,
  }
  
  # Bitcoin Cash fork block specification
  BITCOIN_CASH_FORK_BLOCK_HEIGHT = 478559
  BITCOIN_CASH_FORK_BLOCK_HASH = "000000000000000000651ef99cb9fcbe0dadde1d424bd9f15ff20136191a5eec"
  
  
  class NetworkConstants:
  
      @classmethod
      def set_mainnet(cls):
          cls.TESTNET = False
          cls.WIF_PREFIX = 0x8c
          cls.ADDRTYPE_P2PKH = 28
          cls.ADDRTYPE_P2SH = 50
          cls.SEGWIT_HRP = "bc"
          cls.HEADERS_URL = "https://www.commercium.net/files/blockchain_headers"
          cls.GENESIS = "00045ada91749106ec529f0544ad15e9f0c2855fea37bf2952971de06e6251d2"
          cls.DEFAULT_PORTS = {'t': '50001', 's': '50002'}
          cls.DEFAULT_SERVERS = read_json_dict('servers.json')
  
      @classmethod
      def set_testnet(cls):
          cls.TESTNET = True
          cls.WIF_PREFIX = 0xef
          cls.ADDRTYPE_P2PKH = 111
          cls.ADDRTYPE_P2SH = 196
          cls.SEGWIT_HRP = "tb"
          cls.HEADERS_URL = "http://commerciumelectro.com/files/testnet_headers"
          cls.GENESIS = "000000000933ea01ad0ee984209779baaec3ced90fa3f408719526f8d77f4943"
          cls.DEFAULT_PORTS = {'t':'51001', 's':'51002'}
          cls.DEFAULT_SERVERS = read_json_dict('servers_testnet.json')
  
  
  NetworkConstants.set_mainnet()
  
  ################################## transactions
  
  FEE_STEP = 10000
  MAX_FEE_RATE = 20000
  FEE_TARGETS = [25, 10, 5, 2]
  
  COINBASE_MATURITY = 100
  COIN = 100000000
  
  # supported types of transction outputs
  TYPE_ADDRESS = 0
  TYPE_PUBKEY  = 1
  TYPE_SCRIPT  = 2
  
  # AES encryption
  try:
      from Cryptodome.Cipher import AES
  except:
      AES = None
  
  
  class InvalidPadding(Exception):
      pass
  
  
  def append_PKCS7_padding(data):
      assert_bytes(data)
      padlen = 16 - (len(data) % 16)
      return data + bytes([padlen]) * padlen
  
  
  def strip_PKCS7_padding(data):
      assert_bytes(data)
      if len(data) % 16 != 0 or len(data) == 0:
          raise InvalidPadding("invalid length")
      padlen = data[-1]
      if padlen > 16:
          raise InvalidPadding("invalid padding byte (large)")
      for i in data[-padlen:]:
          if i != padlen:
              raise InvalidPadding("invalid padding byte (inconsistent)")
      return data[0:-padlen]
  
  
  def aes_encrypt_with_iv(key, iv, data):
      assert_bytes(key, iv, data)
      data = append_PKCS7_padding(data)
      if AES:
          e = AES.new(key, AES.MODE_CBC, iv).encrypt(data)
      else:
          aes_cbc = pyaes.AESModeOfOperationCBC(key, iv=iv)
          aes = pyaes.Encrypter(aes_cbc, padding=pyaes.PADDING_NONE)
          e = aes.feed(data) + aes.feed()  # empty aes.feed() flushes buffer
      return e
  
  
  def aes_decrypt_with_iv(key, iv, data):
      assert_bytes(key, iv, data)
      if AES:
          cipher = AES.new(key, AES.MODE_CBC, iv)
          data = cipher.decrypt(data)
      else:
          aes_cbc = pyaes.AESModeOfOperationCBC(key, iv=iv)
          aes = pyaes.Decrypter(aes_cbc, padding=pyaes.PADDING_NONE)
          data = aes.feed(data) + aes.feed()  # empty aes.feed() flushes buffer
      try:
          return strip_PKCS7_padding(data)
      except InvalidPadding:
          raise InvalidPassword()
  
  
  def EncodeAES(secret, s):
      assert_bytes(s)
      iv = bytes(os.urandom(16))
      ct = aes_encrypt_with_iv(secret, iv, s)
      e = iv + ct
      return base64.b64encode(e)
  
  def DecodeAES(secret, e):
      e = bytes(base64.b64decode(e))
      iv, e = e[:16], e[16:]
      s = aes_decrypt_with_iv(secret, iv, e)
      return s
  
  def pw_encode(s, password):
      if password:
          secret = Hash(password)
          return EncodeAES(secret, to_bytes(s, "utf8")).decode('utf8')
      else:
          return s
  
  def pw_decode(s, password):
      if password is not None:
          secret = Hash(password)
          try:
              d = to_string(DecodeAES(secret, s), "utf8")
          except Exception:
              raise InvalidPassword()
          return d
      else:
          return s
  
  
  def rev_hex(s):
      return bh2u(bfh(s)[::-1])
      #return s.decode('hex')[::-1].encode('hex')
  
  def int_to_hex(i, length=1):
      assert isinstance(i, int)
      s = hex(i)[2:].rstrip('L')
      s = "0"*(2*length - len(s)) + s
      return rev_hex(s)
  
  def rev_hex_V(s):
      s1 = s.decode('hex')
      s2 = s1[::-1]
      s3 = s2.encode('hex')
      return s3
      #return s.decode('hex')[::-1].encode('hex')
  
  def int_to_hex_V(i, length=1):
      assert isinstance(i, int)
      s = hex(i)[2:].rstrip('L')
      s = "0"*(2*length - len(s)) + s
      return rev_hex_V(s)
  
  
  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 push_script(x):
      return op_push(len(x)//2) + x
  
  def sha256(x):
      x = to_bytes(x, 'utf8')
      return bytes(hashlib.sha256(x).digest())
  
  
  def Hash(x):
      x = to_bytes(x, 'utf8')
      out = bytes(sha256(sha256(x)))
      return out
  
  
  hash_encode = lambda x: bh2u(x[::-1])
  hash_decode = lambda x: bfh(x)[::-1]
  hmac_sha_512 = lambda x, y: hmac.new(x, y, hashlib.sha512).digest()
  
  
  def is_new_seed(x, prefix=version.SEED_PREFIX):
      from . import mnemonic
      x = mnemonic.normalize_text(x)
      s = bh2u(hmac_sha_512(b"Seed version", x.encode('utf8')))
      return s.startswith(prefix)
  
  
  def is_old_seed(seed):
      from . import old_mnemonic, mnemonic
      seed = mnemonic.normalize_text(seed)
      words = seed.split()
      try:
          # checks here are deliberately left weak for legacy reasons, see #3149
          old_mnemonic.mn_decode(words)
          uses_electrum_words = True
      except Exception:
          uses_electrum_words = False
      try:
          seed = bfh(seed)
          is_hex = (len(seed) == 16 or len(seed) == 32)
      except Exception:
          is_hex = False
      return is_hex or (uses_electrum_words and (len(words) == 12 or len(words) == 24))
  
  
  def seed_type(x):
      if is_old_seed(x):
          return 'old'
      elif is_new_seed(x):
          return 'standard'
      return ''
  
  is_seed = lambda x: bool(seed_type(x))
  
  # pywallet openssl private key implementation
  
  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 bfh(key)
  # end pywallet openssl private key implementation
  
  
  ############ functions from pywallet #####################
  def hash_160(public_key):
      try:
          md = hashlib.new('ripemd160')
          md.update(sha256(public_key))
          return md.digest()
      except BaseException:
          from . import ripemd
          md = ripemd.new(sha256(public_key))
          return md.digest()
  
  
  def hash160_to_b58_address(h160, addrtype):
      s = bytes([addrtype])
      s += h160
      return base_encode(s+Hash(s)[0:4], base=58)
  
  
  def b58_address_to_hash160(addr):
      addr = to_bytes(addr, 'ascii')
      _bytes = base_decode(addr, 25, base=58)
      return _bytes[0], _bytes[1:21]
  
  
  def hash160_to_p2pkh(h160):
      return hash160_to_b58_address(h160, NetworkConstants.ADDRTYPE_P2PKH)
  
  def hash160_to_p2sh(h160):
      return hash160_to_b58_address(h160, NetworkConstants.ADDRTYPE_P2SH)
  
  def public_key_to_p2pkh(public_key):
      return hash160_to_p2pkh(hash_160(public_key))
  
  def pubkey_to_address(txin_type, pubkey):
      if txin_type == 'p2pkh':
          return public_key_to_p2pkh(bfh(pubkey))
      else:
          raise NotImplementedError(txin_type)
  
  def redeem_script_to_address(txin_type, redeem_script):
      if txin_type == 'p2sh':
          return hash160_to_p2sh(hash_160(bfh(redeem_script)))
      else:
          raise NotImplementedError(txin_type)
  
  
  def script_to_address(script):
      from .transaction import get_address_from_output_script
      t, addr = get_address_from_output_script(bfh(script))
      assert t == TYPE_ADDRESS
      return addr
  
  def address_to_script(addr):
      witver, witprog = segwit_addr.decode(NetworkConstants.SEGWIT_HRP, addr)
      if witprog is not None:
          assert (0 <= witver <= 16)
          OP_n = witver + 0x50 if witver > 0 else 0
          script = bh2u(bytes([OP_n]))
          script += push_script(bh2u(bytes(witprog)))
          return script
      addrtype, hash_160 = b58_address_to_hash160(addr)
      if addrtype == NetworkConstants.ADDRTYPE_P2PKH:
          script = '76a9'                                      # op_dup, op_hash_160
          script += push_script(bh2u(hash_160))
          script += '88ac'                                     # op_equalverify, op_checksig
      elif addrtype == NetworkConstants.ADDRTYPE_P2SH:
          script = 'a9'                                        # op_hash_160
          script += push_script(bh2u(hash_160))
          script += '87'                                       # op_equal
      else:
          raise BaseException('unknown address type')
      return script
  
  def address_to_scripthash(addr):
      script = address_to_script(addr)
      return script_to_scripthash(script)
  
  def script_to_scripthash(script):
      h = sha256(bytes.fromhex(script))[0:32]
      return bh2u(bytes(reversed(h)))
  
  def public_key_to_p2pk_script(pubkey):
      script = push_script(pubkey)
      script += 'ac'                                           # op_checksig
      return script
  
  __b58chars = b'123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz'
  assert len(__b58chars) == 58
  
  __b43chars = b'0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ$*+-./:'
  assert len(__b43chars) == 43
  
  
  def base_encode(v, base):
      """ encode v, which is a string of bytes, to base58."""
      assert_bytes(v)
      assert base in (58, 43)
      chars = __b58chars
      if base == 43:
          chars = __b43chars
      long_value = 0
      for (i, c) in enumerate(v[::-1]):
          long_value += (256**i) * c
      result = bytearray()
      while long_value >= base:
          div, mod = divmod(long_value, base)
          result.append(chars[mod])
          long_value = div
      result.append(chars[long_value])
      # Bitcoin does a little leading-zero-compression:
      # leading 0-bytes in the input become leading-1s
      nPad = 0
      for c in v:
          if c == 0x00:
              nPad += 1
          else:
              break
      result.extend([chars[0]] * nPad)
      result.reverse()
      return result.decode('ascii')
  
  
  def base_decode(v, length, base):
      """ decode v into a string of len bytes."""
      # assert_bytes(v)
      v = to_bytes(v, 'ascii')
      assert base in (58, 43)
      chars = __b58chars
      if base == 43:
          chars = __b43chars
      long_value = 0
      for (i, c) in enumerate(v[::-1]):
          long_value += chars.find(bytes([c])) * (base**i)
      result = bytearray()
      while long_value >= 256:
          div, mod = divmod(long_value, 256)
          result.append(mod)
          long_value = div
      result.append(long_value)
      nPad = 0
      for c in v:
          if c == chars[0]:
              nPad += 1
          else:
              break
      result.extend(b'\x00' * nPad)
      if length is not None and len(result) != length:
          return None
      result.reverse()
      return bytes(result)
  
  
  def EncodeBase58Check(vchIn):
      hash = Hash(vchIn)
      return base_encode(vchIn + hash[0:4], base=58)
  
  
  def DecodeBase58Check(psz):
      vchRet = base_decode(psz, None, base=58)
      key = vchRet[0:-4]
      csum = vchRet[-4:]
      hash = Hash(key)
      cs32 = hash[0:4]
      if cs32 != csum:
          return None
      else:
          return key
  
  
  
  SCRIPT_TYPES = {
      'p2pkh':0,
      'p2sh':5,
  }
  
  
  def serialize_privkey(secret, compressed, txin_type):
      prefix = bytes([(SCRIPT_TYPES[txin_type]+NetworkConstants.WIF_PREFIX)&255])
      suffix = b'\01' if compressed else b''
      vchIn = prefix + secret + suffix
      return EncodeBase58Check(vchIn)
  
  
  def deserialize_privkey(key):
      # whether the pubkey is compressed should be visible from the keystore
      vch = DecodeBase58Check(key)
      if is_minikey(key):
          return 'p2pkh', minikey_to_private_key(key), True
      elif vch:
          txin_type = inv_dict(SCRIPT_TYPES)[vch[0] - NetworkConstants.WIF_PREFIX]
          assert len(vch) in [33, 34]
          compressed = len(vch) == 34
          return txin_type, vch[1:33], compressed
      else:
          raise BaseException("cannot deserialize", key)
  
  def regenerate_key(pk):
      assert len(pk) == 32
      return EC_KEY(pk)
  
  
  def GetPubKey(pubkey, compressed=False):
      return i2o_ECPublicKey(pubkey, compressed)
  
  
  def GetSecret(pkey):
      return bfh('%064x' % pkey.secret)
  
  
  def is_compressed(sec):
      return deserialize_privkey(sec)[2]
  
  
  def public_key_from_private_key(pk, compressed):
      pkey = regenerate_key(pk)
      public_key = GetPubKey(pkey.pubkey, compressed)
      return bh2u(public_key)
  
  def address_from_private_key(sec):
      txin_type, privkey, compressed = deserialize_privkey(sec)
      public_key = public_key_from_private_key(privkey, compressed)
      return pubkey_to_address(txin_type, public_key)
  
  def is_b58_address(addr):
      try:
          addrtype, h = b58_address_to_hash160(addr)
      except Exception as e:
          return False
      if addrtype not in [NetworkConstants.ADDRTYPE_P2PKH, NetworkConstants.ADDRTYPE_P2SH]:
          return False
      return addr == hash160_to_b58_address(h, addrtype)
  
  def is_address(addr):
      return is_b58_address(addr)
  
  
  def is_private_key(key):
      try:
          k = deserialize_privkey(key)
          return k is not False
      except:
          return False
  
  
  ########### end pywallet functions #######################
  
  def is_minikey(text):
      # Minikeys are typically 22 or 30 characters, but this routine
      # permits any length of 20 or more provided the minikey is valid.
      # A valid minikey must begin with an 'S', be in base58, and when
      # suffixed with '?' have its SHA256 hash begin with a zero byte.
      # They are widely used in Casascius physical bitcoins.
      return (len(text) >= 20 and text[0] == 'S'
              and all(ord(c) in __b58chars for c in text)
              and sha256(text + '?')[0] == 0x00)
  
  def minikey_to_private_key(text):
      return sha256(text)
  
  from ecdsa.ecdsa import curve_secp256k1, generator_secp256k1
  from ecdsa.curves import SECP256k1
  from ecdsa.ellipticcurve import Point
  from ecdsa.util import string_to_number, number_to_string
  
  
  def msg_magic(message):
      length = bfh(var_int(len(message)))
      return b"\x18Commercium Signed Message:\n" + length + message
  
  
  def verify_message(address, sig, message):
      assert_bytes(sig, message)
      try:
          h = Hash(msg_magic(message))
          public_key, compressed = pubkey_from_signature(sig, h)
          # check public key using the address
          pubkey = point_to_ser(public_key.pubkey.point, compressed)
          for txin_type in ['p2pkh']:
              addr = pubkey_to_address(txin_type, bh2u(pubkey))
              if address == addr:
                  break
          else:
              raise Exception("Bad signature")
          # check message
          public_key.verify_digest(sig[1:], h, sigdecode = ecdsa.util.sigdecode_string)
          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, bfh(pubkey))
  
  
  def chunks(l, n):
      return [l[i:i+n] for i in range(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 bfh( ('%02x'%(2+(P.y()&1)))+('%064x'%P.x()) )
      return bfh( '04'+('%064x'%P.x())+('%064x'%P.y()) )
  
  
  def ser_to_point(Aser):
      curve = curve_secp256k1
      generator = generator_secp256k1
      _r  = generator.order()
      assert Aser[0] in [0x02, 0x03, 0x04]
      if Aser[0] == 0x04:
          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] == 0x03)[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
          from . 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 )
  
  
  def pubkey_from_signature(sig, h):
      if len(sig) != 65:
          raise Exception("Wrong encoding")
      nV = sig[0]
      if nV < 27 or nV >= 35:
          raise Exception("Bad encoding")
      if nV >= 31:
          compressed = True
          nV -= 4
      else:
          compressed = False
      recid = nV - 27
      return MyVerifyingKey.from_signature(sig[1:], recid, h, curve = SECP256k1), compressed
  
  
  class MySigningKey(ecdsa.SigningKey):
      """Enforce low S values in signatures"""
  
      def sign_number(self, number, entropy=None, k=None):
          curve = SECP256k1
          G = curve.generator
          order = G.order()
          r, s = ecdsa.SigningKey.sign_number(self, number, entropy, k)
          if s > order//2:
              s = order - s
          return r, s
  
  
  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 bh2u(point_to_ser(self.pubkey.point, compressed))
  
      def sign(self, msg_hash):
          private_key = MySigningKey.from_secret_exponent(self.secret, curve = SECP256k1)
          public_key = private_key.get_verifying_key()
          signature = private_key.sign_digest_deterministic(msg_hash, hashfunc=hashlib.sha256, sigencode = ecdsa.util.sigencode_string)
          assert public_key.verify_digest(signature, msg_hash, sigdecode = ecdsa.util.sigdecode_string)
          return signature
  
      def sign_message(self, message, is_compressed):
          message = to_bytes(message, 'utf8')
          signature = self.sign(Hash(msg_magic(message)))
          for i in range(4):
              sig = bytes([27 + i + (4 if is_compressed else 0)]) + signature
              try:
                  self.verify_message(sig, message)
                  return sig
              except Exception as e:
                  continue
          else:
              raise Exception("error: cannot sign message")
  
      def verify_message(self, sig, message):
          assert_bytes(message)
          h = Hash(msg_magic(message))
          public_key, compressed = pubkey_from_signature(sig, h)
          # check public key
          if point_to_ser(public_key.pubkey.point, compressed) != point_to_ser(self.pubkey.point, compressed):
              raise Exception("Bad signature")
          # check message
          public_key.verify_digest(sig[1:], h, sigdecode = ecdsa.util.sigdecode_string)
  
  
      # ECIES encryption/decryption methods; AES-128-CBC with PKCS7 is used as the cipher; hmac-sha256 is used as the mac
  
      @classmethod
      def encrypt_message(self, message, pubkey):
          assert_bytes(message)
  
          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 = point_to_ser(pk * ephemeral.privkey.secret_multiplier)
          key = hashlib.sha512(ecdh_key).digest()
          iv, key_e, key_m = key[0:16], key[16:32], key[32:]
          ciphertext = aes_encrypt_with_iv(key_e, iv, message)
          ephemeral_pubkey = bfh(ephemeral.get_public_key(compressed=True))
          encrypted = b'BIE1' + ephemeral_pubkey + 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]
          ciphertext = encrypted[37:-32]
          mac = encrypted[-32:]
          if magic != b'BIE1':
              raise Exception('invalid ciphertext: invalid magic bytes')
          try:
              ephemeral_pubkey = ser_to_point(ephemeral_pubkey)
          except AssertionError as 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 = point_to_ser(ephemeral_pubkey * self.privkey.secret_multiplier)
          key = hashlib.sha512(ecdh_key).digest()
          iv, key_e, key_m = key[0:16], key[16:32], key[32:]
          if mac != hmac.new(key_m, encrypted[:-32], hashlib.sha256).digest():
              raise InvalidPassword()
          return aes_decrypt_with_iv(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, bfh(rev_hex(int_to_hex(n,4))), is_prime)
  
  
  def _CKD_priv(k, c, s, is_prime):
      order = generator_secp256k1.order()
      keypair = EC_KEY(k)
      cK = GetPubKey(keypair.pubkey,True)
      data = bytes([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, bfh(rev_hex(int_to_hex(n,4))))
  
  # helper function, callable with arbitrary string
  def _CKD_pub(cK, c, s):
      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
  
  
  def xprv_header(xtype):
      return bfh("%08x" % XPRV_HEADERS[xtype])
  
  
  def xpub_header(xtype):
      return bfh("%08x" % XPUB_HEADERS[xtype])
  
  
  def serialize_xprv(xtype, c, k, depth=0, fingerprint=b'\x00'*4, child_number=b'\x00'*4):
      xprv = xprv_header(xtype) + bytes([depth]) + fingerprint + child_number + c + bytes([0]) + k
      return EncodeBase58Check(xprv)
  
  
  def serialize_xpub(xtype, c, cK, depth=0, fingerprint=b'\x00'*4, child_number=b'\x00'*4):
      xpub = xpub_header(xtype) + bytes([depth]) + fingerprint + child_number + c + cK
      return EncodeBase58Check(xpub)
  
  
  def deserialize_xkey(xkey, prv):
      xkey = DecodeBase58Check(xkey)
      if len(xkey) != 78:
          raise BaseException('Invalid length')
      depth = xkey[4]
      fingerprint = xkey[5:9]
      child_number = xkey[9:13]
      c = xkey[13:13+32]
      header = int('0x' + bh2u(xkey[0:4]), 16)
      headers = XPRV_HEADERS if prv else XPUB_HEADERS
      if header not in headers.values():
          raise BaseException('Invalid xpub format', hex(header))
      xtype = list(headers.keys())[list(headers.values()).index(header)]
      n = 33 if prv else 32
      K_or_k = xkey[13+n:]
      return xtype, depth, fingerprint, child_number, c, K_or_k
  
  
  def deserialize_xpub(xkey):
      return deserialize_xkey(xkey, False)
  
  def deserialize_xprv(xkey):
      return deserialize_xkey(xkey, True)
  
  def xpub_type(x):
      return deserialize_xpub(x)[0]
  
  
  def is_xpub(text):
      try:
          deserialize_xpub(text)
          return True
      except:
          return False
  
  
  def is_xprv(text):
      try:
          deserialize_xprv(text)
          return True
      except:
          return False
  
  
  def xpub_from_xprv(xprv):
      xtype, depth, fingerprint, child_number, c, k = deserialize_xprv(xprv)
      K, cK = get_pubkeys_from_secret(k)
      return serialize_xpub(xtype, c, cK, depth, fingerprint, child_number)
  
  
  def bip32_root(seed, xtype):
      I = hmac.new(b"Bitcoin seed", seed, hashlib.sha512).digest()
      master_k = I[0:32]
      master_c = I[32:]
      K, cK = get_pubkeys_from_secret(master_k)
      xprv = serialize_xprv(xtype, master_c, master_k)
      xpub = serialize_xpub(xtype, master_c, cK)
      return xprv, xpub
  
  
  def xpub_from_pubkey(xtype, cK):
      assert cK[0] in [0x02, 0x03]
      return serialize_xpub(xtype, b'\x00'*32, cK)
  
  
  def bip32_derivation(s):
      assert s.startswith('m/')
      s = s[2:]
      for n in s.split('/'):
          if n == '': continue
          i = int(n[:-1]) + BIP32_PRIME if n[-1] == "'" else int(n)
          yield i
  
  def is_bip32_derivation(x):
      try:
          [ i for i in bip32_derivation(x)]
          return True
      except :
          return False
  
  def bip32_private_derivation(xprv, branch, sequence):
      assert sequence.startswith(branch)
      if branch == sequence:
          return xprv, xpub_from_xprv(xprv)
      xtype, depth, fingerprint, child_number, c, k = deserialize_xprv(xprv)
      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 = bfh("%08X"%i)
      K, cK = get_pubkeys_from_secret(k)
      xpub = serialize_xpub(xtype, c, cK, depth, fingerprint, child_number)
      xprv = serialize_xprv(xtype, c, k, depth, fingerprint, child_number)
      return xprv, xpub
  
  
  def bip32_public_derivation(xpub, branch, sequence):
      xtype, depth, fingerprint, child_number, c, cK = deserialize_xpub(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 = bfh("%08X"%i)
      return serialize_xpub(xtype, c, cK, depth, fingerprint, child_number)
  
  
  def bip32_private_key(sequence, k, chain):
      for i in sequence:
          k, chain = CKD_priv(k, chain, i)
      return k
  
  
  
  