text: # -*- coding: utf-8 -*-
  """
  A BIP0032-style hierarchical wallet.
  
  Implement a BIP0032-style hierarchical wallet which can create public
  or private wallet keys. Each key can create many child nodes. Each node
  has a wallet key and a corresponding private & public key, which can
  be used to generate Bitcoin addresses or WIF private keys.
  
  At any stage, the private information can be stripped away, after which
  descendants can only produce public keys.
  
  Private keys can also generate "hardened" children, which cannot be
  generated by the corresponding public keys. This is useful for generating
  "change" addresses, for example, which there is no need to share with people
  you give public keys to.
  
  
  The MIT License (MIT)
  
  Copyright (c) 2013 by Richard Kiss
  
  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 hmac
  import logging
  import struct
  
  from .. import ecdsa
  
  from ..encoding import public_pair_to_sec, from_bytes_32, to_bytes_32
  from ..ecdsa.ellipticcurve import INFINITY
  
  logger = logging.getLogger(__name__)
  
  ORDER = ecdsa.generator_secp256k1.order()
  
  _SUBKEY_VALIDATION_LOG_ERR_FMT = """
  BUY A LOTTO TICKET RIGHT NOW! (And consider giving up your wallet to
  science!)
  
  You have stumbled across an astronomically unlikely scenario. Your HD
  wallet contains an invalid subkey. Having access to this information would
  be incredibly valuable to the Bitcoin development community.
  
  If you are inclined to help, please make sure to back up this wallet (or
  any outputted information) onto a USB drive and e-mail "Richard Kiss"
  <him@richardkiss.com> or "Matt Bogosian" <mtb19@columbia.edu> for
  instructions on how best to donate it without losing your bitcoins.
  
  WARNING: DO NOT SEND ANY WALLET INFORMATION UNLESS YOU WANT TO LOSE ALL
  THE BITCOINS IT CONTAINS.
  """.strip()
  
  
  class DerivationError(ValueError):
      pass
  
  
  def subkey_secret_exponent_chain_code_pair(
          secret_exponent, chain_code_bytes, i, is_hardened, public_pair=None):
      """
      Yield info for a child node for this node.
  
      secret_exponent:
          base secret exponent
      chain_code:
          base chain code
      i:
          the index for this node.
      is_hardened:
          use "hardened key derivation". The public version of this node cannot calculate this child.
      public_pair:
          the public_pair for the given secret exponent. If you leave it None, it's calculated for you
          (but then it's slower)
  
      Returns a pair (new_secret_exponent, new_chain_code)
      """
      i_as_bytes = struct.pack(">L", i)
  
      if is_hardened:
          data = b'\0' + to_bytes_32(secret_exponent) + i_as_bytes
      else:
          if public_pair is None:
              public_pair = ecdsa.public_pair_for_secret_exponent(ecdsa.generator_secp256k1, secret_exponent)
          sec = public_pair_to_sec(public_pair, compressed=True)
          data = sec + i_as_bytes
  
      I64 = hmac.HMAC(key=chain_code_bytes, msg=data, digestmod=hashlib.sha512).digest()
      I_left_as_exponent = from_bytes_32(I64[:32])
      if I_left_as_exponent >= ORDER:
          logger.critical(_SUBKEY_VALIDATION_LOG_ERR_FMT)
          raise DerivationError('I_L >= {}'.format(ORDER))
      new_secret_exponent = (I_left_as_exponent + secret_exponent) % ORDER
      if new_secret_exponent == 0:
          logger.critical(_SUBKEY_VALIDATION_LOG_ERR_FMT)
          raise DerivationError('k_{} == 0'.format(i))
      new_chain_code = I64[32:]
      return new_secret_exponent, new_chain_code
  
  
  def subkey_public_pair_chain_code_pair(public_pair, chain_code_bytes, i):
      """
      Yield info for a child node for this node.
  
      public_pair:
          base public pair
      chain_code:
          base chain code
      i:
          the index for this node.
  
      Returns a pair (new_public_pair, new_chain_code)
      """
      i_as_bytes = struct.pack(">l", i)
      sec = public_pair_to_sec(public_pair, compressed=True)
      data = sec + i_as_bytes
  
      I64 = hmac.HMAC(key=chain_code_bytes, msg=data, digestmod=hashlib.sha512).digest()
  
      I_left_as_exponent = from_bytes_32(I64[:32])
      x, y = public_pair
  
      the_point = I_left_as_exponent * ecdsa.generator_secp256k1 + \
          ecdsa.Point(ecdsa.generator_secp256k1.curve(), x, y, ORDER)
      if the_point == INFINITY:
          logger.critical(_SUBKEY_VALIDATION_LOG_ERR_FMT)
          raise DerivationError('K_{} == {}'.format(i, the_point))
  
      I_left_as_exponent = from_bytes_32(I64[:32])
      if I_left_as_exponent >= ORDER:
          logger.critical(_SUBKEY_VALIDATION_LOG_ERR_FMT)
          raise DerivationError('I_L >= {}'.format(ORDER))
      new_public_pair = the_point.pair()
      new_chain_code = I64[32:]
      return new_public_pair, new_chain_code
  