Category: Bitcoin

    def __rmul__(self, coefficient):
        product = self.__class__(Nonee, None, self.a, self.b)
        for _ in range(coefficient):
            product += self
        return product

coefficient の和訳は係数です。係数の数だけ点を加算します。

ビットの倍算だと以下のようになる。2進展開。

    def __rmul__(self, coefficient):
        coef = coefficient 
        current = self 
        result = self.__class__(Nonee, None, self.a, self.b)
        while coef:
            if coef & 1:
                result += current
            current += current
        return result

ecc.py

from unittest import TestCase

class ECCTest(TestCase):

    def test_on_curve(self):
        prime = 223
        a = FieldElement(0, prime)
        b = FieldElement(7, prime)  
        valid_points = ((192, 105),(17,56),(1,193))
        invalid_points = ((200, 119),(42, 99))
        for x_raw, y_raw in valid_points:
            x = FieldElement(x_raw, prime)
            y = FieldElement(y_raw, prime)
            Point(x, y, a, b)
        for x_raw, y_raw in invalid_points:
            x = FieldElement(x_raw, prime)
            y = FieldElement(y_raw, prime)
            with self.assertRaises(ValueError):
                Point(x, y, a, b)

helper.py

from unittest import TestSuite, TextTestRunner

def run(test):
    suite = TestSuite()
    suite.addTest(test)
    TextTestRunner().run(suite)

main.py

import ecc
from helper import run

run(ecc.ECCTest('test_on_curve'))

$ python3 main.py
.
———————————————————————-
Ran 1 test in 0.000s

OK

位数が有限である体
四則演算が定義され閉じている有限集

整数の集合は無限の要素だが、有限体は要素が有限で、四則演算(足し算・引き算・掛け算・割り算)が閉じている
=> 閉じているとは、演算結果が、有理数でなくなるということがない
=> 演算を施した結果がふたたびもとの集合に属する
素数 P で割った余り

これ、初手でいきなりつまづくな…

HMACは暗号ハッシュ関数を使用してメッセージ認証を行う仕組み

import hmac
import hashlib

key=b"secret2"
text=b"foo bar"
signature=hmac.new(key,text,hashlib.md5).hexdigest()
print(signature)

b””としないと、エラーになる。
self._hmac = _hashopenssl.hmac_new(key, msg, digestmod=digestmod)
TypeError: Strings must be encoded before hashing

import os
import binascii
import ecdsa
import hmac
import hashlib

seed = os.urandom(32)
root_key = b'Bitcoin Seed'

def hmac_sha512(data, keymessage):
    hash = hmac.new(data, keymessage, hashlib.sha512).digest()
    return hash

def create_pubkey(private_key):
    publickey = ecdsa.SigningKey.from_string(private_key, curve=ecdsa.SECP256k1).verifying_key.to_string()
    return publickey

master = hmac_sha512(seed, root_key)
master_secretkey = master[:32]
master_chaincode = master[32:]

master_publickey = create_pubkey(master_secretkey)
master_publickey_integer = int.from_bytes(master_publickey[32:], byteorder="big")

if master_publickey_integer % 2 == 0:
    master_publickey_x = b"\x02" + master_publickey[:32]
else:
    master_publickey_x = b"\x03" + master_publickey[:32]

print("マスター秘密鍵")
print(binascii.hexlify(master_secretkey))
print("\n")
print("マスターチェーンコード")
print(binascii.hexlify(master_chaincode))
print("\n")
print("マスター公開鍵")
print(binascii.hexlify(master_publickey_x))

index = 0
index_bytes = index.to_bytes(8, "big")
data = master_publickey_x + index_bytes
result_hmac512 = hmac_sha512(data, master_chaincode)

sum_integer = int.from_bytes(master_secretkey, "big") + int.from_bytes(result_hmac512[:32], "big")

p = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 - 1
child_secretkey = (sum_integer % p).to_bytes(32, "big")

print("\n")
print("子秘密鍵")
print(binascii.hexlify(child_secretkey))

import os
import ecdsa
import hashlib
import base58
from Crypto.Hash import RIPEMD160

private_key = os.urandom(32)
public_key = ecdsa.SigningKey.from_string(private_key, curve=ecdsa.SECP256k1).verifying_key.to_string()

prefix_and_pubkey = b"\x04" + public_key

intermediate = hashlib.sha256(prefix_and_pubkey).digest()
ripemd160 = RIPEMD160.new()
ripemd160.update(intermediate)
hash160 = ripemd160.digest()

prefix_and_hash160 = b"\x00" + hash160

double_hash = hashlib.sha256(hashlib.sha256(prefix_and_hash160).digest()).digest()
checksum = double_hash[:4]
pre_address = prefix_and_hash160 + checksum

address = base58.b58encode(pre_address)
print(address.decode())

hashlibで以下のように書くとエラーになる。
ripemd160 = hashlib.new(‘ripemd160’)

$ python3 address.py
Traceback (most recent call last):
File “/usr/lib/python3.10/hashlib.py”, line 160, in __hash_new
return _hashlib.new(name, data, **kwargs)
ValueError: [digital envelope routines] unsupported

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
File “/home/vagrant/dev/work/address.py”, line 12, in
ripemd160 = hashlib.new(‘ripemd160’)
File “/usr/lib/python3.10/hashlib.py”, line 166, in __hash_new
return __get_builtin_constructor(name)(data)
File “/usr/lib/python3.10/hashlib.py”, line 123, in __get_builtin_constructor
raise ValueError(‘unsupported hash type ‘ + name)
ValueError: unsupported hash type ripemd160

従って、pycryptodomeをインストールして、ripemd160を使う
$ pip install pycryptodome

import pandas as pd
import datetime
from ecdsa import SigningKey, SECP256k1
import binascii
import json

secret_key_A_str = "47c5c280197c691be3f80462b72d60b7b2915753f1a81a6eedbfbb2f01f55cae"
public_key_B_str = "02cfbf50fe5873ac6e5352e7524c4934e32f01281fc7d6112fed86cf58e72b09bb302f1f7d10d7c37d13eb7e62fd8bb1950b263c51ac76581f8b0a38d0d8853e"

secret_key_A = SigningKey.from_string(binascii.unhexlify(secret_key_A_str), curve=SECP256k1)
public_key_A = secret_key_A.verifying_key
public_key_A_str = public_key_A.to_string().hex()
time_now = datetime.datetime.now(datetime.timezone.utc).isoformat()

unsigned_transaction = {"time": time_now, "sender": public_key_A_str, "receiver": public_key_B_str, "amount": 3}
signature = secret_key_A.sign(json.dumps(unsigned_transaction).encode('utf-8'))
transaction = {"time": time_now, "sender": public_key_A_str, "receiver": public_key_B_str, "amount": 3, "signature": signature.hex()}

pd.to_pickle(transaction, "signed_transaction.pkl")

取引記録の検証

import pandas as pd
from ecdsa import VerifyingKey, BadSignatureError, SECP256k1
import binascii
import json

transaction = pd.read_pickle("signed_transaction.pkl")
public_key_A = VerifyingKey.from_string(binascii.unhexlify(transaction["sender"]), curve=SECP256k1)
signature = binascii.unhexlify(transaction["signature"])

unsigned_transaction = {
	"time": transaction["time"],
	"sender": transaction["sender"],
	"receiver": transaction["receiver"],
	"amount": transaction["amount"]
}

try:
	public_key_A.verify(signature, json.dumps(unsigned_transaction).encode('utf-8'))
	print("トランザクションは改竄されていません。")
except BadSignatureError:
	print("トランザクションは改竄されています。")

$ python3 verify_transaction.py
トランザクションは改竄されていません。

cheat.py

import pandas as pd

transaction = pd.read_pickle("signed_transaction.pkl")
print("改竄前のトランザクション:")
print(transaction)

transaction = {"time": transaction["time"], "sender": transaction["sender"], "receiver": transaction["receiver"], "amount": 30, "signature": transaction["signature"]}
print("改竄後のトランザクション:")
print(transaction)
pd.to_pickle(transaction, "signed_transaction.pkl")

改竄するとsignatureが変更されていないので、改竄されていることがわかる