1 # -*- coding: utf-8 -*-
4 # Electrum - lightweight Bitcoin client
5 # Copyright (C) 2011 thomasv@gitorious
7 # This program is free software: you can redistribute it and/or modify
8 # it under the terms of the GNU General Public License as published by
9 # the Free Software Foundation, either version 3 of the License, or
10 # (at your option) any later version.
12 # This program is distributed in the hope that it will be useful,
13 # but WITHOUT ANY WARRANTY; without even the implied warranty of
14 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 # GNU General Public License for more details.
17 # You should have received a copy of the GNU General Public License
18 # along with this program. If not, see <http://www.gnu.org/licenses/>.
21 import hashlib, base64, ecdsa, re
22 from util import print_error
25 return s.decode('hex')[::-1].encode('hex')
27 def int_to_hex(i, length=1):
28 s = hex(i)[2:].rstrip('L')
29 s = "0"*(2*length - len(s)) + s
33 # https://en.bitcoin.it/wiki/Protocol_specification#Variable_length_integer
37 return "fd"+int_to_hex(i,2)
39 return "fe"+int_to_hex(i,4)
41 return "ff"+int_to_hex(i,8)
47 return '4c' + int_to_hex(i)
49 return '4d' + int_to_hex(i,2)
51 return '4e' + int_to_hex(i,4)
55 Hash = lambda x: hashlib.sha256(hashlib.sha256(x).digest()).digest()
56 hash_encode = lambda x: x[::-1].encode('hex')
57 hash_decode = lambda x: x.decode('hex')[::-1]
60 # pywallet openssl private key implementation
62 def i2d_ECPrivateKey(pkey, compressed=False):
64 key = '3081d30201010420' + \
65 '%064x' % pkey.secret + \
66 'a081a53081a2020101302c06072a8648ce3d0101022100' + \
68 '3006040100040107042102' + \
74 key = '308201130201010420' + \
75 '%064x' % pkey.secret + \
76 'a081a53081a2020101302c06072a8648ce3d0101022100' + \
78 '3006040100040107044104' + \
85 return key.decode('hex') + i2o_ECPublicKey(pkey.pubkey, compressed)
87 def i2o_ECPublicKey(pubkey, compressed=False):
88 # public keys are 65 bytes long (520 bits)
89 # 0x04 + 32-byte X-coordinate + 32-byte Y-coordinate
90 # 0x00 = point at infinity, 0x02 and 0x03 = compressed, 0x04 = uncompressed
91 # compressed keys: <sign> <x> where <sign> is 0x02 if y is even and 0x03 if y is odd
93 if pubkey.point.y() & 1:
94 key = '03' + '%064x' % pubkey.point.x()
96 key = '02' + '%064x' % pubkey.point.x()
99 '%064x' % pubkey.point.x() + \
100 '%064x' % pubkey.point.y()
102 return key.decode('hex')
104 # end pywallet openssl private key implementation
108 ############ functions from pywallet #####################
110 def hash_160(public_key):
112 md = hashlib.new('ripemd160')
113 md.update(hashlib.sha256(public_key).digest())
117 md = ripemd.new(hashlib.sha256(public_key).digest())
121 def public_key_to_bc_address(public_key):
122 h160 = hash_160(public_key)
123 return hash_160_to_bc_address(h160)
125 def hash_160_to_bc_address(h160, addrtype = 0):
126 vh160 = chr(addrtype) + h160
128 addr = vh160 + h[0:4]
129 return b58encode(addr)
131 def bc_address_to_hash_160(addr):
132 bytes = b58decode(addr, 25)
133 return ord(bytes[0]), bytes[1:21]
135 def encode_point(pubkey, compressed=False):
136 order = generator_secp256k1.order()
137 p = pubkey.pubkey.point
138 x_str = ecdsa.util.number_to_string(p.x(), order)
139 y_str = ecdsa.util.number_to_string(p.y(), order)
141 return chr(2 + (p.y() & 1)) + x_str
143 return chr(4) + pubkey.to_string() #x_str + y_str
145 __b58chars = '123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz'
146 __b58base = len(__b58chars)
149 """ encode v, which is a string of bytes, to base58."""
152 for (i, c) in enumerate(v[::-1]):
153 long_value += (256**i) * ord(c)
156 while long_value >= __b58base:
157 div, mod = divmod(long_value, __b58base)
158 result = __b58chars[mod] + result
160 result = __b58chars[long_value] + result
162 # Bitcoin does a little leading-zero-compression:
163 # leading 0-bytes in the input become leading-1s
166 if c == '\0': nPad += 1
169 return (__b58chars[0]*nPad) + result
171 def b58decode(v, length):
172 """ decode v into a string of len bytes."""
174 for (i, c) in enumerate(v[::-1]):
175 long_value += __b58chars.find(c) * (__b58base**i)
178 while long_value >= 256:
179 div, mod = divmod(long_value, 256)
180 result = chr(mod) + result
182 result = chr(long_value) + result
186 if c == __b58chars[0]: nPad += 1
189 result = chr(0)*nPad + result
190 if length is not None and len(result) != length:
196 def EncodeBase58Check(vchIn):
198 return b58encode(vchIn + hash[0:4])
200 def DecodeBase58Check(psz):
201 vchRet = b58decode(psz, None)
211 def PrivKeyToSecret(privkey):
212 return privkey[9:9+32]
214 def SecretToASecret(secret, compressed=False, addrtype=0):
215 vchIn = chr((addrtype+128)&255) + secret
216 if compressed: vchIn += '\01'
217 return EncodeBase58Check(vchIn)
219 def ASecretToSecret(key, addrtype=0):
220 vch = DecodeBase58Check(key)
221 if vch and vch[0] == chr((addrtype+128)&255):
226 def regenerate_key(sec):
227 b = ASecretToSecret(sec)
231 secret = int('0x' + b.encode('hex'), 16)
232 return EC_KEY(secret)
234 def GetPubKey(pubkey, compressed=False):
235 return i2o_ECPublicKey(pubkey, compressed)
237 def GetPrivKey(pkey, compressed=False):
238 return i2d_ECPrivateKey(pkey, compressed)
241 return ('%064x' % pkey.secret).decode('hex')
243 def is_compressed(sec):
244 b = ASecretToSecret(sec)
248 def public_key_from_private_key(sec):
249 # rebuild public key from private key, compressed or uncompressed
250 pkey = regenerate_key(sec)
252 compressed = is_compressed(sec)
253 public_key = GetPubKey(pkey.pubkey, compressed)
254 return public_key.encode('hex')
257 def address_from_private_key(sec):
258 public_key = public_key_from_private_key(sec)
259 address = public_key_to_bc_address(public_key.decode('hex'))
264 ADDRESS_RE = re.compile('[1-9A-HJ-NP-Za-km-z]{26,}\\Z')
265 if not ADDRESS_RE.match(addr): return False
267 addrtype, h = bc_address_to_hash_160(addr)
270 return addr == hash_160_to_bc_address(h, addrtype)
273 ########### end pywallet functions #######################
275 # secp256k1, http://www.oid-info.com/get/1.3.132.0.10
276 _p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2FL
277 _r = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141L
278 _b = 0x0000000000000000000000000000000000000000000000000000000000000007L
279 _a = 0x0000000000000000000000000000000000000000000000000000000000000000L
280 _Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798L
281 _Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8L
282 curve_secp256k1 = ecdsa.ellipticcurve.CurveFp( _p, _a, _b )
283 generator_secp256k1 = ecdsa.ellipticcurve.Point( curve_secp256k1, _Gx, _Gy, _r )
284 oid_secp256k1 = (1,3,132,0,10)
285 SECP256k1 = ecdsa.curves.Curve("SECP256k1", curve_secp256k1, generator_secp256k1, oid_secp256k1 )
287 from ecdsa.util import string_to_number, number_to_string
289 def msg_magic(message):
290 message = message.encode('utf-8')
291 print_error(("message", message))
292 varint = var_int(len(message))
293 encoded_varint = "".join([chr(int(varint[i:i+2], 16)) for i in xrange(0, len(varint), 2)])
295 return "\x18Bitcoin Signed Message:\n" + encoded_varint + message
298 class EC_KEY(object):
299 def __init__( self, secret ):
300 self.pubkey = ecdsa.ecdsa.Public_key( generator_secp256k1, generator_secp256k1 * secret )
301 self.privkey = ecdsa.ecdsa.Private_key( self.pubkey, secret )
304 def sign_message(self, message, compressed, address):
305 private_key = ecdsa.SigningKey.from_secret_exponent( self.secret, curve = SECP256k1 )
306 public_key = private_key.get_verifying_key()
307 signature = private_key.sign_digest( Hash( msg_magic(message) ), sigencode = ecdsa.util.sigencode_string )
308 assert public_key.verify_digest( signature, Hash( msg_magic(message) ), sigdecode = ecdsa.util.sigdecode_string)
310 sig = base64.b64encode( chr(27 + i + (4 if compressed else 0)) + signature )
312 self.verify_message( address, sig, message)
317 raise BaseException("error: cannot sign message")
320 def verify_message(self, address, signature, message):
321 """ See http://www.secg.org/download/aid-780/sec1-v2.pdf for the math """
322 from ecdsa import numbertheory, ellipticcurve, util
324 curve = curve_secp256k1
325 G = generator_secp256k1
327 # extract r,s from signature
328 sig = base64.b64decode(signature)
329 if len(sig) != 65: raise BaseException("Wrong encoding")
330 r,s = util.sigdecode_string(sig[1:], order)
332 if nV < 27 or nV >= 35:
333 raise BaseException("Bad encoding")
342 x = r + (recid/2) * order
344 alpha = ( x * x * x + curve.a() * x + curve.b() ) % curve.p()
345 beta = msqr.modular_sqrt(alpha, curve.p())
346 y = beta if (beta - recid) % 2 == 0 else curve.p() - beta
347 # 1.4 the constructor checks that nR is at infinity
348 R = ellipticcurve.Point(curve, x, y, order)
349 # 1.5 compute e from message:
350 h = Hash( msg_magic(message) )
351 e = string_to_number(h)
353 # 1.6 compute Q = r^-1 (sR - eG)
354 inv_r = numbertheory.inverse_mod(r,order)
355 Q = inv_r * ( s * R + minus_e * G )
356 public_key = ecdsa.VerifyingKey.from_public_point( Q, curve = SECP256k1 )
357 # check that Q is the public key
358 public_key.verify_digest( sig[1:], h, sigdecode = ecdsa.util.sigdecode_string)
359 # check that we get the original signing address
360 addr = public_key_to_bc_address( encode_point(public_key, compressed) )
362 raise BaseException("Bad signature")
365 ###################################### BIP32 ##############################
367 random_seed = lambda n: "%032x"%ecdsa.util.randrange( pow(2,n) )
368 BIP32_PRIME = 0x80000000
370 def bip32_init(seed):
372 seed = seed.decode('hex')
373 I = hmac.new("Bitcoin seed", seed, hashlib.sha512).digest()
375 master_secret = I[0:32]
376 master_chain = I[32:]
378 K, K_compressed = get_pubkeys_from_secret(master_secret)
379 return master_secret, master_chain, K, K_compressed
382 def get_pubkeys_from_secret(secret):
385 private_key = ecdsa.SigningKey.from_string( secret, curve = SECP256k1 )
386 public_key = private_key.get_verifying_key()
387 K = public_key.to_string()
388 K_compressed = GetPubKey(public_key.pubkey,True)
389 return K, K_compressed
396 from ecdsa.util import string_to_number, number_to_string
397 order = generator_secp256k1.order()
398 keypair = EC_KEY(string_to_number(k))
399 K = GetPubKey(keypair.pubkey,True)
402 data = chr(0) + k + rev_hex(int_to_hex(n,4)).decode('hex')
403 I = hmac.new(c, data, hashlib.sha512).digest()
405 I = hmac.new(c, K + rev_hex(int_to_hex(n,4)).decode('hex'), hashlib.sha512).digest()
407 k_n = number_to_string( (string_to_number(I[0:32]) + string_to_number(k)) % order , order )
412 def CKD_prime(K, c, n):
414 from ecdsa.util import string_to_number, number_to_string
415 order = generator_secp256k1.order()
417 if n & BIP32_PRIME: raise
419 K_public_key = ecdsa.VerifyingKey.from_string( K, curve = SECP256k1 )
420 K_compressed = GetPubKey(K_public_key.pubkey,True)
422 I = hmac.new(c, K_compressed + rev_hex(int_to_hex(n,4)).decode('hex'), hashlib.sha512).digest()
425 pubkey_point = string_to_number(I[0:32])*curve.generator + K_public_key.pubkey.point
426 public_key = ecdsa.VerifyingKey.from_public_point( pubkey_point, curve = SECP256k1 )
428 K_n = public_key.to_string()
429 K_n_compressed = GetPubKey(public_key.pubkey,True)
432 return K_n, K_n_compressed, c_n
436 def bip32_private_derivation(k, c, branch, sequence):
437 assert sequence.startswith(branch)
438 sequence = sequence[len(branch):]
439 for n in sequence.split('/'):
441 n = int(n[:-1]) + BIP32_PRIME if n[-1] == "'" else int(n)
443 K, K_compressed = get_pubkeys_from_secret(k)
444 return k.encode('hex'), c.encode('hex'), K.encode('hex'), K_compressed.encode('hex')
447 def bip32_public_derivation(c, K, branch, sequence):
448 assert sequence.startswith(branch)
449 sequence = sequence[len(branch):]
450 for n in sequence.split('/'):
452 K, cK, c = CKD_prime(K, c, n)
454 return c.encode('hex'), K.encode('hex'), cK.encode('hex')
457 def bip32_private_key(sequence, k, chain):
459 k, chain = CKD(k, chain, i)
460 return SecretToASecret(k, True)
465 ################################## transactions
467 MIN_RELAY_TX_FEE = 10000
471 def test_bip32(seed, sequence):
474 see https://en.bitcoin.it/wiki/BIP_0032_TestVectors
477 master_secret, master_chain, master_public_key, master_public_key_compressed = bip32_init(seed)
479 print "secret key", master_secret.encode('hex')
480 print "chain code", master_chain.encode('hex')
482 key_id = hash_160(master_public_key_compressed)
483 print "keyid", key_id.encode('hex')
485 print "address", hash_160_to_bc_address(key_id)
486 print "secret key", SecretToASecret(master_secret, True)
492 for n in sequence.split('/'):
494 print "Chain [%s]" % '/'.join(s)
496 n = int(n[:-1]) + BIP32_PRIME if n[-1] == "'" else int(n)
497 k0, c0 = CKD(k, c, n)
498 K0, K0_compressed = get_pubkeys_from_secret(k0)
501 print " * (main addr)", hash_160_to_bc_address(hash_160(K0_compressed))
504 print " * (hex)", k0.encode('hex')
505 print " * (wif)", SecretToASecret(k0, True)
508 print " * (hex)", c0.encode('hex')
517 if __name__ == '__main__':
518 test_bip32("000102030405060708090a0b0c0d0e0f", "0'/1/2'/2/1000000000")
519 test_bip32("fffcf9f6f3f0edeae7e4e1dedbd8d5d2cfccc9c6c3c0bdbab7b4b1aeaba8a5a29f9c999693908d8a8784817e7b7875726f6c696663605d5a5754514e4b484542","0/2147483647'/1/2147483646'/2")