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
23 from util import print_error
26 return s.decode('hex')[::-1].encode('hex')
28 def int_to_hex(i, length=1):
29 s = hex(i)[2:].rstrip('L')
30 s = "0"*(2*length - len(s)) + s
34 # https://en.bitcoin.it/wiki/Protocol_specification#Variable_length_integer
38 return "fd"+int_to_hex(i,2)
40 return "fe"+int_to_hex(i,4)
42 return "ff"+int_to_hex(i,8)
48 return '4c' + int_to_hex(i)
50 return '4d' + int_to_hex(i,2)
52 return '4e' + int_to_hex(i,4)
57 return hashlib.sha256(x).digest()
60 if type(x) is unicode: x=x.encode('utf-8')
61 return sha256(sha256(x))
63 hash_encode = lambda x: x[::-1].encode('hex')
64 hash_decode = lambda x: x.decode('hex')[::-1]
65 hmac_sha_512 = lambda x,y: hmac.new(x, y, hashlib.sha512).digest()
67 def mnemonic_to_seed(mnemonic, passphrase):
68 from pbkdf2 import PBKDF2
71 return PBKDF2(mnemonic, 'mnemonic' + passphrase, iterations = PBKDF2_ROUNDS, macmodule = hmac, digestmodule = hashlib.sha512).read(64)
73 from version import SEED_PREFIX
74 is_seed = lambda x: hmac_sha_512("Seed version", x).encode('hex')[0:2].startswith(SEED_PREFIX)
76 # pywallet openssl private key implementation
78 def i2d_ECPrivateKey(pkey, compressed=False):
80 key = '3081d30201010420' + \
81 '%064x' % pkey.secret + \
82 'a081a53081a2020101302c06072a8648ce3d0101022100' + \
84 '3006040100040107042102' + \
90 key = '308201130201010420' + \
91 '%064x' % pkey.secret + \
92 'a081a53081a2020101302c06072a8648ce3d0101022100' + \
94 '3006040100040107044104' + \
101 return key.decode('hex') + i2o_ECPublicKey(pkey.pubkey, compressed)
103 def i2o_ECPublicKey(pubkey, compressed=False):
104 # public keys are 65 bytes long (520 bits)
105 # 0x04 + 32-byte X-coordinate + 32-byte Y-coordinate
106 # 0x00 = point at infinity, 0x02 and 0x03 = compressed, 0x04 = uncompressed
107 # compressed keys: <sign> <x> where <sign> is 0x02 if y is even and 0x03 if y is odd
109 if pubkey.point.y() & 1:
110 key = '03' + '%064x' % pubkey.point.x()
112 key = '02' + '%064x' % pubkey.point.x()
115 '%064x' % pubkey.point.x() + \
116 '%064x' % pubkey.point.y()
118 return key.decode('hex')
120 # end pywallet openssl private key implementation
124 ############ functions from pywallet #####################
126 def hash_160(public_key):
128 md = hashlib.new('ripemd160')
129 md.update(sha256(public_key))
133 md = ripemd.new(sha256(public_key))
137 def public_key_to_bc_address(public_key):
138 h160 = hash_160(public_key)
139 return hash_160_to_bc_address(h160)
141 def hash_160_to_bc_address(h160, addrtype = 0):
142 vh160 = chr(addrtype) + h160
144 addr = vh160 + h[0:4]
145 return b58encode(addr)
147 def bc_address_to_hash_160(addr):
148 bytes = b58decode(addr, 25)
149 return ord(bytes[0]), bytes[1:21]
152 __b58chars = '123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz'
153 __b58base = len(__b58chars)
156 """ encode v, which is a string of bytes, to base58."""
159 for (i, c) in enumerate(v[::-1]):
160 long_value += (256**i) * ord(c)
163 while long_value >= __b58base:
164 div, mod = divmod(long_value, __b58base)
165 result = __b58chars[mod] + result
167 result = __b58chars[long_value] + result
169 # Bitcoin does a little leading-zero-compression:
170 # leading 0-bytes in the input become leading-1s
173 if c == '\0': nPad += 1
176 return (__b58chars[0]*nPad) + result
178 def b58decode(v, length):
179 """ decode v into a string of len bytes."""
181 for (i, c) in enumerate(v[::-1]):
182 long_value += __b58chars.find(c) * (__b58base**i)
185 while long_value >= 256:
186 div, mod = divmod(long_value, 256)
187 result = chr(mod) + result
189 result = chr(long_value) + result
193 if c == __b58chars[0]: nPad += 1
196 result = chr(0)*nPad + result
197 if length is not None and len(result) != length:
203 def EncodeBase58Check(vchIn):
205 return b58encode(vchIn + hash[0:4])
207 def DecodeBase58Check(psz):
208 vchRet = b58decode(psz, None)
218 def PrivKeyToSecret(privkey):
219 return privkey[9:9+32]
221 def SecretToASecret(secret, compressed=False, addrtype=0):
222 vchIn = chr((addrtype+128)&255) + secret
223 if compressed: vchIn += '\01'
224 return EncodeBase58Check(vchIn)
226 def ASecretToSecret(key, addrtype=0):
227 vch = DecodeBase58Check(key)
228 if vch and vch[0] == chr((addrtype+128)&255):
233 def regenerate_key(sec):
234 b = ASecretToSecret(sec)
240 def GetPubKey(pubkey, compressed=False):
241 return i2o_ECPublicKey(pubkey, compressed)
243 def GetPrivKey(pkey, compressed=False):
244 return i2d_ECPrivateKey(pkey, compressed)
247 return ('%064x' % pkey.secret).decode('hex')
249 def is_compressed(sec):
250 b = ASecretToSecret(sec)
254 def public_key_from_private_key(sec):
255 # rebuild public key from private key, compressed or uncompressed
256 pkey = regenerate_key(sec)
258 compressed = is_compressed(sec)
259 public_key = GetPubKey(pkey.pubkey, compressed)
260 return public_key.encode('hex')
263 def address_from_private_key(sec):
264 public_key = public_key_from_private_key(sec)
265 address = public_key_to_bc_address(public_key.decode('hex'))
270 ADDRESS_RE = re.compile('[1-9A-HJ-NP-Za-km-z]{26,}\\Z')
271 if not ADDRESS_RE.match(addr): return False
273 addrtype, h = bc_address_to_hash_160(addr)
276 return addr == hash_160_to_bc_address(h, addrtype)
279 ########### end pywallet functions #######################
282 from ecdsa.ecdsa import curve_secp256k1, generator_secp256k1
284 print "cannot import ecdsa.curve_secp256k1. You probably need to upgrade ecdsa.\nTry: sudo pip install --upgrade ecdsa"
287 from ecdsa.curves import SECP256k1
288 from ecdsa.ellipticcurve import Point
289 from ecdsa.util import string_to_number, number_to_string
291 def msg_magic(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)])
294 return "\x18Bitcoin Signed Message:\n" + encoded_varint + message
297 def verify_message(address, signature, message):
299 EC_KEY.verify_message(address, signature, message)
301 except Exception as e:
302 print_error("Verification error: {0}".format(e))
307 return [l[i:i+n] for i in xrange(0, len(l), n)]
310 def ECC_YfromX(x,curved=curve_secp256k1, odd=True):
314 for offset in range(128):
316 My2 = pow(Mx, 3, _p) + _a * pow(Mx, 2, _p) + _b % _p
317 My = pow(My2, (_p+1)/4, _p )
319 if curved.contains_point(Mx,My):
320 if odd == bool(My&1):
322 return [_p-My,offset]
323 raise Exception('ECC_YfromX: No Y found')
325 def private_header(msg,v):
326 assert v<1, "Can't write version %d private header"%v
329 r += ('%08x'%len(msg)).decode('hex')
331 return ('%02x'%v).decode('hex') + ('%04x'%len(r)).decode('hex') + r
333 def public_header(pubkey,v):
334 assert v<1, "Can't write version %d public header"%v
337 r = sha256(pubkey)[:2]
338 return '\x6a\x6a' + ('%02x'%v).decode('hex') + ('%04x'%len(r)).decode('hex') + r
341 def negative_point(P):
342 return Point( P.curve(), P.x(), -P.y(), P.order() )
345 def point_to_ser(P, comp=True ):
347 return ( ('%02x'%(2+(P.y()&1)))+('%064x'%P.x()) ).decode('hex')
348 return ( '04'+('%064x'%P.x())+('%064x'%P.y()) ).decode('hex')
351 def ser_to_point(Aser):
352 curve = curve_secp256k1
353 generator = generator_secp256k1
354 _r = generator.order()
355 assert Aser[0] in ['\x02','\x03','\x04']
356 if Aser[0] == '\x04':
357 return Point( curve, str_to_long(Aser[1:33]), str_to_long(Aser[33:]), _r )
358 Mx = string_to_number(Aser[1:])
359 return Point( curve, Mx, ECC_YfromX(Mx, curve, Aser[0]=='\x03')[0], _r )
363 class EC_KEY(object):
364 def __init__( self, k ):
365 secret = string_to_number(k)
366 self.pubkey = ecdsa.ecdsa.Public_key( generator_secp256k1, generator_secp256k1 * secret )
367 self.privkey = ecdsa.ecdsa.Private_key( self.pubkey, secret )
370 def sign_message(self, message, compressed, address):
371 private_key = ecdsa.SigningKey.from_secret_exponent( self.secret, curve = SECP256k1 )
372 public_key = private_key.get_verifying_key()
373 signature = private_key.sign_digest_deterministic( Hash( msg_magic(message) ), hashfunc=hashlib.sha256, sigencode = ecdsa.util.sigencode_string )
374 assert public_key.verify_digest( signature, Hash( msg_magic(message) ), sigdecode = ecdsa.util.sigdecode_string)
376 sig = base64.b64encode( chr(27 + i + (4 if compressed else 0)) + signature )
378 self.verify_message( address, sig, message)
383 raise Exception("error: cannot sign message")
387 def verify_message(self, address, signature, message):
388 """ See http://www.secg.org/download/aid-780/sec1-v2.pdf for the math """
389 from ecdsa import numbertheory, util
391 curve = curve_secp256k1
392 G = generator_secp256k1
394 # extract r,s from signature
395 sig = base64.b64decode(signature)
396 if len(sig) != 65: raise Exception("Wrong encoding")
397 r,s = util.sigdecode_string(sig[1:], order)
399 if nV < 27 or nV >= 35:
400 raise Exception("Bad encoding")
409 x = r + (recid/2) * order
411 alpha = ( x * x * x + curve.a() * x + curve.b() ) % curve.p()
412 beta = msqr.modular_sqrt(alpha, curve.p())
413 y = beta if (beta - recid) % 2 == 0 else curve.p() - beta
414 # 1.4 the constructor checks that nR is at infinity
415 R = Point(curve, x, y, order)
416 # 1.5 compute e from message:
417 h = Hash( msg_magic(message) )
418 e = string_to_number(h)
420 # 1.6 compute Q = r^-1 (sR - eG)
421 inv_r = numbertheory.inverse_mod(r,order)
422 Q = inv_r * ( s * R + minus_e * G )
423 public_key = ecdsa.VerifyingKey.from_public_point( Q, curve = SECP256k1 )
424 # check that Q is the public key
425 public_key.verify_digest( sig[1:], h, sigdecode = ecdsa.util.sigdecode_string)
426 # check that we get the original signing address
427 addr = public_key_to_bc_address( point_to_ser(public_key.pubkey.point, compressed) )
429 raise Exception("Bad signature")
432 # ecdsa encryption/decryption methods
433 # credits: jackjack, https://github.com/jackjack-jj/jeeq
436 def encrypt_message(self, message, pubkey):
437 generator = generator_secp256k1
438 curved = curve_secp256k1
440 msg = private_header(message,0) + message
441 msg = msg + ('\x00'*( 32-(len(msg)%32) ))
442 msgs = chunks(msg,32)
444 _r = generator.order()
445 str_to_long = string_to_number
448 if len(pubkey)==33: #compressed
449 pk = Point( curve_secp256k1, str_to_long(pubkey[1:33]), ECC_YfromX(str_to_long(pubkey[1:33]), curve_secp256k1, pubkey[0]=='\x03')[0], _r )
451 pk = Point( curve_secp256k1, str_to_long(pubkey[1:33]), str_to_long(pubkey[33:65]), _r )
453 for i in range(len(msgs)):
454 n = ecdsa.util.randrange( pow(2,256) )
455 Mx = str_to_long(msgs[i])
456 My, xoffset = ECC_YfromX(Mx, curved)
457 M = Point( curved, Mx+xoffset, My, _r )
460 toadd = point_to_ser(T) + point_to_ser(U)
461 toadd = chr(ord(toadd[0])-2 + 2*xoffset) + toadd[1:]
464 return base64.b64encode(public_header(pubkey,0) + r)
467 def decrypt_message(self, enc):
468 G = generator_secp256k1
469 curved = curve_secp256k1
471 pubkeys = [point_to_ser(G*pvk,True), point_to_ser(G*pvk,False)]
472 enc = base64.b64decode(enc)
473 str_to_long = string_to_number
475 assert enc[:2]=='\x6a\x6a'
477 phv = str_to_long(enc[2])
478 assert phv==0, "Can't read version %d public header"%phv
479 hs = str_to_long(enc[3:5])
480 public_header=enc[5:5+hs]
481 checksum_pubkey=public_header[:2]
482 address=filter(lambda x:sha256(x)[:2]==checksum_pubkey, pubkeys)
483 assert len(address)>0, 'Bad private key'
487 for Tser,User in map(lambda x:[x[:33],x[33:]], chunks(enc,66)):
490 Tser = chr(2+(ots&1))+Tser[1:]
491 T = ser_to_point(Tser)
492 U = ser_to_point(User)
494 Mcalc = U + negative_point(V)
495 r += ('%064x'%(Mcalc.x()-xoffset)).decode('hex')
497 pvhv = str_to_long(r[0])
498 assert pvhv==0, "Can't read version %d private header"%pvhv
499 phs = str_to_long(r[1:3])
500 private_header = r[3:3+phs]
501 size = str_to_long(private_header[:4])
502 checksum = private_header[4:6]
506 hashmsg = sha256(msg)[:2]
507 checksumok = hashmsg==checksum
509 return [msg, checksumok, address]
515 ###################################### BIP32 ##############################
517 random_seed = lambda n: "%032x"%ecdsa.util.randrange( pow(2,n) )
518 BIP32_PRIME = 0x80000000
520 def bip32_init(seed):
522 seed = seed.decode('hex')
523 I = hmac.new("Bitcoin seed", seed, hashlib.sha512).digest()
525 master_secret = I[0:32]
526 master_chain = I[32:]
528 K, K_compressed = get_pubkeys_from_secret(master_secret)
529 return master_secret, master_chain, K, K_compressed
532 def get_pubkeys_from_secret(secret):
534 private_key = ecdsa.SigningKey.from_string( secret, curve = SECP256k1 )
535 public_key = private_key.get_verifying_key()
536 K = public_key.to_string()
537 K_compressed = GetPubKey(public_key.pubkey,True)
538 return K, K_compressed
542 # Child private key derivation function (from master private key)
543 # k = master private key (32 bytes)
544 # c = master chain code (extra entropy for key derivation) (32 bytes)
545 # n = the index of the key we want to derive. (only 32 bits will be used)
546 # If n is negative (i.e. the 32nd bit is set), the resulting private key's
547 # corresponding public key can NOT be determined without the master private key.
548 # However, if n is positive, the resulting private key's corresponding
549 # public key can be determined without the master private key.
552 from ecdsa.util import string_to_number, number_to_string
553 order = generator_secp256k1.order()
555 K = GetPubKey(keypair.pubkey,True)
557 if n & BIP32_PRIME: # We want to make a "secret" address that can't be determined from K
558 data = chr(0) + k + rev_hex(int_to_hex(n,4)).decode('hex')
559 I = hmac.new(c, data, hashlib.sha512).digest()
560 else: # We want a "non-secret" address that can be determined from K
561 I = hmac.new(c, K + rev_hex(int_to_hex(n,4)).decode('hex'), hashlib.sha512).digest()
563 k_n = number_to_string( (string_to_number(I[0:32]) + string_to_number(k)) % order , order )
567 # Child public key derivation function (from public key only)
568 # K = master public key
569 # c = master chain code
570 # n = index of key we want to derive
571 # This function allows us to find the nth public key, as long as n is
572 # non-negative. If n is negative, we need the master private key to find it.
573 def CKD_prime(K, c, n):
575 from ecdsa.util import string_to_number, number_to_string
576 order = generator_secp256k1.order()
578 if n & BIP32_PRIME: raise
580 K_public_key = ecdsa.VerifyingKey.from_string( K, curve = SECP256k1 )
581 K_compressed = GetPubKey(K_public_key.pubkey,True)
583 I = hmac.new(c, K_compressed + rev_hex(int_to_hex(n,4)).decode('hex'), hashlib.sha512).digest()
586 pubkey_point = string_to_number(I[0:32])*curve.generator + K_public_key.pubkey.point
587 public_key = ecdsa.VerifyingKey.from_public_point( pubkey_point, curve = SECP256k1 )
589 K_n = public_key.to_string()
590 K_n_compressed = GetPubKey(public_key.pubkey,True)
593 return K_n, K_n_compressed, c_n
597 def bip32_private_derivation(k, c, branch, sequence):
598 assert sequence.startswith(branch)
599 sequence = sequence[len(branch):]
600 for n in sequence.split('/'):
602 n = int(n[:-1]) + BIP32_PRIME if n[-1] == "'" else int(n)
604 K, K_compressed = get_pubkeys_from_secret(k)
605 return k.encode('hex'), c.encode('hex'), K.encode('hex'), K_compressed.encode('hex')
608 def bip32_public_derivation(c, K, branch, sequence):
609 assert sequence.startswith(branch)
610 sequence = sequence[len(branch):]
611 for n in sequence.split('/'):
613 K, cK, c = CKD_prime(K, c, n)
615 return c.encode('hex'), K.encode('hex'), cK.encode('hex')
618 def bip32_private_key(sequence, k, chain):
620 k, chain = CKD(k, chain, i)
621 return SecretToASecret(k, True)
626 ################################## transactions
628 MIN_RELAY_TX_FEE = 10000
632 def test_bip32(seed, sequence):
635 see https://en.bitcoin.it/wiki/BIP_0032_TestVectors
638 master_secret, master_chain, master_public_key, master_public_key_compressed = bip32_init(seed)
640 print "secret key", master_secret.encode('hex')
641 print "chain code", master_chain.encode('hex')
643 key_id = hash_160(master_public_key_compressed)
644 print "keyid", key_id.encode('hex')
646 print "address", hash_160_to_bc_address(key_id)
647 print "secret key", SecretToASecret(master_secret, True)
653 for n in sequence.split('/'):
655 print "Chain [%s]" % '/'.join(s)
657 n = int(n[:-1]) + BIP32_PRIME if n[-1] == "'" else int(n)
658 k0, c0 = CKD(k, c, n)
659 K0, K0_compressed = get_pubkeys_from_secret(k0)
662 print " * (main addr)", hash_160_to_bc_address(hash_160(K0_compressed))
665 print " * (hex)", k0.encode('hex')
666 print " * (wif)", SecretToASecret(k0, True)
669 print " * (hex)", c0.encode('hex')
679 G = generator_secp256k1
681 pvk = ecdsa.util.randrange( pow(2,256) ) %_r
684 pubkey_c = point_to_ser(Pub,True)
685 pubkey_u = point_to_ser(Pub,False)
686 addr_c = public_key_to_bc_address(pubkey_c)
687 addr_u = public_key_to_bc_address(pubkey_u)
689 print "Private key ", '%064x'%pvk
690 print "Compressed public key ", pubkey_c.encode('hex')
691 print "Uncompressed public key", pubkey_u.encode('hex')
693 message = "Chancellor on brink of second bailout for banks"
694 enc = EC_KEY.encrypt_message(message,pubkey_c)
695 eck = EC_KEY(number_to_string(pvk,_r))
696 dec = eck.decrypt_message(enc)
697 print "decrypted", dec
699 signature = eck.sign_message(message, True, addr_c)
701 EC_KEY.verify_message(addr_c, signature, message)
704 if __name__ == '__main__':
706 #test_bip32("000102030405060708090a0b0c0d0e0f", "0'/1/2'/2/1000000000")
707 #test_bip32("fffcf9f6f3f0edeae7e4e1dedbd8d5d2cfccc9c6c3c0bdbab7b4b1aeaba8a5a29f9c999693908d8a8784817e7b7875726f6c696663605d5a5754514e4b484542","0/2147483647'/1/2147483646'/2")