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]
66 hmac_sha_512 = lambda x,y: hmac.new(x, y, hashlib.sha512).digest()
67 mnemonic_hash = lambda x: hmac_sha_512("Bitcoin mnemonic", x).encode('hex')
68 from version import SEED_PREFIX
69 is_seed = lambda x: hmac_sha_512("Seed version", x).encode('hex')[0:2].startswith(SEED_PREFIX)
71 # pywallet openssl private key implementation
73 def i2d_ECPrivateKey(pkey, compressed=False):
75 key = '3081d30201010420' + \
76 '%064x' % pkey.secret + \
77 'a081a53081a2020101302c06072a8648ce3d0101022100' + \
79 '3006040100040107042102' + \
85 key = '308201130201010420' + \
86 '%064x' % pkey.secret + \
87 'a081a53081a2020101302c06072a8648ce3d0101022100' + \
89 '3006040100040107044104' + \
96 return key.decode('hex') + i2o_ECPublicKey(pkey.pubkey, compressed)
98 def i2o_ECPublicKey(pubkey, compressed=False):
99 # public keys are 65 bytes long (520 bits)
100 # 0x04 + 32-byte X-coordinate + 32-byte Y-coordinate
101 # 0x00 = point at infinity, 0x02 and 0x03 = compressed, 0x04 = uncompressed
102 # compressed keys: <sign> <x> where <sign> is 0x02 if y is even and 0x03 if y is odd
104 if pubkey.point.y() & 1:
105 key = '03' + '%064x' % pubkey.point.x()
107 key = '02' + '%064x' % pubkey.point.x()
110 '%064x' % pubkey.point.x() + \
111 '%064x' % pubkey.point.y()
113 return key.decode('hex')
115 # end pywallet openssl private key implementation
119 ############ functions from pywallet #####################
121 def hash_160(public_key):
123 md = hashlib.new('ripemd160')
124 md.update(sha256(public_key))
128 md = ripemd.new(sha256(public_key))
132 def public_key_to_bc_address(public_key):
133 h160 = hash_160(public_key)
134 return hash_160_to_bc_address(h160)
136 def hash_160_to_bc_address(h160, addrtype = 0):
137 vh160 = chr(addrtype) + h160
139 addr = vh160 + h[0:4]
140 return b58encode(addr)
142 def bc_address_to_hash_160(addr):
143 bytes = b58decode(addr, 25)
144 return ord(bytes[0]), bytes[1:21]
147 __b58chars = '123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz'
148 __b58base = len(__b58chars)
151 """ encode v, which is a string of bytes, to base58."""
154 for (i, c) in enumerate(v[::-1]):
155 long_value += (256**i) * ord(c)
158 while long_value >= __b58base:
159 div, mod = divmod(long_value, __b58base)
160 result = __b58chars[mod] + result
162 result = __b58chars[long_value] + result
164 # Bitcoin does a little leading-zero-compression:
165 # leading 0-bytes in the input become leading-1s
168 if c == '\0': nPad += 1
171 return (__b58chars[0]*nPad) + result
173 def b58decode(v, length):
174 """ decode v into a string of len bytes."""
176 for (i, c) in enumerate(v[::-1]):
177 long_value += __b58chars.find(c) * (__b58base**i)
180 while long_value >= 256:
181 div, mod = divmod(long_value, 256)
182 result = chr(mod) + result
184 result = chr(long_value) + result
188 if c == __b58chars[0]: nPad += 1
191 result = chr(0)*nPad + result
192 if length is not None and len(result) != length:
198 def EncodeBase58Check(vchIn):
200 return b58encode(vchIn + hash[0:4])
202 def DecodeBase58Check(psz):
203 vchRet = b58decode(psz, None)
213 def PrivKeyToSecret(privkey):
214 return privkey[9:9+32]
216 def SecretToASecret(secret, compressed=False, addrtype=0):
217 vchIn = chr((addrtype+128)&255) + secret
218 if compressed: vchIn += '\01'
219 return EncodeBase58Check(vchIn)
221 def ASecretToSecret(key, addrtype=0):
222 vch = DecodeBase58Check(key)
223 if vch and vch[0] == chr((addrtype+128)&255):
228 def regenerate_key(sec):
229 b = ASecretToSecret(sec)
233 secret = int('0x' + b.encode('hex'), 16)
234 return EC_KEY(secret)
236 def GetPubKey(pubkey, compressed=False):
237 return i2o_ECPublicKey(pubkey, compressed)
239 def GetPrivKey(pkey, compressed=False):
240 return i2d_ECPrivateKey(pkey, compressed)
243 return ('%064x' % pkey.secret).decode('hex')
245 def is_compressed(sec):
246 b = ASecretToSecret(sec)
250 def public_key_from_private_key(sec):
251 # rebuild public key from private key, compressed or uncompressed
252 pkey = regenerate_key(sec)
254 compressed = is_compressed(sec)
255 public_key = GetPubKey(pkey.pubkey, compressed)
256 return public_key.encode('hex')
259 def address_from_private_key(sec):
260 public_key = public_key_from_private_key(sec)
261 address = public_key_to_bc_address(public_key.decode('hex'))
266 ADDRESS_RE = re.compile('[1-9A-HJ-NP-Za-km-z]{26,}\\Z')
267 if not ADDRESS_RE.match(addr): return False
269 addrtype, h = bc_address_to_hash_160(addr)
272 return addr == hash_160_to_bc_address(h, addrtype)
275 ########### end pywallet functions #######################
278 from ecdsa.ecdsa import curve_secp256k1, generator_secp256k1
280 print "cannot import ecdsa.curve_secp256k1. You probably need to upgrade ecdsa.\nTry: sudo pip install --upgrade ecdsa"
283 from ecdsa.curves import SECP256k1
284 from ecdsa.ellipticcurve import Point
285 from ecdsa.util import string_to_number, number_to_string
287 def msg_magic(message):
288 varint = var_int(len(message))
289 encoded_varint = "".join([chr(int(varint[i:i+2], 16)) for i in xrange(0, len(varint), 2)])
290 return "\x18Bitcoin Signed Message:\n" + encoded_varint + message
293 def verify_message(address, signature, message):
295 EC_KEY.verify_message(address, signature, message)
297 except Exception as e:
298 print_error("Verification error: {0}".format(e))
303 return [l[i:i+n] for i in xrange(0, len(l), n)]
306 def ECC_YfromX(x,curved=curve_secp256k1, odd=True):
310 for offset in range(128):
312 My2 = pow(Mx, 3, _p) + _a * pow(Mx, 2, _p) + _b % _p
313 My = pow(My2, (_p+1)/4, _p )
315 if curved.contains_point(Mx,My):
316 if odd == bool(My&1):
318 return [_p-My,offset]
319 raise Exception('ECC_YfromX: No Y found')
321 def private_header(msg,v):
322 assert v<1, "Can't write version %d private header"%v
325 r += ('%08x'%len(msg)).decode('hex')
327 return ('%02x'%v).decode('hex') + ('%04x'%len(r)).decode('hex') + r
329 def public_header(pubkey,v):
330 assert v<1, "Can't write version %d public header"%v
333 r = sha256(pubkey)[:2]
334 return '\x6a\x6a' + ('%02x'%v).decode('hex') + ('%04x'%len(r)).decode('hex') + r
337 def negative_point(P):
338 return Point( P.curve(), P.x(), -P.y(), P.order() )
341 def point_to_ser(P, comp=True ):
343 return ( ('%02x'%(2+(P.y()&1)))+('%064x'%P.x()) ).decode('hex')
344 return ( '04'+('%064x'%P.x())+('%064x'%P.y()) ).decode('hex')
347 def encode_point(pubkey, compressed=False):
348 order = generator_secp256k1.order()
349 p = pubkey.pubkey.point
350 x_str = ecdsa.util.number_to_string(p.x(), order)
351 y_str = ecdsa.util.number_to_string(p.y(), order)
353 return chr(2 + (p.y() & 1)) + x_str
355 return chr(4) + pubkey.to_string() #x_str + y_str
358 def ser_to_point(Aser):
359 curve = curve_secp256k1
360 generator = generator_secp256k1
361 _r = generator.order()
362 assert Aser[0] in ['\x02','\x03','\x04']
363 if Aser[0] == '\x04':
364 return Point( curve, str_to_long(Aser[1:33]), str_to_long(Aser[33:]), _r )
365 Mx = string_to_number(Aser[1:])
366 return Point( curve, Mx, ECC_YfromX(Mx, curve, Aser[0]=='\x03')[0], _r )
370 class EC_KEY(object):
371 def __init__( self, secret ):
372 self.pubkey = ecdsa.ecdsa.Public_key( generator_secp256k1, generator_secp256k1 * secret )
373 self.privkey = ecdsa.ecdsa.Private_key( self.pubkey, secret )
376 def sign_message(self, message, compressed, address):
377 private_key = ecdsa.SigningKey.from_secret_exponent( self.secret, curve = SECP256k1 )
378 public_key = private_key.get_verifying_key()
379 signature = private_key.sign_digest_deterministic( Hash( msg_magic(message) ), hashfunc=hashlib.sha256, sigencode = ecdsa.util.sigencode_string )
380 assert public_key.verify_digest( signature, Hash( msg_magic(message) ), sigdecode = ecdsa.util.sigdecode_string)
382 sig = base64.b64encode( chr(27 + i + (4 if compressed else 0)) + signature )
384 self.verify_message( address, sig, message)
389 raise Exception("error: cannot sign message")
393 def verify_message(self, address, signature, message):
394 """ See http://www.secg.org/download/aid-780/sec1-v2.pdf for the math """
395 from ecdsa import numbertheory, util
397 curve = curve_secp256k1
398 G = generator_secp256k1
400 # extract r,s from signature
401 sig = base64.b64decode(signature)
402 if len(sig) != 65: raise Exception("Wrong encoding")
403 r,s = util.sigdecode_string(sig[1:], order)
405 if nV < 27 or nV >= 35:
406 raise Exception("Bad encoding")
415 x = r + (recid/2) * order
417 alpha = ( x * x * x + curve.a() * x + curve.b() ) % curve.p()
418 beta = msqr.modular_sqrt(alpha, curve.p())
419 y = beta if (beta - recid) % 2 == 0 else curve.p() - beta
420 # 1.4 the constructor checks that nR is at infinity
421 R = Point(curve, x, y, order)
422 # 1.5 compute e from message:
423 h = Hash( msg_magic(message) )
424 e = string_to_number(h)
426 # 1.6 compute Q = r^-1 (sR - eG)
427 inv_r = numbertheory.inverse_mod(r,order)
428 Q = inv_r * ( s * R + minus_e * G )
429 public_key = ecdsa.VerifyingKey.from_public_point( Q, curve = SECP256k1 )
430 # check that Q is the public key
431 public_key.verify_digest( sig[1:], h, sigdecode = ecdsa.util.sigdecode_string)
432 # check that we get the original signing address
433 addr = public_key_to_bc_address( encode_point(public_key, compressed) )
435 raise Exception("Bad signature")
438 # ecdsa encryption/decryption methods
439 # credits: jackjack, https://github.com/jackjack-jj/jeeq
442 def encrypt_message(self, message, pubkey):
443 generator = generator_secp256k1
444 curved = curve_secp256k1
446 msg = private_header(message,0) + message
447 msg = msg + ('\x00'*( 32-(len(msg)%32) ))
448 msgs = chunks(msg,32)
450 _r = generator.order()
451 str_to_long = string_to_number
454 if len(pubkey)==33: #compressed
455 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 )
457 pk = Point( curve_secp256k1, str_to_long(pubkey[1:33]), str_to_long(pubkey[33:65]), _r )
459 for i in range(len(msgs)):
460 n = ecdsa.util.randrange( pow(2,256) )
461 Mx = str_to_long(msgs[i])
462 My, xoffset = ECC_YfromX(Mx, curved)
463 M = Point( curved, Mx+xoffset, My, _r )
466 toadd = point_to_ser(T) + point_to_ser(U)
467 toadd = chr(ord(toadd[0])-2 + 2*xoffset) + toadd[1:]
470 return base64.b64encode(public_header(pubkey,0) + r)
473 def decrypt_message(self, enc):
474 G = generator_secp256k1
475 curved = curve_secp256k1
477 pubkeys = [point_to_ser(G*pvk,True), point_to_ser(G*pvk,False)]
478 enc = base64.b64decode(enc)
479 str_to_long = string_to_number
481 assert enc[:2]=='\x6a\x6a'
483 phv = str_to_long(enc[2])
484 assert phv==0, "Can't read version %d public header"%phv
485 hs = str_to_long(enc[3:5])
486 public_header=enc[5:5+hs]
487 checksum_pubkey=public_header[:2]
488 address=filter(lambda x:sha256(x)[:2]==checksum_pubkey, pubkeys)
489 assert len(address)>0, 'Bad private key'
493 for Tser,User in map(lambda x:[x[:33],x[33:]], chunks(enc,66)):
496 Tser = chr(2+(ots&1))+Tser[1:]
497 T = ser_to_point(Tser)
498 U = ser_to_point(User)
500 Mcalc = U + negative_point(V)
501 r += ('%064x'%(Mcalc.x()-xoffset)).decode('hex')
503 pvhv = str_to_long(r[0])
504 assert pvhv==0, "Can't read version %d private header"%pvhv
505 phs = str_to_long(r[1:3])
506 private_header = r[3:3+phs]
507 size = str_to_long(private_header[:4])
508 checksum = private_header[4:6]
512 hashmsg = sha256(msg)[:2]
513 checksumok = hashmsg==checksum
515 return [msg, checksumok, address]
521 ###################################### BIP32 ##############################
523 random_seed = lambda n: "%032x"%ecdsa.util.randrange( pow(2,n) )
524 BIP32_PRIME = 0x80000000
526 def bip32_init(seed):
528 seed = seed.decode('hex')
529 I = hmac.new("Bitcoin seed", seed, hashlib.sha512).digest()
531 master_secret = I[0:32]
532 master_chain = I[32:]
534 K, K_compressed = get_pubkeys_from_secret(master_secret)
535 return master_secret, master_chain, K, K_compressed
538 def get_pubkeys_from_secret(secret):
540 private_key = ecdsa.SigningKey.from_string( secret, curve = SECP256k1 )
541 public_key = private_key.get_verifying_key()
542 K = public_key.to_string()
543 K_compressed = GetPubKey(public_key.pubkey,True)
544 return K, K_compressed
548 # Child private key derivation function (from master private key)
549 # k = master private key (32 bytes)
550 # c = master chain code (extra entropy for key derivation) (32 bytes)
551 # n = the index of the key we want to derive. (only 32 bits will be used)
552 # If n is negative (i.e. the 32nd bit is set), the resulting private key's
553 # corresponding public key can NOT be determined without the master private key.
554 # However, if n is positive, the resulting private key's corresponding
555 # public key can be determined without the master private key.
558 from ecdsa.util import string_to_number, number_to_string
559 order = generator_secp256k1.order()
560 keypair = EC_KEY(string_to_number(k))
561 K = GetPubKey(keypair.pubkey,True)
563 if n & BIP32_PRIME: # We want to make a "secret" address that can't be determined from K
564 data = chr(0) + k + rev_hex(int_to_hex(n,4)).decode('hex')
565 I = hmac.new(c, data, hashlib.sha512).digest()
566 else: # We want a "non-secret" address that can be determined from K
567 I = hmac.new(c, K + rev_hex(int_to_hex(n,4)).decode('hex'), hashlib.sha512).digest()
569 k_n = number_to_string( (string_to_number(I[0:32]) + string_to_number(k)) % order , order )
573 # Child public key derivation function (from public key only)
574 # K = master public key
575 # c = master chain code
576 # n = index of key we want to derive
577 # This function allows us to find the nth public key, as long as n is
578 # non-negative. If n is negative, we need the master private key to find it.
579 def CKD_prime(K, c, n):
581 from ecdsa.util import string_to_number, number_to_string
582 order = generator_secp256k1.order()
584 if n & BIP32_PRIME: raise
586 K_public_key = ecdsa.VerifyingKey.from_string( K, curve = SECP256k1 )
587 K_compressed = GetPubKey(K_public_key.pubkey,True)
589 I = hmac.new(c, K_compressed + rev_hex(int_to_hex(n,4)).decode('hex'), hashlib.sha512).digest()
592 pubkey_point = string_to_number(I[0:32])*curve.generator + K_public_key.pubkey.point
593 public_key = ecdsa.VerifyingKey.from_public_point( pubkey_point, curve = SECP256k1 )
595 K_n = public_key.to_string()
596 K_n_compressed = GetPubKey(public_key.pubkey,True)
599 return K_n, K_n_compressed, c_n
603 def bip32_private_derivation(k, c, branch, sequence):
604 assert sequence.startswith(branch)
605 sequence = sequence[len(branch):]
606 for n in sequence.split('/'):
608 n = int(n[:-1]) + BIP32_PRIME if n[-1] == "'" else int(n)
610 K, K_compressed = get_pubkeys_from_secret(k)
611 return k.encode('hex'), c.encode('hex'), K.encode('hex'), K_compressed.encode('hex')
614 def bip32_public_derivation(c, K, branch, sequence):
615 assert sequence.startswith(branch)
616 sequence = sequence[len(branch):]
617 for n in sequence.split('/'):
619 K, cK, c = CKD_prime(K, c, n)
621 return c.encode('hex'), K.encode('hex'), cK.encode('hex')
624 def bip32_private_key(sequence, k, chain):
626 k, chain = CKD(k, chain, i)
627 return SecretToASecret(k, True)
632 ################################## transactions
634 MIN_RELAY_TX_FEE = 10000
638 def test_bip32(seed, sequence):
641 see https://en.bitcoin.it/wiki/BIP_0032_TestVectors
644 master_secret, master_chain, master_public_key, master_public_key_compressed = bip32_init(seed)
646 print "secret key", master_secret.encode('hex')
647 print "chain code", master_chain.encode('hex')
649 key_id = hash_160(master_public_key_compressed)
650 print "keyid", key_id.encode('hex')
652 print "address", hash_160_to_bc_address(key_id)
653 print "secret key", SecretToASecret(master_secret, True)
659 for n in sequence.split('/'):
661 print "Chain [%s]" % '/'.join(s)
663 n = int(n[:-1]) + BIP32_PRIME if n[-1] == "'" else int(n)
664 k0, c0 = CKD(k, c, n)
665 K0, K0_compressed = get_pubkeys_from_secret(k0)
668 print " * (main addr)", hash_160_to_bc_address(hash_160(K0_compressed))
671 print " * (hex)", k0.encode('hex')
672 print " * (wif)", SecretToASecret(k0, True)
675 print " * (hex)", c0.encode('hex')
685 G = generator_secp256k1
687 pvk = ecdsa.util.randrange( pow(2,256) ) %_r
690 pubkey_c = point_to_ser(Pub,True)
691 pubkey_u = point_to_ser(Pub,False)
692 addr_c = public_key_to_bc_address(pubkey_c)
693 addr_u = public_key_to_bc_address(pubkey_u)
695 print "Private key ", '%064x'%pvk
696 print "Compressed public key ", pubkey_c.encode('hex')
697 print "Uncompressed public key", pubkey_u.encode('hex')
699 message = "Chancellor on brink of second bailout for banks"
700 enc = EC_KEY.encrypt_message(message,pubkey_c)
702 dec = eck.decrypt_message(enc)
703 print "decrypted", dec
705 signature = eck.sign_message(message, True, addr_c)
707 EC_KEY.verify_message(addr_c, signature, message)
710 if __name__ == '__main__':
712 #test_bip32("000102030405060708090a0b0c0d0e0f", "0'/1/2'/2/1000000000")
713 #test_bip32("fffcf9f6f3f0edeae7e4e1dedbd8d5d2cfccc9c6c3c0bdbab7b4b1aeaba8a5a29f9c999693908d8a8784817e7b7875726f6c696663605d5a5754514e4b484542","0/2147483647'/1/2147483646'/2")