1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
|
#!/usr/bin/python
# Copyright 2014, The Tor Project, Inc
# See LICENSE for licensing information
"""
Reference implementations for the ed25519 tweaks that Tor uses.
Includes self-tester and test vector generator.
"""
from slow_ed25519 import *
import os
import random
import slownacl_curve25519
import unittest
import binascii
#define a synonym that doesn't look like 1
ell = l
# This replaces expmod above and makes it go a lot faster.
def expmod(b,e,m):
return pow(b,e,m)
def curve25519ToEd25519(c, sign):
u = decodeint(c)
y = ((u - 1) * inv(u + 1)) % q
x = xrecover(y)
if x & 1 != sign: x = q-x
return encodepoint([x,y])
def blindESK(esk, param):
h = H("Derive temporary signing key" + param)
mult = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2))
s = decodeint(esk[:32])
s_prime = (s * mult) % ell
k = esk[32:]
assert(len(k) == 32)
k_prime = H("Derive temporary signing key hash input" + k)[:32]
return encodeint(s_prime) + k_prime
def blindPK(pk, param):
h = H("Derive temporary signing key" + param)
mult = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2))
P = decodepoint(pk)
return encodepoint(scalarmult(P, mult))
def expandSK(sk):
h = H(sk)
a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2))
k = ''.join([h[i] for i in range(b/8,b/4)])
assert len(k) == 32
return encodeint(a)+k
def publickeyFromESK(h):
a = decodeint(h[:32])
A = scalarmult(B,a)
return encodepoint(A)
def signatureWithESK(m,h,pk):
a = decodeint(h[:32])
r = Hint(''.join([h[i] for i in range(b/8,b/4)]) + m)
R = scalarmult(B,r)
S = (r + Hint(encodepoint(R) + pk + m) * a) % l
return encodepoint(R) + encodeint(S)
def newSK():
return os.urandom(32)
# ------------------------------------------------------------
MSG = "This is extremely silly. But it is also incredibly serious business!"
class SelfTest(unittest.TestCase):
def _testSignatures(self, esk, pk):
sig = signatureWithESK(MSG, esk, pk)
checkvalid(sig, MSG, pk)
bad = False
try:
checkvalid(sig, MSG*2, pk)
bad = True
except Exception:
pass
self.failIf(bad)
def testExpand(self):
sk = newSK()
pk = publickey(sk)
esk = expandSK(sk)
sig1 = signature(MSG, sk, pk)
sig2 = signatureWithESK(MSG, esk, pk)
self.assertEquals(sig1, sig2)
def testSignatures(self):
sk = newSK()
esk = expandSK(sk)
pk = publickeyFromESK(esk)
pk2 = publickey(sk)
self.assertEquals(pk, pk2)
self._testSignatures(esk, pk)
def testDerivation(self):
priv = slownacl_curve25519.Private()
pub = priv.get_public()
ed_pub0 = publickeyFromESK(priv.private)
sign = (ord(ed_pub0[31]) & 255) >> 7
ed_pub1 = curve25519ToEd25519(pub.public, sign)
self.assertEquals(ed_pub0, ed_pub1)
def testBlinding(self):
sk = newSK()
esk = expandSK(sk)
pk = publickeyFromESK(esk)
param = os.urandom(32)
besk = blindESK(esk, param)
bpk = blindPK(pk, param)
bpk2 = publickeyFromESK(besk)
self.assertEquals(bpk, bpk2)
self._testSignatures(besk, bpk)
# ------------------------------------------------------------
# From pprint.pprint([ binascii.b2a_hex(os.urandom(32)) for _ in xrange(8) ])
RAND_INPUTS = [
'26c76712d89d906e6672dafa614c42e5cb1caac8c6568e4d2493087db51f0d36',
'fba7a5366b5cb98c2667a18783f5cf8f4f8d1a2ce939ad22a6e685edde85128d',
'67e3aa7a14fac8445d15e45e38a523481a69ae35513c9e4143eb1c2196729a0e',
'd51385942033a76dc17f089a59e6a5a7fe80d9c526ae8ddd8c3a506b99d3d0a6',
'5c8eac469bb3f1b85bc7cd893f52dc42a9ab66f1b02b5ce6a68e9b175d3bb433',
'eda433d483059b6d1ff8b7cfbd0fe406bfb23722c8f3c8252629284573b61b86',
'4377c40431c30883c5fbd9bc92ae48d1ed8a47b81d13806beac5351739b5533d',
'c6bbcce615839756aed2cc78b1de13884dd3618f48367a17597a16c1cd7a290b']
# From pprint.pprint([ binascii.b2a_hex(os.urandom(16)) for _ in xrange(8) ])
BLINDING_PARAMS = [
'54a513898b471d1d448a2f3c55c1de2c0ef718c447b04497eeb999ed32027823',
'831e9b5325b5d31b7ae6197e9c7a7baf2ec361e08248bce055908971047a2347',
'ac78a1d46faf3bfbbdc5af5f053dc6dc9023ed78236bec1760dadfd0b2603760',
'f9c84dc0ac31571507993df94da1b3d28684a12ad14e67d0a068aba5c53019fc',
'b1fe79d1dec9bc108df69f6612c72812755751f21ecc5af99663b30be8b9081f',
'81f1512b63ab5fb5c1711a4ec83d379c420574aedffa8c3368e1c3989a3a0084',
'97f45142597c473a4b0e9a12d64561133ad9e1155fe5a9807fe6af8a93557818',
'3f44f6a5a92cde816635dfc12ade70539871078d2ff097278be2a555c9859cd0']
PREFIX = "ED25519_"
def writeArray(name, array):
print "static const char *{prefix}{name}[] = {{".format(
prefix=PREFIX,name=name)
for a in array:
h = binascii.b2a_hex(a)
if len(h) > 70:
h1 = h[:70]
h2 = h[70:]
print ' "{0}"\n "{1}",'.format(h1,h2)
else:
print ' "{0}",'.format(h)
print "};\n"
def makeTestVectors():
secretKeys = [ binascii.a2b_hex(r) for r in RAND_INPUTS ]
writeArray("SECRET_KEYS", secretKeys)
expandedSecretKeys = [ expandSK(sk) for sk in secretKeys ]
writeArray("EXPANDED_SECRET_KEYS", expandedSecretKeys)
publicKeys = [ publickey(sk) for sk in secretKeys ]
writeArray("PUBLIC_KEYS", publicKeys)
writeArray("CURVE25519_PUBLIC_KEYS",
(slownacl_curve25519.smult_curve25519_base(sk[:32])
for sk in expandedSecretKeys))
blindingParams = [ binascii.a2b_hex(r) for r in BLINDING_PARAMS ]
writeArray("BLINDING_PARAMS", blindingParams)
writeArray("BLINDED_SECRET_KEYS",
(blindESK(expandSK(sk), bp)
for sk,bp in zip(secretKeys,blindingParams)))
writeArray("BLINDED_PUBLIC_KEYS",
(blindPK(pk, bp) for pk,bp in zip(publicKeys,blindingParams)))
writeArray("SELF_SIGNATURES",
(signature(pk, sk, pk) for pk,sk in zip(publicKeys,secretKeys)))
if __name__ == '__main__':
import sys
if len(sys.argv) == 1 or sys.argv[1] not in ("SelfTest", "MakeVectors"):
print "You should specify one of 'SelfTest' or 'MakeVectors'"
sys.exit(1)
if sys.argv[1] == 'SelfTest':
unittest.main()
else:
makeTestVectors()
|
