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
|
'''
RFC 6979:
Deterministic Usage of the Digital Signature Algorithm (DSA) and
Elliptic Curve Digital Signature Algorithm (ECDSA)
http://tools.ietf.org/html/rfc6979
Many thanks to Coda Hale for his implementation in Go language:
https://github.com/codahale/rfc6979
'''
import hmac
from binascii import hexlify
from util import number_to_string, number_to_string_crop
try:
bin(0)
except NameError:
binmap = {"0": "0000", "1": "0001", "2": "0010", "3": "0011",
"4": "0100", "5": "0101", "6": "0110", "7": "0111",
"8": "1000", "9": "1001", "a": "1010", "b": "1011",
"c": "1100", "d": "1101", "e": "1110", "f": "1111"}
def bin(value): # for python2.5
v = "".join(binmap[x] for x in "%x"%abs(value)).lstrip("0")
if value < 0:
return "-0b" + v
return "0b" + v
def bit_length(num):
# http://docs.python.org/dev/library/stdtypes.html#int.bit_length
s = bin(num) # binary representation: bin(-37) --> '-0b100101'
s = s.lstrip('-0b') # remove leading zeros and minus sign
return len(s) # len('100101') --> 6
def bits2int(data, qlen):
x = int(hexlify(data), 16)
l = len(data) * 8
if l > qlen:
return x >> (l-qlen)
return x
def bits2octets(data, order):
z1 = bits2int(data, bit_length(order))
z2 = z1 - order
if z2 < 0:
z2 = z1
return number_to_string_crop(z2, order)
# https://tools.ietf.org/html/rfc6979#section-3.2
def generate_k(generator, secexp, hash_func, data):
'''
generator - ECDSA generator used in the signature
secexp - secure exponent (private key) in numeric form
hash_func - reference to the same hash function used for generating hash
data - hash in binary form of the signing data
'''
qlen = bit_length(generator.order())
holen = hash_func().digestsize
rolen = (qlen + 7) / 8
bx = number_to_string(secexp, generator.order()) + bits2octets(data, generator.order())
# Step B
v = '\x01' * holen
# Step C
k = '\x00' * holen
# Step D
k = hmac.new(k, v+'\x00'+bx, hash_func).digest()
# Step E
v = hmac.new(k, v, hash_func).digest()
# Step F
k = hmac.new(k, v+'\x01'+bx, hash_func).digest()
# Step G
v = hmac.new(k, v, hash_func).digest()
# Step H
while True:
# Step H1
t = ''
# Step H2
while len(t) < rolen:
v = hmac.new(k, v, hash_func).digest()
t += v
# Step H3
secret = bits2int(t, qlen)
if secret >= 1 and secret < generator.order():
return secret
k = hmac.new(k, v+'\x00', hash_func).digest()
v = hmac.new(k, v, hash_func).digest()
|
