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
|
/*************************************************
* ECDSA Operation *
* (C) 2007 FlexSecure GmbH *
* 2008 Jack Lloyd *
*************************************************/
#include <botan/eng_def.h>
#include <botan/numthry.h>
namespace Botan {
bool Default_ECDSA_Op::verify(const byte signature[], u32bit sig_len,
const byte message[], u32bit mess_len) const
{
if(sig_len % 2 != 0)
throw Invalid_Argument("Erroneous length of signature");
//NOTE: it is not checked whether the public point is set
if(m_dom_pars.get_curve().get_p() == 0)
throw Internal_Error("domain parameters not set");
BigInt e(message, mess_len);
u32bit rs_len = sig_len/2;
SecureVector<byte> sv_r;
SecureVector<byte> sv_s;
sv_r.set(signature, rs_len);
sv_s.set(signature+rs_len, rs_len);
BigInt r = BigInt::decode ( sv_r, sv_r.size());
BigInt s = BigInt::decode (sv_s, sv_s.size());
if(r < 0 || r >= m_dom_pars.get_order())
throw Invalid_Argument("r in ECDSA signature has an illegal value");
if(s < 0 || s >= m_dom_pars.get_order())
throw Invalid_Argument("s in ECDSA signature has an illegal value");
BigInt w = inverse_mod(s, m_dom_pars.get_order());
PointGFp R = w*(e*m_dom_pars.get_base_point() + r*m_pub_key);
if(R.is_zero())
return false;
BigInt x = R.get_affine_x().get_value();
bool result = (x % m_dom_pars.get_order() == r);
return result;
}
SecureVector<byte> Default_ECDSA_Op::sign(const byte message[],
u32bit mess_len,
RandomNumberGenerator& rng) const
{
if(m_priv_key == 0)
throw Internal_Error("Default_ECDSA_Op::sign(): no private key");
if(m_dom_pars.get_curve().get_p() == 0)
throw Internal_Error("Default_ECDSA_Op::sign(): domain parameters not set");
BigInt e(message, mess_len);
// generate k
BigInt k;
BigInt r(0);
const BigInt n(m_dom_pars.get_order());
while(r == 0)
{
k = BigInt::random_integer(rng, 1, n);
PointGFp k_times_P(m_dom_pars.get_base_point());
k_times_P.mult_this_secure(k, n, n-1);
k_times_P.check_invariants();
r = k_times_P.get_affine_x().get_value() % n;
}
BigInt k_inv = inverse_mod(k, n);
// use randomization against attacks on s:
// a = k_inv * (r*(d + x) + e) mod n
// b = k_inv * r * x mod n
// s = a - b mod n
// where x is a random integer
#ifdef CMS_RAND
BigInt x = BigInt::random_integer(0, n);
BigInt s = m_priv_key + x; // obscure the secret from the beginning
// all following operations thus are randomized
s *= r;
s += e;
s *= k_inv;
s %= n;
BigInt b = x; // again, start with the random number
b *= r;
b *= k_inv;
b %= n;
s -= b; // s = a - b
if(s <= 0) // s %= n
{
s += n;
}
#else // CMS_RAND
// no countermeasure here
BigInt s(r);
s *= m_priv_key;
s += e;
s *= k_inv;
s %= n;
#endif // CMS_RAND
SecureVector<byte> sv_r = BigInt::encode_1363 ( r, m_dom_pars.get_order().bytes() );
SecureVector<byte> sv_s = BigInt::encode_1363 ( s, m_dom_pars.get_order().bytes() );
SecureVector<byte> result(sv_r);
result.append(sv_s);
return result;
}
Default_ECDSA_Op::Default_ECDSA_Op(const EC_Domain_Params& dom_pars, const BigInt& priv_key, const PointGFp& pub_key)
: m_dom_pars(dom_pars),
m_pub_key(pub_key),
m_priv_key(priv_key)
{
}
/*************************************************
* Acquire a ECDSA op *
*************************************************/
ECDSA_Operation* Default_Engine::ecdsa_op(const EC_Domain_Params& dom_pars,
const BigInt& priv_key,
const PointGFp& pub_key) const
{
return new Default_ECDSA_Op(dom_pars, priv_key, pub_key);
}
}
|
