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
|
/*
* Rabin-Williams
* (C) 1999-2008 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#include <botan/rw.h>
#include <botan/numthry.h>
#include <botan/keypair.h>
#include <botan/look_pk.h>
#include <botan/parsing.h>
#include <algorithm>
namespace Botan {
/*
* Rabin-Williams Public Operation
*/
BigInt RW_PublicKey::public_op(const BigInt& i) const
{
if((i > (n >> 1)) || i.is_negative())
throw Invalid_Argument(algo_name() + "::public_op: i > n / 2 || i < 0");
BigInt r = core.public_op(i);
if(r % 16 == 12) return r;
if(r % 8 == 6) return 2*r;
r = n - r;
if(r % 16 == 12) return r;
if(r % 8 == 6) return 2*r;
throw Invalid_Argument(algo_name() + "::public_op: Invalid input");
}
/*
* Rabin-Williams Verification Function
*/
SecureVector<byte> RW_PublicKey::verify(const byte in[], u32bit len) const
{
BigInt i(in, len);
return BigInt::encode(public_op(i));
}
/*
* Create a Rabin-Williams private key
*/
RW_PrivateKey::RW_PrivateKey(RandomNumberGenerator& rng,
u32bit bits, u32bit exp)
{
if(bits < 512)
throw Invalid_Argument(algo_name() + ": Can't make a key that is only " +
to_string(bits) + " bits long");
if(exp < 2 || exp % 2 == 1)
throw Invalid_Argument(algo_name() + ": Invalid encryption exponent");
e = exp;
p = random_prime(rng, (bits + 1) / 2, e / 2, 3, 4);
q = random_prime(rng, bits - p.bits(), e / 2, ((p % 8 == 3) ? 7 : 3), 8);
d = inverse_mod(e, lcm(p - 1, q - 1) >> 1);
PKCS8_load_hook(rng, true);
if(n.bits() != bits)
throw Self_Test_Failure(algo_name() + " private key generation failed");
}
/*
* Rabin-Williams Signature Operation
*/
SecureVector<byte> RW_PrivateKey::sign(const byte in[], u32bit len,
RandomNumberGenerator&) const
{
BigInt i(in, len);
if(i >= n || i % 16 != 12)
throw Invalid_Argument(algo_name() + "::sign: Invalid input");
BigInt r;
if(jacobi(i, n) == 1) r = core.private_op(i);
else r = core.private_op(i >> 1);
r = std::min(r, n - r);
if(i != public_op(r))
throw Self_Test_Failure(algo_name() + " private operation check failed");
return BigInt::encode_1363(r, n.bytes());
}
/*
* Check Private Rabin-Williams Parameters
*/
bool RW_PrivateKey::check_key(RandomNumberGenerator& rng, bool strong) const
{
if(!IF_Scheme_PrivateKey::check_key(rng, strong))
return false;
if(!strong)
return true;
if((e * d) % (lcm(p - 1, q - 1) / 2) != 1)
return false;
try
{
KeyPair::check_key(rng,
get_pk_signer(*this, "EMSA2(SHA-1)"),
get_pk_verifier(*this, "EMSA2(SHA-1)")
);
}
catch(Self_Test_Failure)
{
return false;
}
return true;
}
}
|