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
|
/*
* SRP-6a (RFC 5054 compatatible)
* (C) 2011,2012 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#include <botan/srp6.h>
#include <botan/dl_group.h>
#include <botan/libstate.h>
#include <botan/numthry.h>
#include <memory>
namespace Botan {
namespace {
BigInt hash_seq(const std::string& hash_id,
size_t pad_to,
const BigInt& in1,
const BigInt& in2)
{
std::unique_ptr<HashFunction> hash_fn(
global_state().algorithm_factory().make_hash_function(hash_id));
hash_fn->update(BigInt::encode_1363(in1, pad_to));
hash_fn->update(BigInt::encode_1363(in2, pad_to));
return BigInt::decode(hash_fn->final());
}
BigInt hash_seq(const std::string& hash_id,
size_t pad_to,
const BigInt& in1,
const BigInt& in2,
const BigInt& in3)
{
std::unique_ptr<HashFunction> hash_fn(
global_state().algorithm_factory().make_hash_function(hash_id));
hash_fn->update(BigInt::encode_1363(in1, pad_to));
hash_fn->update(BigInt::encode_1363(in2, pad_to));
hash_fn->update(BigInt::encode_1363(in3, pad_to));
return BigInt::decode(hash_fn->final());
}
BigInt compute_x(const std::string& hash_id,
const std::string& identifier,
const std::string& password,
const std::vector<byte>& salt)
{
std::unique_ptr<HashFunction> hash_fn(
global_state().algorithm_factory().make_hash_function(hash_id));
hash_fn->update(identifier);
hash_fn->update(":");
hash_fn->update(password);
secure_vector<byte> inner_h = hash_fn->final();
hash_fn->update(salt);
hash_fn->update(inner_h);
secure_vector<byte> outer_h = hash_fn->final();
return BigInt::decode(outer_h);
}
}
std::string srp6_group_identifier(const BigInt& N, const BigInt& g)
{
/*
This function assumes that only one 'standard' SRP parameter set has
been defined for a particular bitsize. As of this writing that is the case.
*/
try
{
const std::string group_name = "modp/srp/" + std::to_string(N.bits());
DL_Group group(group_name);
if(group.get_p() == N && group.get_g() == g)
return group_name;
throw std::runtime_error("Unknown SRP params");
}
catch(...)
{
throw Invalid_Argument("Bad SRP group parameters");
}
}
std::pair<BigInt, SymmetricKey>
srp6_client_agree(const std::string& identifier,
const std::string& password,
const std::string& group_id,
const std::string& hash_id,
const std::vector<byte>& salt,
const BigInt& B,
RandomNumberGenerator& rng)
{
DL_Group group(group_id);
const BigInt& g = group.get_g();
const BigInt& p = group.get_p();
const size_t p_bytes = group.get_p().bytes();
if(B % p == 0)
throw std::runtime_error("Invalid SRP parameter from server");
BigInt k = hash_seq(hash_id, p_bytes, p, g);
BigInt a(rng, 256);
BigInt A = power_mod(g, a, p);
BigInt u = hash_seq(hash_id, p_bytes, A, B);
const BigInt x = compute_x(hash_id, identifier, password, salt);
BigInt S = power_mod((B - (k * power_mod(g, x, p))) % p, (a + (u * x)), p);
SymmetricKey Sk(BigInt::encode_1363(S, p_bytes));
return std::make_pair(A, Sk);
}
BigInt generate_srp6_verifier(const std::string& identifier,
const std::string& password,
const std::vector<byte>& salt,
const std::string& group_id,
const std::string& hash_id)
{
const BigInt x = compute_x(hash_id, identifier, password, salt);
DL_Group group(group_id);
return power_mod(group.get_g(), x, group.get_p());
}
BigInt SRP6_Server_Session::step1(const BigInt& v,
const std::string& group_id,
const std::string& hash_id,
RandomNumberGenerator& rng)
{
DL_Group group(group_id);
const BigInt& g = group.get_g();
const BigInt& p = group.get_p();
p_bytes = p.bytes();
BigInt k = hash_seq(hash_id, p_bytes, p, g);
BigInt b(rng, 256);
B = (v*k + power_mod(g, b, p)) % p;
this->v = v;
this->b = b;
this->p = p;
this->hash_id = hash_id;
return B;
}
SymmetricKey SRP6_Server_Session::step2(const BigInt& A)
{
if(A % p == 0)
throw std::runtime_error("Invalid SRP parameter from client");
BigInt u = hash_seq(hash_id, p_bytes, A, B);
BigInt S = power_mod(A * power_mod(v, u, p), b, p);
return BigInt::encode_1363(S, p_bytes);
}
}
|
