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
207
208
|
/*
* ECKCDSA (ISO/IEC 14888-3:2006/Cor.2:2009)
* (C) 2016 René Korthaus, Sirrix AG
* (C) 2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/eckcdsa.h>
#include <botan/internal/pk_ops_impl.h>
#include <botan/internal/point_mul.h>
#include <botan/keypair.h>
#include <botan/reducer.h>
#include <botan/emsa.h>
#include <botan/hash.h>
#include <botan/rng.h>
namespace Botan {
bool ECKCDSA_PrivateKey::check_key(RandomNumberGenerator& rng,
bool strong) const
{
if(!public_point().on_the_curve())
{
return false;
}
if(!strong)
{
return true;
}
return KeyPair::signature_consistency_check(rng, *this, "EMSA1(SHA-256)");
}
namespace {
/**
* ECKCDSA signature operation
*/
class ECKCDSA_Signature_Operation final : public PK_Ops::Signature_with_EMSA
{
public:
ECKCDSA_Signature_Operation(const ECKCDSA_PrivateKey& eckcdsa,
const std::string& emsa) :
PK_Ops::Signature_with_EMSA(emsa),
m_group(eckcdsa.domain()),
m_x(eckcdsa.private_value()),
m_prefix()
{
const BigInt public_point_x = eckcdsa.public_point().get_affine_x();
const BigInt public_point_y = eckcdsa.public_point().get_affine_y();
m_prefix.resize(public_point_x.bytes() + public_point_y.bytes());
public_point_x.binary_encode(m_prefix.data());
public_point_y.binary_encode(&m_prefix[public_point_x.bytes()]);
m_prefix.resize(HashFunction::create(hash_for_signature())->hash_block_size()); // use only the "hash input block size" leftmost bits
}
secure_vector<uint8_t> raw_sign(const uint8_t msg[], size_t msg_len,
RandomNumberGenerator& rng) override;
size_t signature_length() const override { return 2*m_group.get_order_bytes(); }
size_t max_input_bits() const override { return m_group.get_order_bits(); }
bool has_prefix() override { return true; }
secure_vector<uint8_t> message_prefix() const override { return m_prefix; }
private:
const EC_Group m_group;
const BigInt& m_x;
secure_vector<uint8_t> m_prefix;
std::vector<BigInt> m_ws;
};
secure_vector<uint8_t>
ECKCDSA_Signature_Operation::raw_sign(const uint8_t msg[], size_t,
RandomNumberGenerator& rng)
{
const BigInt k = m_group.random_scalar(rng);
const BigInt k_times_P_x = m_group.blinded_base_point_multiply_x(k, rng, m_ws);
secure_vector<uint8_t> to_be_hashed(k_times_P_x.bytes());
k_times_P_x.binary_encode(to_be_hashed.data());
std::unique_ptr<EMSA> emsa = this->clone_emsa();
emsa->update(to_be_hashed.data(), to_be_hashed.size());
secure_vector<uint8_t> c = emsa->raw_data();
c = emsa->encoding_of(c, max_input_bits(), rng);
const BigInt r(c.data(), c.size());
xor_buf(c, msg, c.size());
BigInt w(c.data(), c.size());
w = m_group.mod_order(w);
const BigInt s = m_group.multiply_mod_order(m_x, k - w);
if(s.is_zero())
throw Internal_Error("During ECKCDSA signature generation created zero s");
secure_vector<uint8_t> output = BigInt::encode_1363(r, c.size());
output += BigInt::encode_1363(s, m_group.get_order_bytes());
return output;
}
/**
* ECKCDSA verification operation
*/
class ECKCDSA_Verification_Operation final : public PK_Ops::Verification_with_EMSA
{
public:
ECKCDSA_Verification_Operation(const ECKCDSA_PublicKey& eckcdsa,
const std::string& emsa) :
PK_Ops::Verification_with_EMSA(emsa),
m_group(eckcdsa.domain()),
m_gy_mul(m_group.get_base_point(), eckcdsa.public_point()),
m_prefix()
{
const BigInt public_point_x = eckcdsa.public_point().get_affine_x();
const BigInt public_point_y = eckcdsa.public_point().get_affine_y();
m_prefix.resize(public_point_x.bytes() + public_point_y.bytes());
public_point_x.binary_encode(&m_prefix[0]);
public_point_y.binary_encode(&m_prefix[public_point_x.bytes()]);
m_prefix.resize(HashFunction::create(hash_for_signature())->hash_block_size()); // use only the "hash input block size" leftmost bits
}
bool has_prefix() override { return true; }
secure_vector<uint8_t> message_prefix() const override { return m_prefix; }
size_t max_input_bits() const override { return m_group.get_order_bits(); }
bool with_recovery() const override { return false; }
bool verify(const uint8_t msg[], size_t msg_len,
const uint8_t sig[], size_t sig_len) override;
private:
const EC_Group m_group;
const PointGFp_Multi_Point_Precompute m_gy_mul;
secure_vector<uint8_t> m_prefix;
};
bool ECKCDSA_Verification_Operation::verify(const uint8_t msg[], size_t,
const uint8_t sig[], size_t sig_len)
{
const std::unique_ptr<HashFunction> hash = HashFunction::create(hash_for_signature());
//calculate size of r
const size_t order_bytes = m_group.get_order_bytes();
const size_t size_r = std::min(hash -> output_length(), order_bytes);
if(sig_len != size_r + order_bytes)
{
return false;
}
secure_vector<uint8_t> r(sig, sig + size_r);
// check that 0 < s < q
const BigInt s(sig + size_r, order_bytes);
if(s <= 0 || s >= m_group.get_order())
{
return false;
}
secure_vector<uint8_t> r_xor_e(r);
xor_buf(r_xor_e, msg, r.size());
BigInt w(r_xor_e.data(), r_xor_e.size());
w = m_group.mod_order(w);
const PointGFp q = m_gy_mul.multi_exp(w, s);
const BigInt q_x = q.get_affine_x();
secure_vector<uint8_t> c(q_x.bytes());
q_x.binary_encode(c.data());
std::unique_ptr<EMSA> emsa = this->clone_emsa();
emsa->update(c.data(), c.size());
secure_vector<uint8_t> v = emsa->raw_data();
Null_RNG rng;
v = emsa->encoding_of(v, max_input_bits(), rng);
return (v == r);
}
}
std::unique_ptr<PK_Ops::Verification>
ECKCDSA_PublicKey::create_verification_op(const std::string& params,
const std::string& provider) const
{
if(provider == "base" || provider.empty())
return std::unique_ptr<PK_Ops::Verification>(new ECKCDSA_Verification_Operation(*this, params));
throw Provider_Not_Found(algo_name(), provider);
}
std::unique_ptr<PK_Ops::Signature>
ECKCDSA_PrivateKey::create_signature_op(RandomNumberGenerator& /*rng*/,
const std::string& params,
const std::string& provider) const
{
if(provider == "base" || provider.empty())
return std::unique_ptr<PK_Ops::Signature>(new ECKCDSA_Signature_Operation(*this, params));
throw Provider_Not_Found(algo_name(), provider);
}
}
|
