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
|
/*
* Montgomery Exponentiation
* (C) 1999-2010,2012,2018 Jack Lloyd
* 2016 Matthias Gierlings
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/internal/monty_exp.h>
#include <botan/internal/ct_utils.h>
#include <botan/internal/rounding.h>
#include <botan/numthry.h>
#include <botan/reducer.h>
#include <botan/monty.h>
namespace Botan {
class Montgomery_Exponentation_State
{
public:
Montgomery_Exponentation_State(std::shared_ptr<const Montgomery_Params> params,
const BigInt& g,
size_t window_bits);
BigInt exponentiation(const BigInt& k) const;
private:
std::shared_ptr<const Montgomery_Params> m_params;
std::vector<Montgomery_Int> m_g;
size_t m_window_bits;
};
Montgomery_Exponentation_State::Montgomery_Exponentation_State(std::shared_ptr<const Montgomery_Params> params,
const BigInt& g,
size_t window_bits) :
m_params(params),
m_window_bits(window_bits == 0 ? 4 : window_bits)
{
if(m_window_bits < 1 || m_window_bits > 12) // really even 8 is too large ...
throw Invalid_Argument("Invalid window bits for Montgomery exponentiation");
const size_t window_size = (1U << m_window_bits);
m_g.reserve(window_size);
m_g.push_back(Montgomery_Int(m_params, m_params->R1(), false));
m_g.push_back(Montgomery_Int(m_params, g));
const Montgomery_Int& monty_g = m_g[1];
for(size_t i = 2; i != window_size; ++i)
{
m_g.push_back(monty_g * m_g[i - 1]);
}
// Resize each element to exactly p words
for(size_t i = 0; i != window_size; ++i)
{
m_g[i].fix_size();
}
}
namespace {
void const_time_lookup(secure_vector<word>& output,
const std::vector<Montgomery_Int>& g,
size_t nibble)
{
const size_t words = output.size();
clear_mem(output.data(), output.size());
for(size_t i = 0; i != g.size(); ++i)
{
const secure_vector<word>& vec = g[i].repr().get_word_vector();
BOTAN_ASSERT(vec.size() >= words,
"Word size as expected in const_time_lookup");
const word mask = CT::is_equal<word>(i, nibble);
for(size_t w = 0; w != words; ++w)
output[w] |= (mask & vec[w]);
}
}
}
BigInt Montgomery_Exponentation_State::exponentiation(const BigInt& scalar) const
{
const size_t exp_nibbles = (scalar.bits() + m_window_bits - 1) / m_window_bits;
Montgomery_Int x(m_params, m_params->R1(), false);
secure_vector<word> e_bits(m_params->p_words());
secure_vector<word> ws;
for(size_t i = exp_nibbles; i > 0; --i)
{
for(size_t j = 0; j != m_window_bits; ++j)
{
x.square_this(ws);
}
const uint32_t nibble = scalar.get_substring(m_window_bits*(i-1), m_window_bits);
const_time_lookup(e_bits, m_g, nibble);
x.mul_by(e_bits, ws);
}
return x.value();
}
std::shared_ptr<const Montgomery_Exponentation_State>
monty_precompute(std::shared_ptr<const Montgomery_Params> params,
const BigInt& g,
size_t window_bits)
{
return std::make_shared<const Montgomery_Exponentation_State>(params, g, window_bits);
}
BigInt monty_execute(const Montgomery_Exponentation_State& precomputed_state,
const BigInt& k)
{
return precomputed_state.exponentiation(k);
}
BigInt monty_multi_exp(std::shared_ptr<const Montgomery_Params> params_p,
const BigInt& x_bn,
const BigInt& z1,
const BigInt& y_bn,
const BigInt& z2)
{
if(z1.is_negative() || z2.is_negative())
throw Invalid_Argument("multi_exponentiate exponents must be positive");
const size_t z_bits = round_up(std::max(z1.bits(), z2.bits()), 2);
secure_vector<word> ws;
const Montgomery_Int one(params_p, params_p->R1(), false);
//const Montgomery_Int one(params_p, 1);
const Montgomery_Int x1(params_p, x_bn);
const Montgomery_Int x2 = x1.square(ws);
const Montgomery_Int x3 = x2.mul(x1, ws);
const Montgomery_Int y1(params_p, y_bn);
const Montgomery_Int y2 = y1.square(ws);
const Montgomery_Int y3 = y2.mul(y1, ws);
const Montgomery_Int y1x1 = y1.mul(x1, ws);
const Montgomery_Int y1x2 = y1.mul(x2, ws);
const Montgomery_Int y1x3 = y1.mul(x3, ws);
const Montgomery_Int y2x1 = y2.mul(x1, ws);
const Montgomery_Int y2x2 = y2.mul(x2, ws);
const Montgomery_Int y2x3 = y2.mul(x3, ws);
const Montgomery_Int y3x1 = y3.mul(x1, ws);
const Montgomery_Int y3x2 = y3.mul(x2, ws);
const Montgomery_Int y3x3 = y3.mul(x3, ws);
const Montgomery_Int* M[16] = {
&one,
&x1, // 0001
&x2, // 0010
&x3, // 0011
&y1, // 0100
&y1x1,
&y1x2,
&y1x3,
&y2, // 1000
&y2x1,
&y2x2,
&y2x3,
&y3, // 1100
&y3x1,
&y3x2,
&y3x3
};
Montgomery_Int H = one;
for(size_t i = 0; i != z_bits; i += 2)
{
if(i > 0)
{
H.square_this(ws);
H.square_this(ws);
}
const uint8_t z1_b = z1.get_substring(z_bits - i - 2, 2);
const uint8_t z2_b = z2.get_substring(z_bits - i - 2, 2);
const uint8_t z12 = (4*z2_b) + z1_b;
H.mul_by(*M[z12], ws);
}
return H.value();
}
}
|
