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
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
|
/*
* (C) Copyright Projet SECRET, INRIA, Rocquencourt
* (C) Bhaskar Biswas and Nicolas Sendrier
*
* (C) 2014 cryptosource GmbH
* (C) 2014 Falko Strenzke fstrenzke@cryptosource.de
*
* Botan is released under the Simplified BSD License (see license.txt)
*
*/
#include <botan/internal/mce_internal.h>
#include <botan/internal/code_based_util.h>
namespace Botan {
namespace {
void matrix_arr_mul(std::vector<uint32_t> matrix,
uint32_t numo_rows,
uint32_t words_per_row,
const uint8_t* input_vec,
uint32_t* output_vec, uint32_t output_vec_len)
{
for(size_t j = 0; j < numo_rows; j++)
{
if((input_vec[j / 8] >> (j % 8)) & 1)
{
for(size_t i = 0; i < output_vec_len; i ++)
{
output_vec[i] ^= matrix[ j * (words_per_row) + i];
}
}
}
}
/**
* returns the error vector to the syndrome
*/
secure_vector<gf2m> goppa_decode(const polyn_gf2m & syndrom_polyn,
const polyn_gf2m & g,
const std::vector<polyn_gf2m> & sqrtmod,
const std::vector<gf2m> & Linv)
{
gf2m a;
uint32_t code_length = Linv.size();
uint32_t t = g.get_degree();
std::shared_ptr<GF2m_Field> sp_field = g.get_sp_field();
std::pair<polyn_gf2m, polyn_gf2m> h_aux = polyn_gf2m::eea_with_coefficients( syndrom_polyn, g, 1);
polyn_gf2m & h = h_aux.first;
polyn_gf2m & aux = h_aux.second;
a = sp_field->gf_inv(aux.get_coef(0));
gf2m log_a = sp_field->gf_log(a);
for(int i = 0; i <= h.get_degree(); ++i)
{
h.set_coef(i,sp_field->gf_mul_zrz(log_a,h.get_coef(i)));
}
// compute h(z) += z
h.add_to_coef( 1, 1);
// compute S square root of h (using sqrtmod)
polyn_gf2m S(t - 1, g.get_sp_field());
for(uint32_t i=0;i<t;i++)
{
a = sp_field->gf_sqrt(h.get_coef(i));
if(i & 1)
{
for(uint32_t j=0;j<t;j++)
{
S.add_to_coef( j, sp_field->gf_mul(a, sqrtmod[i/2].get_coef(j)));
}
}
else
{
S.add_to_coef( i/2, a);
}
} /* end for loop (i) */
S.get_degree();
std::pair<polyn_gf2m, polyn_gf2m> v_u = polyn_gf2m::eea_with_coefficients(S, g, t/2+1);
polyn_gf2m & u = v_u.second;
polyn_gf2m & v = v_u.first;
// sigma = u^2+z*v^2
polyn_gf2m sigma ( t , g.get_sp_field());
const size_t u_deg = u.get_degree();
for(size_t i = 0; i <= u_deg; ++i)
{
sigma.set_coef(2*i, sp_field->gf_square(u.get_coef(i)));
}
const int v_deg = v.get_degree();
BOTAN_ASSERT(v_deg > 0, "Valid degree");
for(int i = 0; i <= v_deg; ++i)
{
sigma.set_coef(2*i+1, sp_field->gf_square(v.get_coef(i)));
}
secure_vector<gf2m> res = find_roots_gf2m_decomp(sigma, code_length);
size_t d = res.size();
secure_vector<gf2m> result(d);
for(uint32_t i = 0; i < d; ++i)
{
gf2m current = res[i];
gf2m tmp;
tmp = gray_to_lex(current);
if(tmp >= code_length) /* invalid root */
{
result[i] = i;
}
result[i] = Linv[tmp];
}
return result;
}
}
void mceliece_decrypt(secure_vector<uint8_t>& plaintext_out,
secure_vector<uint8_t>& error_mask_out,
const secure_vector<uint8_t>& ciphertext,
const McEliece_PrivateKey& key)
{
mceliece_decrypt(plaintext_out, error_mask_out, ciphertext.data(), ciphertext.size(), key);
}
void mceliece_decrypt(
secure_vector<uint8_t>& plaintext,
secure_vector<uint8_t> & error_mask,
const uint8_t ciphertext[],
size_t ciphertext_len,
const McEliece_PrivateKey & key)
{
secure_vector<gf2m> error_pos;
plaintext = mceliece_decrypt(error_pos, ciphertext, ciphertext_len, key);
const size_t code_length = key.get_code_length();
secure_vector<uint8_t> result((code_length+7)/8);
for(auto&& pos : error_pos)
{
if(pos > code_length)
{
throw Invalid_Argument("error position larger than code size");
}
result[pos / 8] |= (1 << (pos % 8));
}
error_mask = result;
}
/**
* @p p_err_pos_len must point to the available length of @p error_pos on input, the
* function will set it to the actual number of errors returned in the @p error_pos
* array */
secure_vector<uint8_t> mceliece_decrypt(
secure_vector<gf2m> & error_pos,
const uint8_t *ciphertext, uint32_t ciphertext_len,
const McEliece_PrivateKey & key)
{
uint32_t dimension = key.get_dimension();
uint32_t codimension = key.get_codimension();
uint32_t t = key.get_goppa_polyn().get_degree();
polyn_gf2m syndrome_polyn(key.get_goppa_polyn().get_sp_field()); // init as zero polyn
const unsigned unused_pt_bits = dimension % 8;
const uint8_t unused_pt_bits_mask = (1 << unused_pt_bits) - 1;
if(ciphertext_len != (key.get_code_length()+7)/8)
{
throw Invalid_Argument("wrong size of McEliece ciphertext");
}
uint32_t cleartext_len = (key.get_message_word_bit_length()+7)/8;
if(cleartext_len != bit_size_to_byte_size(dimension))
{
throw Invalid_Argument("mce-decryption: wrong length of cleartext buffer");
}
secure_vector<uint32_t> syndrome_vec(bit_size_to_32bit_size(codimension));
matrix_arr_mul(key.get_H_coeffs(),
key.get_code_length(),
bit_size_to_32bit_size(codimension),
ciphertext,
syndrome_vec.data(), syndrome_vec.size());
secure_vector<uint8_t> syndrome_byte_vec(bit_size_to_byte_size(codimension));
uint32_t syndrome_byte_vec_size = syndrome_byte_vec.size();
for(uint32_t i = 0; i < syndrome_byte_vec_size; i++)
{
syndrome_byte_vec[i] = syndrome_vec[i/4] >> (8* (i % 4));
}
syndrome_polyn = polyn_gf2m(t-1, syndrome_byte_vec.data(), bit_size_to_byte_size(codimension), key.get_goppa_polyn().get_sp_field());
syndrome_polyn.get_degree();
error_pos = goppa_decode(syndrome_polyn, key.get_goppa_polyn(), key.get_sqrtmod(), key.get_Linv());
uint32_t nb_err = error_pos.size();
secure_vector<uint8_t> cleartext(cleartext_len);
copy_mem(cleartext.data(), ciphertext, cleartext_len);
for(uint32_t i = 0; i < nb_err; i++)
{
gf2m current = error_pos[i];
if(current >= cleartext_len * 8)
{
// an invalid position, this shouldn't happen
continue;
}
cleartext[current / 8] ^= (1 << (current % 8));
}
if(unused_pt_bits)
{
cleartext[cleartext_len - 1] &= unused_pt_bits_mask;
}
return cleartext;
}
}
|
