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
|
/**
* (C) Copyright Projet SECRET, INRIA, Rocquencourt
* (C) Bhaskar Biswas and Nicolas Sendrier
*
* (C) 2014 cryptosource GmbH
* (C) 2014 Falko Strenzke fstrenzke@cryptosource.de
*
* Distributed under the terms of the Botan license
*
*/
#include <botan/internal/code_based_key_gen.h>
#include <botan/code_based_util.h>
#include <botan/gf2m_rootfind_dcmp.h>
#include <botan/internal/binary_matrix.h>
#include <botan/loadstor.h>
#include <botan/polyn_gf2m.h>
namespace Botan {
namespace {
void randomize_support(u32bit n, std::vector<gf2m> & L, RandomNumberGenerator & rng)
{
unsigned int i, j;
gf2m_small_m::gf2m tmp;
for (i = 0; i < n; ++i)
{
gf2m_small_m::gf2m rnd;
rng.randomize(reinterpret_cast<byte*>(&rnd), sizeof(rnd));
j = rnd % n; // no rejection sampling, but for useful code-based parameters with n <= 13 this seem tolerable
tmp = L[j];
L[j] = L[i];
L[i] = tmp;
}
}
std::unique_ptr<binary_matrix> generate_R(std::vector<gf2m> &L, polyn_gf2m* g, std::shared_ptr<gf2m_small_m::Gf2m_Field> sp_field, u32bit code_length, u32bit t )
{
//L- Support
//t- Number of errors
//n- Length of the Goppa code
//m- The extension degree of the GF
//g- The generator polynomial.
gf2m_small_m::gf2m x,y;
u32bit i,j,k,r,n;
std::vector<int> Laux(code_length);
n=code_length;
r=t*sp_field->get_extension_degree();
binary_matrix H(r, n) ;
for(i=0;i< n;i++)
{
x = g->eval(lex_to_gray(L[i]));//evaluate the polynomial at the point L[i].
x = sp_field->gf_inv(x);
y = x;
for(j=0;j<t;j++)
{
for(k=0;k<sp_field->get_extension_degree();k++)
{
if(y & (1<<k))
{
//the co-eff. are set in 2^0,...,2^11 ; 2^0,...,2^11 format along the rows/cols?
H.set_coef_to_one(j*sp_field->get_extension_degree()+ k,i);
}
}
y = sp_field->gf_mul(y,lex_to_gray(L[i]));
}
}//The H matrix is fed.
secure_vector<int> perm = H.row_reduced_echelon_form();
if (perm.size() == 0)
{
// result still is NULL
throw Invalid_State("could not bring matrix in row reduced echelon form");
}
std::unique_ptr<binary_matrix> result(new binary_matrix(n-r,r)) ;
for (i = 0; i < (*result).m_rown; ++i)
{
for (j = 0; j < (*result).m_coln; ++j)
{
if (H.coef(j,perm[i]))
{
result->toggle_coeff(i,j);
}
}
}
for (i = 0; i < code_length; ++i)
{
Laux[i] = L[perm[i]];
}
for (i = 0; i < code_length; ++i)
{
L[i] = Laux[i];
}
return result;
}
}
McEliece_PrivateKey generate_mceliece_key( RandomNumberGenerator & rng, u32bit ext_deg, u32bit code_length, u32bit t)
{
u32bit i, j, k, l;
std::unique_ptr<binary_matrix> R;
u32bit codimension = t * ext_deg;
if(code_length <= codimension)
{
throw Invalid_Argument("invalid McEliece parameters");
}
std::shared_ptr<gf2m_small_m::Gf2m_Field> sp_field ( new Gf2m_Field(ext_deg ));
//pick the support.........
std::vector<gf2m> L(code_length);
for(i=0;i<code_length;i++)
{
L[i]=i;
}
randomize_support(code_length,L,rng);
polyn_gf2m g(sp_field); // create as zero
bool success = false;
do
{
// create a random irreducible polynomial
g = polyn_gf2m (t, rng, sp_field);
try{
R = generate_R(L,&g, sp_field, code_length, t);
success = true;
}
catch(const Invalid_State &)
{
}
} while (!success);
std::vector<polyn_gf2m> sqrtmod = polyn_gf2m::sqrt_mod_init( g);
std::vector<polyn_gf2m> F = syndrome_init(g, L, code_length);
// Each F[i] is the (precomputed) syndrome of the error vector with
// a single '1' in i-th position.
// We do not store the F[i] as polynomials of degree t , but
// as binary vectors of length ext_deg * t (this will
// speed up the syndrome computation)
//
//
std::vector<u32bit> H(bit_size_to_32bit_size(codimension) * code_length );
u32bit* sk = &H[0];
for (i = 0; i < code_length; ++i)
{
for (l = 0; l < t; ++l)
{
k = (l * ext_deg) / 32;
j = (l * ext_deg) % 32;
sk[k] ^= F[i].get_coef( l) << j;
if (j + ext_deg > 32)
{
sk[k + 1] ^= F[i].get_coef( l) >> (32 - j);
}
}
sk += bit_size_to_32bit_size(codimension);
}
// We need the support L for decoding (decryption). In fact the
// inverse is needed
std::vector<gf2m> Linv(code_length) ;
for (i = 0; i < code_length; ++i)
{
Linv[L[i]] = i;
}
std::vector<byte> pubmat (R->m_alloc_size);
for(i = 0; i < R->m_alloc_size/4; i++)
{
store_le(R->m_elem[i], &pubmat[i*4] );
}
return McEliece_PrivateKey(g, H, sqrtmod, Linv, pubmat);
}
}
|
