132 lines
2.6 KiB
C++
132 lines
2.6 KiB
C++
|
|
/*
|
|
* This file is part of Codecrypt.
|
|
*
|
|
* Codecrypt is free software: you can redistribute it and/or modify it
|
|
* under the terms of the GNU Lesser General Public License as published by
|
|
* the Free Software Foundation, either version 3 of the License, or (at
|
|
* your option) any later version.
|
|
*
|
|
* Codecrypt is distributed in the hope that it will be useful, but WITHOUT
|
|
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
|
|
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
|
|
* License for more details.
|
|
*
|
|
* You should have received a copy of the GNU Lesser General Public License
|
|
* along with Codecrypt. If not, see <http://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
#include "gf2m.h"
|
|
|
|
/*
|
|
* helpful stuff for arithmetic in GF(2^m) - polynomials over GF(2).
|
|
*/
|
|
|
|
int gf2p_degree (uint p)
|
|
{
|
|
int r = 0;
|
|
while (p) {
|
|
++r;
|
|
p >>= 1;
|
|
}
|
|
return r - 1;
|
|
}
|
|
|
|
uint gf2p_mod (uint a, uint p)
|
|
{
|
|
if (!p) return 0;
|
|
int t, degp = gf2p_degree (p);
|
|
while ( (t = gf2p_degree (a)) >= degp) {
|
|
a ^= (p << (t - degp));
|
|
}
|
|
return a;
|
|
}
|
|
|
|
uint gf2p_gcd (uint a, uint b)
|
|
{
|
|
if (!a) return b;
|
|
while (b) {
|
|
uint c = gf2p_mod (a, b);
|
|
a = b;
|
|
b = c;
|
|
}
|
|
return a;
|
|
}
|
|
|
|
uint gf2p_modmult (uint a, uint b, uint p)
|
|
{
|
|
a = gf2p_mod (a, p);
|
|
b = gf2p_mod (b, p);
|
|
uint r = 0;
|
|
uint d = 1 << gf2p_degree (p);
|
|
if (b) while (a) {
|
|
if (a & 1) r ^= b;
|
|
a >>= 1;
|
|
b <<= 1;
|
|
if (b >= d) b ^= p;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
bool is_irreducible_gf2_poly (uint p)
|
|
{
|
|
if (!p) return false;
|
|
int d = gf2p_degree (p) / 2;
|
|
uint test = 2; //x^1+0
|
|
for (int i = 1; i <= d; ++i) {
|
|
test = gf2p_modmult (test, test, p);
|
|
|
|
if (gf2p_gcd (test ^ 2 /* test - x^1 */, p) != 1)
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool gf2m::create (uint M)
|
|
{
|
|
if (M < 1) return false; //too small.
|
|
m = M;
|
|
n = 1 << m;
|
|
if (!n) return false; //too big.
|
|
poly = 0;
|
|
|
|
/*
|
|
* find a conway polynomial for given degree. First we "filter out" the
|
|
* possibilities that cannot be conway (reducible ones), then we check
|
|
* that Z2[x]/poly is a field.
|
|
*/
|
|
for (uint t = (1 << m) + 1, e = 1 << (m + 1); t < e; t += 2) {
|
|
|
|
if (!is_irreducible_gf2_poly (t)) continue;
|
|
|
|
//try to prepare log and antilog tables
|
|
log.resize (n, 0);
|
|
antilog.resize (n, 0);
|
|
log[0] = n - 1;
|
|
antilog[n - 1] = 0;
|
|
|
|
uint i, xi = 1; //x^0
|
|
for (i = 0; i < n - 1; ++i) {
|
|
if (log[xi] != 0) { //not a cyclic group
|
|
log.clear();
|
|
antilog.clear();
|
|
break;
|
|
}
|
|
log[xi] = i;
|
|
antilog[i] = xi;
|
|
|
|
xi <<= 1; //multiply by x
|
|
xi = gf2p_mod (xi, t);
|
|
}
|
|
|
|
//if it broke...
|
|
if (i < n - 1) continue;
|
|
poly = t;
|
|
break;
|
|
}
|
|
|
|
if (!poly) return false;
|
|
|
|
return true;
|
|
}
|