120 lines
1.7 KiB
C++
120 lines
1.7 KiB
C++
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#include "codecrypt.h"
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using namespace ccr;
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/*
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* helpful stuff for arithmetic in GF(2^m) - polynomials over GF(2).
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*/
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int gf2p_degree (uint p)
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{
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int r = -1;
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for (int i = 0; p; p >>= 1, ++i) r = i;
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return r;
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}
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inline uint gf2p_add (uint a, uint b)
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{
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return a ^ b;
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}
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uint gf2p_mod (uint a, uint p)
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{
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if (!p) return 0;
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int t, degp = gf2p_degree (p);
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while ( (t = gf2p_degree (a) ) >= degp) {
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a ^= p << (t - degp);
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}
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return a;
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}
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uint gf2p_gcd (uint a, uint b)
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{
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uint c;
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if (!a) return b;
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while (b) {
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c = gf2p_mod (a, b);
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a = b;
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b = c;
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}
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return a;
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}
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uint gf2p_modmult (uint a, uint b, uint p)
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{
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a = gf2p_mod (a, p);
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b = gf2p_mod (b, p);
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uint r = 0;
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uint d = 1 << gf2p_degree (p);
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while (a) {
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if (a & 1) r ^= b;
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a >>= 1;
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b <<= 1;
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if (b >= d) b ^= p;
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}
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return r;
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}
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bool is_irreducible_gf2_poly (uint p)
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{
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if (!p) return false;
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int d = gf2p_degree (p) / 2;
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uint test = 2; //x^1+0
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for (int i = 0; i < d; ++i) {
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test = gf2p_modmult (test, test, p);
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if (gf2p_gcd (test ^ 2 /* test - x^1 */, p) != 1)
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return false;
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}
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return true;
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}
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bool gf2m::create (uint M)
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{
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if (M < 1) return false; //too small.
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m = M;
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n = 1 << m;
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if (!n) return false; //too big.
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for (uint t = 1 + (1 << m), e = 1 << (1 + m); t < e; t += 2)
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if (is_irreducible_gf2_poly (t) ) {
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poly = t;
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return true;
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}
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return false;
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}
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uint gf2m::add (uint a, uint b)
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{
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return gf2p_add (a, b);
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}
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uint gf2m::mult (uint a, uint b)
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{
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return gf2p_modmult (a, b, poly);
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}
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uint gf2m::exp (uint a, sint k)
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{
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if (!a) return 0;
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if (a == 1) return 1;
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if (k < 0) {
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a = inv (a);
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k = -k;
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}
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uint r = 1;
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while (k) {
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if (k & 1) r = mult (r, a);
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a = mult (a, a);
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k >>= 1;
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}
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return r;
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}
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uint gf2m::inv (uint a)
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{
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if (n == 2) return a;
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return exp (a, n - 2);
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}
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