121 lines
2.3 KiB
C++
121 lines
2.3 KiB
C++
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#include "codecrypt.h"
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using namespace ccr;
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#if 0
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#include <iostream>
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using namespace std;
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void dump (const polynomial&t)
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{
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for (uint i = 0; i < t.size(); ++i) cout << t[i];
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cout << endl;
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}
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#endif
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int polynomial::degree() const
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{
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int r = -1;
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for (uint i = 0; i < size(); ++i) if (item (i) ) r = i;
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return r;
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}
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void polynomial::strip()
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{
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resize (degree() + 1);
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}
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bool polynomial::zero() const
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{
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for (uint i = 0; i < size(); ++i) if (item (i) ) return false;
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return true;
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}
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void polynomial::add (const polynomial&f)
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{
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int df = f.degree();
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if (df > degree() ) resize (df + 1);
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for (int i = 0; i <= df; ++i) item (i) = item (i) ^ f[i];
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}
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void polynomial::mod (const polynomial&f)
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{
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int df = f.degree();
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int d;
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// while there's place to substract, reduce by x^(d-df)-multiply of f
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while ( (d = degree() ) >= df) {
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for (int i = 0; i <= df; ++i)
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item (i + d - df) = item (i + d - df) ^ f[i];
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}
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strip();
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}
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void polynomial::mult (const polynomial&b)
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{
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polynomial a = *this;
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clear();
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uint i, j, da, db;
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da = a.degree();
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db = b.degree();
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resize (da + db + 1, 0);
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for (i = 0; i <= da; ++i)
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if (a[i]) for (j = 0; j <= db; ++j)
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item (i + j) = item (i + j) ^ b[j];
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}
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polynomial polynomial::gcd (polynomial b)
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{
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polynomial a = *this;
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//eukleides
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if (a.degree() < 0) return b;
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for (;;) {
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if (b.zero() ) return a;
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a.mod (b);
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if (a.zero() ) return b;
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b.mod (a);
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}
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//unreachable
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return polynomial();
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}
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bool polynomial::is_irreducible()
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{
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//Ben-Or irreducibility test
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polynomial xi; //x^(2^i) in our case
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polynomial xmodf, t;
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xmodf.resize (2); //precompute (x mod f) although it is usually just x
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xmodf[0] = 0;
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xmodf[1] = 1; //x
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xi = xmodf;
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xmodf.mod (*this); //mod f
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uint n = degree();
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for (uint i = 1; i <= n / 2; ++i) {
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t = xi;
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t.mult (xi); //because mult would destroy xi on xi.mult(xi)
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t.mod(*this);
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xi = t;
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t.add (xmodf);
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t = t.gcd (*this);
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if (t.degree() != 0) //gcd(f,x^2^i - x mod f) != 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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void polynomial::generate_random_irreducible (uint s, prng & rng)
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{
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resize (s + 1);
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item (s) = 1; //degree s
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item (0) = 1; //not divisible by x^1
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for (uint i = 1; i < s; ++i) item (i) = rng.random (2);
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while (!is_irreducible() ) {
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uint pos = 1 + rng.random (s - 1);
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item (pos) = !item (pos);
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}
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}
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