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irreducible polynomials work

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This commit is contained in:
Mirek Kratochvil 2012-04-02 00:44:19 +02:00
parent 5cbbaa2151
commit c47a651d0f
2 changed files with 32 additions and 13 deletions
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7
include/codecrypt.h
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@ -35,8 +35,8 @@ public:
class prng class prng
{ {
public: public:
virtual int random (uint) = 0; virtual uint random (uint) = 0;
virtual void request_seed (uint) = 0; virtual void seed (uint) = 0;
}; };
/* /*
@ -80,7 +80,8 @@ class polynomial : public bvector
{ {
public: public:
void strip(); void strip();
uint degree() const; int degree() const;
bool zero() const;
void add (const polynomial&); void add (const polynomial&);
void mod (const polynomial&); void mod (const polynomial&);
void mult (const polynomial&); void mult (const polynomial&);

38
lib/polynomial.cpp
View file

@ -3,9 +3,19 @@
using namespace ccr; using namespace ccr;
uint polynomial::degree() const #if 0
#include <iostream>
using namespace std;
void dump (const polynomial&t)
{ {
uint r = -1; for (uint i = 0; i < t.size(); ++i) cout << t[i];
cout << endl;
}
#endif
int polynomial::degree() const
{
int r = -1;
for (uint i = 0; i < size(); ++i) if (item (i) ) r = i; for (uint i = 0; i < size(); ++i) if (item (i) ) r = i;
return r; return r;
} }
@ -15,20 +25,26 @@ void polynomial::strip()
resize (degree() + 1); resize (degree() + 1);
} }
bool polynomial::zero() const
{
for (uint i = 0; i < size(); ++i) if (item (i) ) return false;
return true;
}
void polynomial::add (const polynomial&f) void polynomial::add (const polynomial&f)
{ {
uint df = f.degree(); int df = f.degree();
if (df > degree() ) resize (df + 1); if (df > degree() ) resize (df + 1);
for (uint i = 0; i <= df; ++i) item (i) = item (i) ^ f[i]; for (int i = 0; i <= df; ++i) item (i) = item (i) ^ f[i];
} }
void polynomial::mod (const polynomial&f) void polynomial::mod (const polynomial&f)
{ {
uint df = f.degree(); int df = f.degree();
uint d; int d;
// while there's place to substract, reduce by x^(d-df)-multiply of f // while there's place to substract, reduce by x^(d-df)-multiply of f
while ( (d = degree() ) >= df) { while ( (d = degree() ) >= df) {
for (uint i = 0; i <= df; ++i) for (int i = 0; i <= df; ++i)
item (i + d - df) = item (i + d - df) ^ f[i]; item (i + d - df) = item (i + d - df) ^ f[i];
} }
strip(); strip();
@ -54,9 +70,9 @@ polynomial polynomial::gcd (polynomial b)
//eukleides //eukleides
if (a.degree() < 0) return b; if (a.degree() < 0) return b;
for (;;) { for (;;) {
if (b.degree() < 0) return a; if (b.zero() ) return a;
a.mod (b); a.mod (b);
if (a.degree() < 0) return b; if (a.zero() ) return b;
b.mod (a); b.mod (a);
} }
//unreachable //unreachable
@ -69,15 +85,17 @@ bool polynomial::is_irreducible()
polynomial xi; //x^(2^i) in our case polynomial xi; //x^(2^i) in our case
polynomial xmodf, t; polynomial xmodf, t;
xmodf.resize (2); //precompute (x mod f) xmodf.resize (2); //precompute (x mod f) although it is usually just x
xmodf[0] = 0; xmodf[0] = 0;
xmodf[1] = 1; //x xmodf[1] = 1; //x
xi = xmodf;
xmodf.mod (*this); //mod f xmodf.mod (*this); //mod f
uint n = degree(); uint n = degree();
for (uint i = 1; i <= n / 2; ++i) { for (uint i = 1; i <= n / 2; ++i) {
t = xi; t = xi;
t.mult (xi); //because mult would destroy xi on xi.mult(xi) t.mult (xi); //because mult would destroy xi on xi.mult(xi)
t.mod(*this);
xi = t; xi = t;
t.add (xmodf); t.add (xmodf);