public static PolynomZ2 GenerateIrreducablePolynomZ2(int m)
{
//random Polynom
bool found = false;
PolynomZ2 f;
do
{
Random r = new Random();
f = new PolynomZ2((1 + (1 << m)));
for (int i = 1; i < m; i++)
{
f.p |= r.Next(2) << i;
}
PolynomZ2 u = new PolynomZ2(2);
PolynomZ2 d;
bool Irreducable = true;
for (int i = 1; i <= m / 2; i++)
{
u = u * u % f;
d = GCD(f, u - new PolynomZ2(2));
if (d.CompareTo(new PolynomZ2(1)) != 0)
{
Irreducable = false;
}
}
if (Irreducable)
{
found = true;
}
} while (!found);
return(f);
}
static public PolynomZ2 operator -(PolynomZ2 a, PolynomZ2 b)
{
PolynomZ2 c = new PolynomZ2();
c.p = a.p ^ b.p;
return(c);
}
public static PolynomZ2 GCD(PolynomZ2 a, PolynomZ2 b)
{
if (b.p == 0)
{
return(a);
}
else
{
return(GCD(b, a % b));
}
}
public static PolynomZ2 operator %(PolynomZ2 a, PolynomZ2 b)
{
PolynomZ2 c = new PolynomZ2(a); // остатое
PolynomZ2 d = new PolynomZ2(0); // частнок
while (c.CompareTo(new PolynomZ2(0)) > 0 && c.Deg >= b.Deg)
{
d.p |= 1 << (c.Deg - b.Deg);
c.p ^= b.p << (c.Deg - b.Deg);
}
return(c);
}
public static PolynomZ2 operator /(PolynomZ2 a, PolynomZ2 b)
{
PolynomZ2 c = new PolynomZ2(a); // остаток
PolynomZ2 d = new PolynomZ2(0); // частнок
while (c.Deg >= b.Deg)
{
d.p |= 1 << (c.Deg - b.Deg);
c.p ^= b.p << (c.Deg - b.Deg);
}
return(d);
}
static public PolynomZ2 operator *(PolynomZ2 a, PolynomZ2 b)
{
PolynomZ2 c = new PolynomZ2();
for (int i = 0; i <= 31; i++)
{
if ((a.p >> i & 1) == 1)
{
c.p ^= b.p << i;
}
}
return(c);
}
public void xtime()
{
PolynomZ2 c = new PolynomZ2();
PolynomZ2 b = new PolynomZ2(0x02);
for (int i = 0; i <= 31; i++)
{
if ((this.p >> i & 1) == 1)
{
c.p ^= b.p << i;
}
}
this.p = c.p;
}
public PolynomZ2(PolynomZ2 a)
{
p = a.p;
}