/* quick and dirty check for common factor with n */
public bool cfactor(int s)
{
int r, n = length;
int g;
FF x = new FF(n);
FF y = new FF(n);
y.set(s);
x.copy(this);
x.norm();
do
{
x.sub(y);
x.norm();
while (!x.iszilch() && x.parity() == 0)
{
x.shr();
}
} while (comp(x, y) > 0);
g = (int)x.v[0].get(0);
r = igcd(s, g);
if (r > 1)
{
return(true);
}
return(false);
}
/* Set return=1/this mod p. Binary method - a<p on entry */
public void invmodp(FF p)
{
int n = p.length;
FF u = new FF(n);
FF v = new FF(n);
FF x1 = new FF(n);
FF x2 = new FF(n);
FF t = new FF(n);
FF one = new FF(n);
one.one();
u.copy(this);
v.copy(p);
x1.copy(one);
x2.zero();
// reduce n in here as well!
while (comp(u, one) != 0 && comp(v, one) != 0)
{
while (u.parity() == 0)
{
u.shr();
if (x1.parity() != 0)
{
x1.add(p);
x1.norm();
}
x1.shr();
}
while (v.parity() == 0)
{
v.shr();
if (x2.parity() != 0)
{
x2.add(p);
x2.norm();
}
x2.shr();
}
if (comp(u, v) >= 0)
{
u.sub(v);
u.norm();
if (comp(x1, x2) >= 0)
{
x1.sub(x2);
}
else
{
t.copy(p);
t.sub(x2);
x1.add(t);
}
x1.norm();
}
else
{
v.sub(u);
v.norm();
if (comp(x2, x1) >= 0)
{
x2.sub(x1);
}
else
{
t.copy(p);
t.sub(x1);
x2.add(t);
}
x2.norm();
}
}
if (comp(u, one) == 0)
{
copy(x1);
}
else
{
copy(x2);
}
}
/* Miller-Rabin test for primality. Slow. */
public static bool prime(FF p, RAND rng)
{
int i, j, s = 0, n = p.length;
bool loop;
FF d = new FF(n);
FF x = new FF(n);
FF unity = new FF(n);
FF nm1 = new FF(n);
int sf = 4849845; // 3*5*.. *19
p.norm();
if (p.cfactor(sf))
{
return(false);
}
unity.one();
nm1.copy(p);
nm1.sub(unity);
nm1.norm();
d.copy(nm1);
while (d.parity() == 0)
{
d.shr();
s++;
}
if (s == 0)
{
return(false);
}
for (i = 0; i < 10; i++)
{
x.randomnum(p, rng);
x.pow(d, p);
if (comp(x, unity) == 0 || comp(x, nm1) == 0)
{
continue;
}
loop = false;
for (j = 1; j < s; j++)
{
x.power(2, p);
if (comp(x, unity) == 0)
{
return(false);
}
if (comp(x, nm1) == 0)
{
loop = true;
break;
}
}
if (loop)
{
continue;
}
return(false);
}
return(true);
}