/* 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 r=this mod b */
/* this is of length - 2*n */
/* r,b is of length - n */
public FF dmod(FF b)
{
int k, n = b.length;
FF m = new FF(2 * n);
FF x = new FF(2 * n);
FF r = new FF(n);
x.copy(this);
x.norm();
m.dsucopy(b);
k = 256 * n;
while (k > 0)
{
m.shr();
if (comp(x, m) >= 0)
{
x.sub(m);
x.norm();
}
k--;
}
r.copy(x);
r.mod(b);
return(r);
}
/* RSA decryption with the private key */
public static void DECRYPT(rsa_private_key PRIV, sbyte[] G, sbyte[] F)
{
int n = PRIV.p.getlen();
FF g = new FF(2 * n);
FF.fromBytes(g, G);
FF jp = g.dmod(PRIV.p);
FF jq = g.dmod(PRIV.q);
jp.skpow(PRIV.dp, PRIV.p);
jq.skpow(PRIV.dq, PRIV.q);
g.zero();
g.dscopy(jp);
jp.mod(PRIV.q);
if (FF.comp(jp, jq) > 0)
{
jq.add(PRIV.q);
}
jq.sub(jp);
jq.norm();
FF t = FF.mul(PRIV.c, jq);
jq = t.dmod(PRIV.q);
t = FF.mul(jq, PRIV.p);
g.add(t);
g.norm();
g.toBytes(F);
}
/* U=1/a mod 2^m - Arazi & Qi */
private FF invmod2m()
{
int i, n = length;
FF b = new FF(n);
FF c = new FF(n);
FF U = new FF(n);
FF t;
U.zero();
U.v[0].copy(v[0]);
U.v[0].invmod2m();
for (i = 1; i < n; i <<= 1)
{
b.copy(this);
b.mod2m(i);
t = mul(U, b);
t.shrw(i);
b.copy(t);
c.copy(this);
c.shrw(i);
c.mod2m(i);
c.lmul(U);
c.mod2m(i);
b.add(c);
b.norm();
b.lmul(U);
b.mod2m(i);
c.one();
c.shlw(i);
b.revsub(c);
b.norm();
b.shlw(i);
U.add(b);
}
U.norm();
return(U);
}
/* return This mod modulus, N is modulus, ND is Montgomery Constant */
public FF reduce(FF N, FF ND)
{ // fast karatsuba Montgomery reduction
int n = N.length;
FF t = new FF(2 * n);
FF r = new FF(n);
FF m = new FF(n);
r.sducopy(this);
m.karmul_lower(0, this, 0, ND, 0, t, 0, n);
karmul_upper(N, m, t, n);
m.sducopy(this);
r.add(N);
r.sub(m);
r.norm();
return(r);
}
/* 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);
}