/* a=1/a mod 2^256. This is very fast! */
public virtual void InvMod2m()
{
int i;
BIG U = new BIG(0);
BIG b = new BIG(0);
BIG c = new BIG(0);
U.Inc(InvMod256(LastBits(8)));
for (i = 8; i < BIGBITS; i <<= 1)
{
U.Norm();
b.Copy(this);
b.Mod2m(i);
BIG t1 = SMul(U, b);
t1.Shr(i);
c.Copy(this);
c.Shr(i);
c.Mod2m(i);
BIG t2 = SMul(U, c);
t2.Mod2m(i);
t1.Add(t2);
t1.Norm();
b = SMul(t1, U);
t1.Copy(b);
t1.Mod2m(i);
t2.One();
t2.Shl(i);
t1.RSub(t2);
t1.Norm();
t1.Shl(i);
U.Add(t1);
}
U.Mod2m(BIGBITS);
Copy(U);
Norm();
}
/* divide this by m */
public virtual void Div(BIG m1)
{
int d, k = 0;
Norm();
BIG e = new BIG(1);
BIG m = new BIG(m1);
BIG b = new BIG(this);
BIG r = new BIG(0);
Zero();
while (Comp(b, m) >= 0)
{
e.FShl(1);
m.FShl(1);
k++;
}
while (k > 0)
{
m.FShr(1);
e.FShr(1);
r.Copy(b);
r.Sub(m);
r.Norm();
d = (int)(1 - ((r.w[NLEN - 1] >> (CHUNK - 1)) & 1));
b.CMove(r, d);
r.Copy(this);
r.Add(e);
r.Norm();
CMove(r, d);
k--;
}
}
/* Return e.this+f.Q */
public ECP Mul2(BIG e, ECP Q, BIG f)
{
BIG te = new BIG();
BIG tf = new BIG();
BIG mt = new BIG();
ECP S = new ECP();
ECP T = new ECP();
ECP C = new ECP();
ECP[] W = new ECP[8];
sbyte[] w = new sbyte[1 + (BIG.NLEN * BIG.BASEBITS + 1) / 2];
int i, s, ns, nb;
sbyte a, b;
//affine();
//Q.affine();
te.Copy(e);
tf.Copy(f);
// precompute table
W[1] = new ECP();
W[1].Copy(this);
W[1].Sub(Q);
W[2] = new ECP();
W[2].Copy(this);
W[2].Add(Q);
S.Copy(Q);
S.Dbl();
W[0] = new ECP();
W[0].Copy(W[1]);
W[0].Sub(S);
W[3] = new ECP();
W[3].Copy(W[2]);
W[3].Add(S);
T.Copy(this);
T.Dbl();
W[5] = new ECP();
W[5].Copy(W[1]);
W[5].Add(T);
W[6] = new ECP();
W[6].Copy(W[2]);
W[6].Add(T);
W[4] = new ECP();
W[4].Copy(W[5]);
W[4].Sub(S);
W[7] = new ECP();
W[7].Copy(W[6]);
W[7].Add(S);
// if multiplier is odd, add 2, else add 1 to multiplier, and add 2P or P to correction
s = te.Parity();
te.Inc(1);
te.Norm();
ns = te.Parity();
mt.Copy(te);
mt.Inc(1);
mt.Norm();
te.CMove(mt, s);
T.CMove(this, ns);
C.Copy(T);
s = tf.Parity();
tf.Inc(1);
tf.Norm();
ns = tf.Parity();
mt.Copy(tf);
mt.Inc(1);
mt.Norm();
tf.CMove(mt, s);
S.CMove(Q, ns);
C.Add(S);
mt.Copy(te);
mt.Add(tf);
mt.Norm();
nb = 1 + (mt.NBits() + 1) / 2;
// convert exponent to signed 2-bit window
for (i = 0; i < nb; i++)
{
a = (sbyte)(te.LastBits(3) - 4);
te.Dec(a);
te.Norm();
te.FShr(2);
b = (sbyte)(tf.LastBits(3) - 4);
tf.Dec(b);
tf.Norm();
tf.FShr(2);
w[i] = (sbyte)(4 * a + b);
}
w[nb] = (sbyte)(4 * te.LastBits(3) + tf.LastBits(3));
S.Copy(W[(w[nb] - 1) / 2]);
for (i = nb - 1; i >= 0; i--)
{
T.Select(W, w[i]);
S.Dbl();
S.Dbl();
S.Add(T);
}
S.Sub(C); // apply correction
S.Affine();
return(S);
}
/* this=1/this mod p. Binary method */
public virtual void InvModp(BIG p)
{
Mod(p);
BIG u = new BIG(this);
BIG v = new BIG(p);
BIG x1 = new BIG(1);
BIG x2 = new BIG(0);
BIG t = new BIG(0);
BIG one = new BIG(1);
while (Comp(u, one) != 0 && Comp(v, one) != 0)
{
while (u.Parity() == 0)
{
u.FShr(1);
if (x1.Parity() != 0)
{
x1.Add(p);
x1.Norm();
}
x1.FShr(1);
}
while (v.Parity() == 0)
{
v.FShr(1);
if (x2.Parity() != 0)
{
x2.Add(p);
x2.Norm();
}
x2.FShr(1);
}
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);
}
}