/* copy this=P */
public void copy(ECP2 P)
{
x.copy(P.x);
y.copy(P.y);
z.copy(P.z);
INF = P.INF;
}
/* this*=y */
public void mul(FP4 y)
{
norm();
FP2 t1 = new FP2(a);
FP2 t2 = new FP2(b);
FP2 t3 = new FP2(0);
FP2 t4 = new FP2(b);
t1.mul(y.a);
t2.mul(y.b);
t3.copy(y.b);
t3.add(y.a);
t4.add(a);
t4.mul(t3);
t4.sub(t1);
// t4.norm();
b.copy(t4);
b.sub(t2);
t2.mul_ip();
a.copy(t2);
a.add(t1);
norm();
}
/* this*=this */
public void sqr()
{
norm();
FP2 t1 = new FP2(a);
FP2 t2 = new FP2(b);
FP2 t3 = new FP2(a);
t3.mul(b);
t1.add(b);
t2.mul_ip();
t2.add(a);
a.copy(t1);
a.mul(t2);
t2.copy(t3);
t2.mul_ip();
t2.add(t3);
t2.neg();
a.add(t2);
b.copy(t3);
b.add(t3);
norm();
}
/* normalises m-array of ECP2 points. Requires work vector of m FP2s */
public static void multiaffine(int m, ECP2[] P)
{
int i;
FP2 t1 = new FP2(0);
FP2 t2 = new FP2(0);
FP2[] work = new FP2[m];
work[0] = new FP2(1);
work[1] = new FP2(P[0].z);
for (i = 2; i < m; i++)
{
work[i] = new FP2(work[i - 1]);
work[i].mul(P[i - 1].z);
}
t1.copy(work[m - 1]);
t1.mul(P[m - 1].z);
t1.inverse();
t2.copy(P[m - 1].z);
work[m - 1].mul(t1);
for (i = m - 2;; i--)
{
if (i == 0)
{
work[0].copy(t1);
work[0].mul(t2);
break;
}
work[i].mul(t2);
work[i].mul(t1);
t2.mul(P[i].z);
}
/* now work[] contains inverses of all Z coordinates */
for (i = 0; i < m; i++)
{
P[i].z.one();
t1.copy(work[i]);
t1.sqr();
P[i].x.mul(t1);
t1.mul(work[i]);
P[i].y.mul(t1);
}
}
/* this+=this */
public int dbl()
{
if (INF)
{
return(-1);
}
if (y.iszilch())
{
inf();
return(-1);
}
FP2 w1 = new FP2(x);
FP2 w2 = new FP2(0);
FP2 w3 = new FP2(x);
FP2 w8 = new FP2(x);
w1.sqr();
w8.copy(w1);
w8.imul(3);
w2.copy(y);
w2.sqr();
w3.copy(x);
w3.mul(w2);
w3.imul(4);
w1.copy(w3);
w1.neg();
// w1.norm();
x.copy(w8);
x.sqr();
x.add(w1);
x.add(w1);
x.norm();
z.mul(y);
z.add(z);
w2.add(w2);
w2.sqr();
w2.add(w2);
w3.sub(x);
y.copy(w8);
y.mul(w3);
// w2.norm();
y.sub(w2);
y.norm();
z.norm();
return(1);
}
/* set this=-this */
public void neg()
{
FP2 m = new FP2(a);
FP2 t = new FP2(0);
m.add(b);
m.neg();
m.norm();
t.copy(m);
t.add(b);
b.copy(m);
b.add(a);
a.copy(t);
}
/* construct this from x - but set to O if not on curve */
public ECP2(FP2 ix)
{
x = new FP2(ix);
y = new FP2(1);
z = new FP2(1);
FP2 rhs = RHS(x);
if (rhs.sqrt())
{
y.copy(rhs);
INF = false;
}
else
{
x.zero();
INF = true;
}
}
/* this+=Q - return 0 for add, 1 for double, -1 for O */
public int add(ECP2 Q)
{
if (INF)
{
copy(Q);
return(-1);
}
if (Q.INF)
{
return(-1);
}
bool aff = false;
if (Q.z.isunity())
{
aff = true;
}
FP2 A, C;
FP2 B = new FP2(z);
FP2 D = new FP2(z);
if (!aff)
{
A = new FP2(Q.z);
C = new FP2(Q.z);
A.sqr();
B.sqr();
C.mul(A);
D.mul(B);
A.mul(x);
C.mul(y);
}
else
{
A = new FP2(x);
C = new FP2(y);
B.sqr();
D.mul(B);
}
B.mul(Q.x);
B.sub(A);
D.mul(Q.y);
D.sub(C);
if (B.iszilch())
{
if (D.iszilch())
{
dbl();
return(1);
}
else
{
INF = true;
return(-1);
}
}
if (!aff)
{
z.mul(Q.z);
}
z.mul(B);
FP2 e = new FP2(B);
e.sqr();
B.mul(e);
A.mul(e);
e.copy(A);
e.add(A);
e.add(B);
x.copy(D);
x.sqr();
x.sub(e);
A.sub(x);
y.copy(A);
y.mul(D);
C.mul(B);
y.sub(C);
x.norm();
y.norm();
z.norm();
return(0);
}
/* copy this=x */
public void copy(FP4 x)
{
a.copy(x.a);
b.copy(x.b);
}