/* 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();
}
/* 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);
}
/* 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*=i where i = sqrt(-1+sqrt(-1)) */
public void times_i()
{
norm();
FP2 s = new FP2(b);
FP2 t = new FP2(b);
s.times_i();
t.add(s);
// t.norm();
b.copy(a);
a.copy(t);
}
/* Calculate RHS of twisted curve equation x^3+B/i */
public static FP2 RHS(FP2 x)
{
x.norm();
FP2 r = new FP2(x);
r.sqr();
FP2 b = new FP2(new BIG(ROM.CURVE_B));
b.div_ip();
r.mul(x);
r.add(b);
r.reduce();
return(r);
}
/* 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);
}
/* this+=x */
public void add(FP4 x)
{
a.add(x.a);
b.add(x.b);
}
/* Line function */
public static FP12 line(ECP2 A, ECP2 B, FP Qx, FP Qy)
{
ECP2 P = new ECP2();
FP4 a, b, c;
P.copy(A);
FP2 ZZ = new FP2(P.getz());
ZZ.sqr();
int D;
if (A == B)
{
D = A.dbl(); // Check this return value in amcl_ec2.c
}
else
{
D = A.add(B);
}
if (D < 0)
{
return(new FP12(1));
}
FP2 Z3 = new FP2(A.getz());
c = new FP4(0);
if (D == 0)
{ // Addition
FP2 X = new FP2(B.getx());
FP2 Y = new FP2(B.gety());
FP2 T = new FP2(P.getz());
T.mul(Y);
ZZ.mul(T);
FP2 NY = new FP2(P.gety());
NY.neg();
ZZ.add(NY);
Z3.pmul(Qy);
T.mul(P.getx());
X.mul(NY);
T.add(X);
a = new FP4(Z3, T);
ZZ.neg();
ZZ.pmul(Qx);
b = new FP4(ZZ);
}
else
{ // Doubling
FP2 X = new FP2(P.getx());
FP2 Y = new FP2(P.gety());
FP2 T = new FP2(P.getx());
T.sqr();
T.imul(3);
Y.sqr();
Y.add(Y);
Z3.mul(ZZ);
Z3.pmul(Qy);
X.mul(T);
X.sub(Y);
a = new FP4(Z3, X);
T.neg();
ZZ.mul(T);
ZZ.pmul(Qx);
b = new FP4(ZZ);
}
return(new FP12(a, b, c));
}