/* 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);
}
/* 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=this^p using Frobenius */
public void frob(FP2 f)
{
FP2 f2 = new FP2(f);
FP2 f3 = new FP2(f);
f2.sqr();
f3.mul(f2);
a.frob(f3);
b.frob(f3);
c.frob(f3);
b.pmul(f);
c.pmul(f2);
}
/* this=1/this */
public void inverse()
{
norm();
FP2 t1 = new FP2(a);
FP2 t2 = new FP2(b);
t1.sqr();
t2.sqr();
t2.mul_ip();
t1.sub(t2);
t1.inverse();
a.mul(t1);
t1.neg();
b.mul(t1);
}
/* 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);
}
}
/* set this*=q, where q is Modulus, using Frobenius */
public void frob(FP2 X)
{
if (INF)
{
return;
}
FP2 X2 = new FP2(X);
X2.sqr();
x.conj();
y.conj();
z.conj();
z.reduce();
x.mul(X2);
y.mul(X2);
y.mul(X);
}
/* construct this from (x,y) - but set to O if not on curve */
public ECP2(FP2 ix, FP2 iy)
{
x = new FP2(ix);
y = new FP2(iy);
z = new FP2(1);
FP2 rhs = RHS(x);
FP2 y2 = new FP2(y);
y2.sqr();
if (y2.Equals(rhs))
{
INF = false;
}
else
{
x.zero();
INF = true;
}
}
/* Test if P == Q */
public bool Equals(ECP2 Q)
{
if (is_infinity() && Q.is_infinity())
{
return(true);
}
if (is_infinity() || Q.is_infinity())
{
return(false);
}
FP2 zs2 = new FP2(z);
zs2.sqr();
FP2 zo2 = new FP2(Q.z);
zo2.sqr();
FP2 zs3 = new FP2(zs2);
zs3.mul(z);
FP2 zo3 = new FP2(zo2);
zo3.mul(Q.z);
zs2.mul(Q.x);
zo2.mul(x);
if (!zs2.Equals(zo2))
{
return(false);
}
zs3.mul(Q.y);
zo3.mul(y);
if (!zs3.Equals(zo3))
{
return(false);
}
return(true);
}
/* set to Affine - (x,y,z) to (x,y) */
public void affine()
{
if (is_infinity())
{
return;
}
FP2 one = new FP2(1);
if (z.Equals(one))
{
return;
}
z.inverse();
FP2 z2 = new FP2(z);
z2.sqr();
x.mul(z2);
x.reduce();
y.mul(z2);
y.mul(z);
y.reduce();
z.copy(one);
}
/* 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);
}
/* 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));
}