/* 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);
t1.Norm();
t2.Norm();
a.Copy(t1);
a.Mul(t2);
t2.Copy(t3);
t2.Mul_Ip();
t2.Add(t3);
t2.Norm();
t2.Neg();
a.Add(t2);
b.Copy(t3);
b.Add(t3);
Norm();
}
/* Multiply P by e in group G2 */
public static ECP2 G2Mul(ECP2 P, BIG e)
{
ECP2 R;
if (USE_GS_G2)
{
ECP2[] Q = new ECP2[4];
FP2 f = new FP2(new BIG(ROM.Fra), new BIG(ROM.Frb));
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
f.Inverse();
f.Norm();
}
BIG q = new BIG(ROM.CURVE_Order);
BIG[] u = GS(e);
BIG t = new BIG(0);
int i, np, nn;
//P.affine();
Q[0] = new ECP2();
Q[0].Copy(P);
for (i = 1; i < 4; i++)
{
Q[i] = new ECP2();
Q[i].Copy(Q[i - 1]);
Q[i].Frob(f);
}
for (i = 0; i < 4; i++)
{
np = u[i].NBits();
t.Copy(BIG.ModNeg(u[i], q));
nn = t.NBits();
if (nn < np)
{
u[i].Copy(t);
Q[i].Neg();
}
u[i].Norm();
//Q[i].affine();
}
R = ECP2.Mul4(Q, u);
}
else
{
R = P.Mul(e);
}
return(R);
}
/* 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);
t3.Norm();
t4.Norm();
t4.Mul(t3);
t3.Copy(t1);
t3.Neg();
t4.Add(t3);
t4.Norm();
// t4.sub(t1);
// t4.norm();
t3.Copy(t2);
t3.Neg();
b.Copy(t4);
b.Add(t3);
// b.copy(t4);
// b.sub(t2);
t2.Mul_Ip();
a.Copy(t2);
a.Add(t1);
Norm();
}
public void Div_2I()
{
FP2 u = new FP2(a);
FP2 v = new FP2(b);
u.Div_Ip2();
v.Add(v);
v.Norm();
a.Copy(v);
b.Copy(u);
}
/* this=1/this */
public void Inverse()
{
// norm();
FP2 t1 = new FP2(a);
FP2 t2 = new FP2(b);
t1.Sqr();
t2.Sqr();
t2.Mul_Ip();
t2.Norm();
t1.Sub(t2);
t1.Inverse();
a.Mul(t1);
t1.Neg();
t1.Norm();
b.Mul(t1);
}
/* sqrt(a+ib) = sqrt(a+sqrt(a*a-n*b*b)/2)+ib/(2*sqrt(a+sqrt(a*a-n*b*b)/2)) */
/* returns true if this is QR */
public bool Sqrt()
{
if (IsZilch())
{
return(true);
}
FP2 wa = new FP2(a);
FP2 ws = new FP2(b);
FP2 wt = new FP2(a);
if (ws.IsZilch())
{
if (wt.Sqrt())
{
a.Copy(wt);
b.Zero();
}
else
{
wt.Div_Ip();
wt.Sqrt();
b.Copy(wt);
a.Zero();
}
return(true);
}
ws.Sqr();
wa.Sqr();
ws.Mul_Ip();
ws.Norm();
wa.Sub(ws);
ws.Copy(wa);
if (!ws.Sqrt())
{
return(false);
}
wa.Copy(wt);
wa.Add(ws);
wa.Norm();
wa.Div2();
if (!wa.Sqrt())
{
wa.Copy(wt);
wa.Sub(ws);
wa.Norm();
wa.Div2();
if (!wa.Sqrt())
{
return(false);
}
}
wt.Copy(b);
ws.Copy(wa);
ws.Add(wa);
ws.Inverse();
wt.Mul(ws);
a.Copy(wa);
b.Copy(wt);
return(true);
}
/* normalise all components of this mod Modulus */
public void Norm()
{
a.Norm();
b.Norm();
}
/* Line function */
public static FP12 Line(ECP2 A, ECP2 B, FP Qx, FP Qy)
{
//System.out.println("Into line");
FP4 a, b, c; // Edits here
// c=new FP4(0);
if (A == B)
{
// Doubling
FP2 XX = new FP2(A.GetX()); //X
FP2 YY = new FP2(A.GetY()); //Y
FP2 ZZ = new FP2(A.GetZ()); //Z
FP2 YZ = new FP2(YY); //Y
YZ.Mul(ZZ); //YZ
XX.Sqr(); //X^2
YY.Sqr(); //Y^2
ZZ.Sqr(); //Z^2
YZ.IMul(4);
YZ.Neg();
YZ.Norm(); //-2YZ
YZ.PMul(Qy); //-2YZ.Ys
XX.IMul(6); //3X^2
XX.PMul(Qx); //3X^2.Xs
int sb = 3 * ROM.CURVE_B_I;
ZZ.IMul(sb);
if (ECP.SEXTIC_TWIST == ECP.D_TYPE)
{
ZZ.Div_Ip2();
}
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
ZZ.Mul_Ip();
ZZ.Add(ZZ);
YZ.Mul_Ip();
YZ.Norm();
}
ZZ.Norm(); // 3b.Z^2
YY.Add(YY);
ZZ.Sub(YY);
ZZ.Norm(); // 3b.Z^2-Y^2
a = new FP4(YZ, ZZ); // -2YZ.Ys | 3b.Z^2-Y^2 | 3X^2.Xs
if (ECP.SEXTIC_TWIST == ECP.D_TYPE)
{
b = new FP4(XX); // L(0,1) | L(0,0) | L(1,0)
c = new FP4(0);
}
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
b = new FP4(0);
c = new FP4(XX);
c.Times_I();
}
A.Dbl();
}
else
{
// Addition - assume B is affine
FP2 X1 = new FP2(A.GetX()); // X1
FP2 Y1 = new FP2(A.GetY()); // Y1
FP2 T1 = new FP2(A.GetZ()); // Z1
FP2 T2 = new FP2(A.GetZ()); // Z1
T1.Mul(B.GetY()); // T1=Z1.Y2
T2.Mul(B.GetX()); // T2=Z1.X2
X1.Sub(T2);
X1.Norm(); // X1=X1-Z1.X2
Y1.Sub(T1);
Y1.Norm(); // Y1=Y1-Z1.Y2
T1.Copy(X1); // T1=X1-Z1.X2
X1.PMul(Qy); // X1=(X1-Z1.X2).Ys
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
X1.Mul_Ip();
X1.Norm();
}
T1.Mul(B.GetY()); // T1=(X1-Z1.X2).Y2
T2.Copy(Y1); // T2=Y1-Z1.Y2
T2.Mul(B.GetX()); // T2=(Y1-Z1.Y2).X2
T2.Sub(T1);
T2.Norm(); // T2=(Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2
Y1.PMul(Qx);
Y1.Neg();
Y1.Norm(); // Y1=-(Y1-Z1.Y2).Xs
a = new FP4(X1, T2); // (X1-Z1.X2).Ys | (Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2 | - (Y1-Z1.Y2).Xs
if (ECP.SEXTIC_TWIST == ECP.D_TYPE)
{
b = new FP4(Y1);
c = new FP4(0);
}
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
b = new FP4(0);
c = new FP4(Y1);
c.Times_I();
}
A.Add(B);
}
//System.out.println("Out of line");
return(new FP12(a, b, c));
}
/* Optimal R-ate double pairing e(P,Q).e(R,S) */
public static FP12 Ate2(ECP2 P1, ECP Q1, ECP2 R1, ECP S1)
{
FP2 f;
BIG x = new BIG(ROM.CURVE_Bnx);
BIG n = new BIG(x);
ECP2 K = new ECP2();
FP12 lv;
int bt;
ECP2 P = new ECP2(P1);
ECP Q = new ECP(Q1);
P.Affine();
Q.Affine();
ECP2 R = new ECP2(R1);
ECP S = new ECP(S1);
R.Affine();
S.Affine();
if (ECP.CURVE_PAIRING_TYPE == ECP.BN)
{
f = new FP2(new BIG(ROM.Fra), new BIG(ROM.Frb));
if (ECP.SEXTIC_TWIST == ECP.M_TYPE)
{
f.Inverse();
f.Norm();
}
n.PMul(6);
if (ECP.SIGN_OF_X == ECP.POSITIVEX)
{
n.Inc(2);
}
else
{
n.Dec(2);
}
}
else
{
n.Copy(x);
}
n.Norm();
BIG n3 = new BIG(n);
n3.PMul(3);
n3.Norm();
FP Qx = new FP(Q.GetX());
FP Qy = new FP(Q.GetY());
FP Sx = new FP(S.GetX());
FP Sy = new FP(S.GetY());
ECP2 A = new ECP2();
ECP2 B = new ECP2();
FP12 r = new FP12(1);
A.Copy(P);
B.Copy(R);
ECP2 MP = new ECP2();
MP.Copy(P);
MP.Neg();
ECP2 MR = new ECP2();
MR.Copy(R);
MR.Neg();
int nb = n3.NBits();
for (int i = nb - 2; i >= 1; i--)
{
r.Sqr();
lv = Line(A, A, Qx, Qy);
r.SMul(lv, ECP.SEXTIC_TWIST);
lv = Line(B, B, Sx, Sy);
r.SMul(lv, ECP.SEXTIC_TWIST);
bt = n3.Bit(i) - n.Bit(i); // bt=n.bit(i);
if (bt == 1)
{
lv = Line(A, P, Qx, Qy);
r.SMul(lv, ECP.SEXTIC_TWIST);
lv = Line(B, R, Sx, Sy);
r.SMul(lv, ECP.SEXTIC_TWIST);
}
if (bt == -1)
{
//P.neg();
lv = Line(A, MP, Qx, Qy);
r.SMul(lv, ECP.SEXTIC_TWIST);
//P.neg();
//R.neg();
lv = Line(B, MR, Sx, Sy);
r.SMul(lv, ECP.SEXTIC_TWIST);
//R.neg();
}
}
if (ECP.SIGN_OF_X == ECP.NEGATIVEX)
{
r.Conj();
}
/* R-ate fixup required for BN curves */
if (ECP.CURVE_PAIRING_TYPE == ECP.BN)
{
if (ECP.SIGN_OF_X == ECP.NEGATIVEX)
{
// r.conj();
A.Neg();
B.Neg();
}
K.Copy(P);
K.Frob(f);
lv = Line(A, K, Qx, Qy);
r.SMul(lv, ECP.SEXTIC_TWIST);
K.Frob(f);
K.Neg();
lv = Line(A, K, Qx, Qy);
r.SMul(lv, ECP.SEXTIC_TWIST);
K.Copy(R);
K.Frob(f);
lv = Line(B, K, Sx, Sy);
r.SMul(lv, ECP.SEXTIC_TWIST);
K.Frob(f);
K.Neg();
lv = Line(B, K, Sx, Sy);
r.SMul(lv, ECP.SEXTIC_TWIST);
}
return(r);
}