/* Multiply P by e in group G1 */
public static ECP G1mul(ECP P, BIG e)
{
ECP R;
if (ROM.USE_GLV)
{
P.affine();
R = new ECP();
R.copy(P);
int i, np, nn;
ECP Q = new ECP();
Q.copy(P);
BIG q = new BIG(ROM.CURVE_Order);
FP cru = new FP(new BIG(ROM.CURVE_Cru));
BIG t = new BIG(0);
BIG[] u = glv(e);
Q.getx().mul(cru);
np = u[0].nbits();
t.copy(BIG.modneg(u[0], q));
nn = t.nbits();
if (nn < np)
{
u[0].copy(t);
R.neg();
}
np = u[1].nbits();
t.copy(BIG.modneg(u[1], q));
nn = t.nbits();
if (nn < np)
{
u[1].copy(t);
Q.neg();
}
R = R.mul2(u[0], Q, u[1]);
}
else
{
R = P.mul(e);
}
return(R);
}
/* Multiply P by e in group G2 */
public static ECP2 G2mul(ECP2 P, BIG e)
{
ECP2 R;
if (ROM.USE_GS_G2)
{
ECP2[] Q = new ECP2[4];
FP2 f = new FP2(new BIG(ROM.CURVE_Fra), new BIG(ROM.CURVE_Frb));
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();
}
}
R = ECP2.mul4(Q, u);
}
else
{
R = P.mul(e);
}
return(R);
}
/* f=f^e */
/* Note that this method requires a lot of RAM! Better to use compressed XTR method, see FP4.java */
public static FP12 GTpow(FP12 d, BIG e)
{
FP12 r;
if (ROM.USE_GS_GT)
{
FP12[] g = new FP12[4];
FP2 f = new FP2(new BIG(ROM.CURVE_Fra), new BIG(ROM.CURVE_Frb));
BIG q = new BIG(ROM.CURVE_Order);
BIG t = new BIG(0);
int i, np, nn;
BIG[] u = gs(e);
g[0] = new FP12(d);
for (i = 1; i < 4; i++)
{
g[i] = new FP12(0);
g[i].copy(g[i - 1]);
g[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);
g[i].conj();
}
}
r = FP12.pow4(g, u);
}
else
{
r = d.pow(e);
}
return(r);
}
