/* p=q0^u0.q1^u1.q2^u2.q3^u3 */
// Bos & Costello https://eprint.iacr.org/2013/458.pdf
// Faz-Hernandez & Longa & Sanchez https://eprint.iacr.org/2013/158.pdf
// Side channel attack secure
public static FP12 Pow4(FP12[] q, BIG[] u)
{
int i, j, nb, pb;
FP12[] g = new FP12[8];
FP12 r = new FP12(1);
FP12 p = new FP12(0);
BIG[] t = new BIG[4];
BIG mt = new BIG(0);
sbyte[] w = new sbyte[BIG.NLEN * BIG.BASEBITS + 1];
sbyte[] s = new sbyte[BIG.NLEN * BIG.BASEBITS + 1];
for (i = 0; i < 4; i++)
{
t[i] = new BIG(u[i]);
t[i].Norm();
}
g[0] = new FP12(q[0]); // q[0]
g[1] = new FP12(g[0]);
g[1].mul(q[1]); // q[0].q[1]
g[2] = new FP12(g[0]);
g[2].mul(q[2]); // q[0].q[2]
g[3] = new FP12(g[1]);
g[3].mul(q[2]); // q[0].q[1].q[2]
g[4] = new FP12(q[0]);
g[4].mul(q[3]); // q[0].q[3]
g[5] = new FP12(g[1]);
g[5].mul(q[3]); // q[0].q[1].q[3]
g[6] = new FP12(g[2]);
g[6].mul(q[3]); // q[0].q[2].q[3]
g[7] = new FP12(g[3]);
g[7].mul(q[3]); // q[0].q[1].q[2].q[3]
// Make it odd
pb = 1 - t[0].Parity();
t[0].Inc(pb);
t[0].Norm();
// Number of bits
mt.Zero();
for (i = 0; i < 4; i++)
{
mt.Or(t[i]);
}
nb = 1 + mt.NBits();
// Sign pivot
s[nb - 1] = 1;
for (i = 0; i < nb - 1; i++)
{
t[0].FShr(1);
s[i] = (sbyte)(2 * t[0].Parity() - 1);
}
// Recoded exponent
for (i = 0; i < nb; i++)
{
w[i] = 0;
int k = 1;
for (j = 1; j < 4; j++)
{
sbyte bt = (sbyte)(s[i] * t[j].Parity());
t[j].FShr(1);
t[j].Dec((int)(bt) >> 1);
t[j].Norm();
w[i] += (sbyte)(bt * (sbyte)k);
k *= 2;
}
}
// Main loop
p.Select(g, (int)(2 * w[nb - 1] + 1));
for (i = nb - 2; i >= 0; i--)
{
p.USqr();
r.Select(g, (int)(2 * w[i] + s[i]));
p.mul(r);
}
// apply correction
r.Copy(q[0]);
r.Conj();
r.mul(p);
p.CMove(r, pb);
p.Reduce();
return(p);
}