/* P=u0.Q0+u1*Q1+u2*Q2+u3*Q3 */
// 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 ECP2 Mul4(ECP2[] Q, BIG[] u)
{
int i, j, nb, pb;
ECP2 W = new ECP2();
ECP2 P = new ECP2();
ECP2[] T = new ECP2[8];
BIG mt = new BIG();
BIG[] t = new BIG[4];
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();
//Q[i].affine();
}
T[0] = new ECP2();
T[0].Copy(Q[0]); // Q[0]
T[1] = new ECP2();
T[1].Copy(T[0]);
T[1].Add(Q[1]); // Q[0]+Q[1]
T[2] = new ECP2();
T[2].Copy(T[0]);
T[2].Add(Q[2]); // Q[0]+Q[2]
T[3] = new ECP2();
T[3].Copy(T[1]);
T[3].Add(Q[2]); // Q[0]+Q[1]+Q[2]
T[4] = new ECP2();
T[4].Copy(T[0]);
T[4].Add(Q[3]); // Q[0]+Q[3]
T[5] = new ECP2();
T[5].Copy(T[1]);
T[5].Add(Q[3]); // Q[0]+Q[1]+Q[3]
T[6] = new ECP2();
T[6].Copy(T[2]);
T[6].Add(Q[3]); // Q[0]+Q[2]+Q[3]
T[7] = new ECP2();
T[7].Copy(T[3]);
T[7].Add(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(T, (int)(2 * w[nb - 1] + 1));
for (i = nb - 2; i >= 0; i--)
{
P.Dbl();
W.Select(T, (int)(2 * w[i] + s[i]));
P.Add(W);
}
// apply correction
W.Copy(P);
W.Sub(Q[0]);
P.CMove(W, pb);
P.Affine();
return(P);
}
/* P*=e */
public ECP2 Mul(BIG e)
{
/* fixed size windows */
int i, nb, s, ns;
BIG mt = new BIG();
BIG t = new BIG();
ECP2 P = new ECP2();
ECP2 Q = new ECP2();
ECP2 C = new ECP2();
ECP2[] W = new ECP2[8];
sbyte[] w = new sbyte[1 + (BIG.NLEN * BIG.BASEBITS + 3) / 4];
if (IsInfinity())
{
return(new ECP2());
}
//affine();
/* precompute table */
Q.Copy(this);
Q.Dbl();
W[0] = new ECP2();
W[0].Copy(this);
for (i = 1; i < 8; i++)
{
W[i] = new ECP2();
W[i].Copy(W[i - 1]);
W[i].Add(Q);
}
/* make exponent odd - add 2P if even, P if odd */
t.Copy(e);
s = t.Parity();
t.Inc(1);
t.Norm();
ns = t.Parity();
mt.Copy(t);
mt.Inc(1);
mt.Norm();
t.CMove(mt, s);
Q.CMove(this, ns);
C.Copy(Q);
nb = 1 + (t.NBits() + 3) / 4;
/* convert exponent to signed 4-bit window */
for (i = 0; i < nb; i++)
{
w[i] = (sbyte)(t.LastBits(5) - 16);
t.Dec(w[i]);
t.Norm();
t.FShr(4);
}
w[nb] = (sbyte)t.LastBits(5);
P.Copy(W[(w[nb] - 1) / 2]);
for (i = nb - 1; i >= 0; i--)
{
Q.Select(W, w[i]);
P.Dbl();
P.Dbl();
P.Dbl();
P.Dbl();
P.Add(Q);
}
P.Sub(C);
P.Affine();
return(P);
}
