/* this*=c mod Modulus, where c is a small int */
public void IMul(int c)
{
// norm();
bool s = false;
if (c < 0)
{
c = -c;
s = true;
}
if (MODTYPE == PSEUDO_MERSENNE || MODTYPE == GENERALISED_MERSENNE)
{
DBIG d = x.PXMul(c);
x.Copy(Mod(d));
XES = 2;
}
else
{
if (XES * c <= FEXCESS)
{
x.PMul(c);
XES *= c;
}
else
{ // this is not good
FP n = new FP(c);
Mul(n);
}
}
/*
* if (c<=BIG.NEXCESS && XES*c<=FEXCESS)
* {
* x.imul(c);
* XES*=c;
* x.norm();
* }
* else
* {
* DBIG d=x.pxmul(c);
* x.copy(mod(d));
* XES=2;
* }
*/
if (s)
{
Neg();
Norm();
}
}
/* this=this^e */
/* Note this is simple square and multiply, so not side-channel safe */
public FP12 Pow(BIG e)
{
Norm();
e.Norm();
BIG e3 = new BIG(e);
e3.PMul(3);
e3.Norm();
FP12 w = new FP12(this);
int nb = e3.NBits();
for (int i = nb - 2; i >= 1; i--)
{
w.USqr();
int bt = e3.Bit(i) - e.Bit(i);
if (bt == 1)
{
w.mul(this);
}
if (bt == -1)
{
Conj();
w.mul(this);
Conj();
}
}
w.Reduce();
return(w);
/*
* BIG z=new BIG(e);
* FP12 r=new FP12(1);
*
* while (true)
* {
* int bt=z.parity();
* z.fshr(1);
* if (bt==1) r.mul(w);
* if (z.iszilch()) break;
* w.usqr();
* }
* r.reduce();
* return r; */
}
/* 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);
}
/// <summary>
///************** 64-bit specific *********************** </summary>
/* reduce a DBIG to a BIG using the appropriate form of the modulus */
public static BIG Mod(DBIG d)
{
if (MODTYPE == PSEUDO_MERSENNE)
{
BIG b;
long v, tw;
BIG t = d.Split(MODBITS);
b = new BIG(d);
v = t.PMul(unchecked ((int)ROM.MConst));
t.Add(b);
t.Norm();
tw = t.w[BIG.NLEN - 1];
t.w[BIG.NLEN - 1] &= FP.TMASK;
t.w[0] += (ROM.MConst * ((tw >> TBITS) + (v << (BIG.BASEBITS - TBITS))));
t.Norm();
return(t);
}
if (FP.MODTYPE == MONTGOMERY_FRIENDLY)
{
BIG b;
long[] cr = new long[2];
for (int i = 0; i < BIG.NLEN; i++)
{
cr = BIG.MulAdd(d.w[i], ROM.MConst - 1, d.w[i], d.w[BIG.NLEN + i - 1]);
d.w[BIG.NLEN + i] += cr[0];
d.w[BIG.NLEN + i - 1] = cr[1];
}
b = new BIG(0);
for (int i = 0; i < BIG.NLEN; i++)
{
b.w[i] = d.w[BIG.NLEN + i];
}
b.Norm();
return(b);
}
if (MODTYPE == GENERALISED_MERSENNE)
{ // GoldiLocks Only
BIG b;
BIG t = d.Split(MODBITS);
b = new BIG(d);
b.Add(t);
DBIG dd = new DBIG(t);
dd.Shl(MODBITS / 2);
BIG tt = dd.Split(MODBITS);
BIG lo = new BIG(dd);
b.Add(tt);
b.Add(lo);
b.Norm();
tt.Shl(MODBITS / 2);
b.Add(tt);
long carry = b.w[BIG.NLEN - 1] >> TBITS;
b.w[BIG.NLEN - 1] &= FP.TMASK;
b.w[0] += carry;
b.w[224 / BIG.BASEBITS] += carry << (224 % BIG.BASEBITS);
b.Norm();
return(b);
}
if (MODTYPE == NOT_SPECIAL)
{
return(BIG.Monty(new BIG(ROM.Modulus), ROM.MConst, d));
}
return(new BIG(0));
}