/* r=x^n using XTR method on traces of FP12s */
public FP4 Xtr_Pow(BIG n)
{
FP4 a = new FP4(3);
FP4 b = new FP4(this);
FP4 c = new FP4(b);
c.Xtr_D();
FP4 t = new FP4(0);
FP4 r = new FP4(0);
n.Norm();
int par = n.Parity();
BIG v = new BIG(n);
v.FShr(1);
if (par == 0)
{
v.Dec(1);
v.Norm();
}
int nb = v.NBits();
for (int i = nb - 1; i >= 0; i--)
{
if (v.Bit(i) != 1)
{
t.Copy(b);
Conj();
c.Conj();
b.Xtr_A(a, this, c);
Conj();
c.Copy(t);
c.Xtr_D();
a.Xtr_D();
}
else
{
t.Copy(a);
t.Conj();
a.Copy(b);
a.Xtr_D();
b.Xtr_A(c, this, t);
c.Xtr_D();
}
}
if (par == 0)
{
r.Copy(c);
}
else
{
r.Copy(b);
}
r.Reduce();
return(r);
}
/* this=1/this */
public void Inverse()
{
FP4 f0 = new FP4(a);
FP4 f1 = new FP4(b);
FP4 f2 = new FP4(a);
FP4 f3 = new FP4(0);
Norm();
f0.Sqr();
f1.Mul(c);
f1.Times_I();
f0.Sub(f1);
f0.Norm();
f1.Copy(c);
f1.Sqr();
f1.Times_I();
f2.Mul(b);
f1.Sub(f2);
f1.Norm();
f2.Copy(b);
f2.Sqr();
f3.Copy(a);
f3.Mul(c);
f2.Sub(f3);
f2.Norm();
f3.Copy(b);
f3.Mul(f2);
f3.Times_I();
a.Mul(f0);
f3.Add(a);
c.Mul(f1);
c.Times_I();
f3.Add(c);
f3.Norm();
f3.Inverse();
a.Copy(f0);
a.Mul(f3);
b.Copy(f1);
b.Mul(f3);
c.Copy(f2);
c.Mul(f3);
}
/* trace function */
public FP4 Trace()
{
FP4 t = new FP4(0);
t.Copy(a);
t.IMul(3);
t.Reduce();
return(t);
}
/* Granger-Scott Unitary Squaring */
public void USqr()
{
//System.out.println("Into usqr");
FP4 A = new FP4(a);
FP4 B = new FP4(c);
FP4 C = new FP4(b);
FP4 D = new FP4(0);
a.Sqr();
D.Copy(a);
D.Add(a);
a.Add(D);
a.Norm();
A.NConj();
A.Add(A);
a.Add(A);
B.Sqr();
B.Times_I();
D.Copy(B);
D.Add(B);
B.Add(D);
B.Norm();
C.Sqr();
D.Copy(C);
D.Add(C);
C.Add(D);
C.Norm();
b.Conj();
b.Add(b);
c.NConj();
c.Add(c);
b.Add(B);
c.Add(C);
//System.out.println("Out of usqr 1");
Reduce();
//System.out.println("Out of usqr 2");
}
/* r=ck^a.cl^n using XTR double exponentiation method on traces of FP12s. See Stam thesis. */
public FP4 Xtr_Pow2(FP4 ck, FP4 ckml, FP4 ckm2l, BIG a, BIG b)
{
a.Norm();
b.Norm();
BIG e = new BIG(a);
BIG d = new BIG(b);
BIG w = new BIG(0);
FP4 cu = new FP4(ck); // can probably be passed in w/o copying
FP4 cv = new FP4(this);
FP4 cumv = new FP4(ckml);
FP4 cum2v = new FP4(ckm2l);
FP4 r = new FP4(0);
FP4 t = new FP4(0);
int f2 = 0;
while (d.Parity() == 0 && e.Parity() == 0)
{
d.FShr(1);
e.FShr(1);
f2++;
}
while (BIG.Comp(d, e) != 0)
{
if (BIG.Comp(d, e) > 0)
{
w.Copy(e);
w.IMul(4);
w.Norm();
if (BIG.Comp(d, w) <= 0)
{
w.Copy(d);
d.Copy(e);
e.RSub(w);
e.Norm();
t.Copy(cv);
t.Xtr_A(cu, cumv, cum2v);
cum2v.Copy(cumv);
cum2v.Conj();
cumv.Copy(cv);
cv.Copy(cu);
cu.Copy(t);
}
else if (d.Parity() == 0)
{
d.FShr(1);
r.Copy(cum2v);
r.Conj();
t.Copy(cumv);
t.Xtr_A(cu, cv, r);
cum2v.Copy(cumv);
cum2v.Xtr_D();
cumv.Copy(t);
cu.Xtr_D();
}
else if (e.Parity() == 1)
{
d.Sub(e);
d.Norm();
d.FShr(1);
t.Copy(cv);
t.Xtr_A(cu, cumv, cum2v);
cu.Xtr_D();
cum2v.Copy(cv);
cum2v.Xtr_D();
cum2v.Conj();
cv.Copy(t);
}
else
{
w.Copy(d);
d.Copy(e);
d.FShr(1);
e.Copy(w);
t.Copy(cumv);
t.Xtr_D();
cumv.Copy(cum2v);
cumv.Conj();
cum2v.Copy(t);
cum2v.Conj();
t.Copy(cv);
t.Xtr_D();
cv.Copy(cu);
cu.Copy(t);
}
}
if (BIG.Comp(d, e) < 0)
{
w.Copy(d);
w.IMul(4);
w.Norm();
if (BIG.Comp(e, w) <= 0)
{
e.Sub(d);
e.Norm();
t.Copy(cv);
t.Xtr_A(cu, cumv, cum2v);
cum2v.Copy(cumv);
cumv.Copy(cu);
cu.Copy(t);
}
else if (e.Parity() == 0)
{
w.Copy(d);
d.Copy(e);
d.FShr(1);
e.Copy(w);
t.Copy(cumv);
t.Xtr_D();
cumv.Copy(cum2v);
cumv.Conj();
cum2v.Copy(t);
cum2v.Conj();
t.Copy(cv);
t.Xtr_D();
cv.Copy(cu);
cu.Copy(t);
}
else if (d.Parity() == 1)
{
w.Copy(e);
e.Copy(d);
w.Sub(d);
w.Norm();
d.Copy(w);
d.FShr(1);
t.Copy(cv);
t.Xtr_A(cu, cumv, cum2v);
cumv.Conj();
cum2v.Copy(cu);
cum2v.Xtr_D();
cum2v.Conj();
cu.Copy(cv);
cu.Xtr_D();
cv.Copy(t);
}
else
{
d.FShr(1);
r.Copy(cum2v);
r.Conj();
t.Copy(cumv);
t.Xtr_A(cu, cv, r);
cum2v.Copy(cumv);
cum2v.Xtr_D();
cumv.Copy(t);
cu.Xtr_D();
}
}
}
r.Copy(cv);
r.Xtr_A(cu, cumv, cum2v);
for (int i = 0; i < f2; i++)
{
r.Xtr_D();
}
r = r.Xtr_Pow(d);
return(r);
}
/* Special case of multiplication arises from special form of ATE pairing line function */
public void SMul(FP12 y, int type)
{
//System.out.println("Into smul");
if (type == ECP.D_TYPE)
{
FP4 z0 = new FP4(a);
FP4 z2 = new FP4(b);
FP4 z3 = new FP4(b);
FP4 t0 = new FP4(0);
FP4 t1 = new FP4(y.a);
z0.Mul(y.a);
z2.PMul(y.b.Real());
b.Add(a);
t1.Real().Add(y.b.Real());
t1.Norm();
b.Norm();
b.Mul(t1);
z3.Add(c);
z3.Norm();
z3.PMul(y.b.Real());
t0.Copy(z0);
t0.Neg();
t1.Copy(z2);
t1.Neg();
b.Add(t0);
b.Add(t1);
z3.Add(t1);
z2.Add(t0);
t0.Copy(a);
t0.Add(c);
t0.Norm();
z3.Norm();
t0.Mul(y.a);
c.Copy(z2);
c.Add(t0);
z3.Times_I();
a.Copy(z0);
a.Add(z3);
}
if (type == ECP.M_TYPE)
{
FP4 z0 = new FP4(a);
FP4 z1 = new FP4(0);
FP4 z2 = new FP4(0);
FP4 z3 = new FP4(0);
FP4 t0 = new FP4(a);
FP4 t1 = new FP4(0);
z0.Mul(y.a);
t0.Add(b);
t0.Norm();
z1.Copy(t0);
z1.Mul(y.a);
t0.Copy(b);
t0.Add(c);
t0.Norm();
z3.Copy(t0); //z3.mul(y.c);
z3.PMul(y.c.GetB());
z3.Times_I();
t0.Copy(z0);
t0.Neg();
z1.Add(t0);
b.Copy(z1);
z2.Copy(t0);
t0.Copy(a);
t0.Add(c);
t1.Copy(y.a);
t1.Add(y.c);
t0.Norm();
t1.Norm();
t0.Mul(t1);
z2.Add(t0);
t0.Copy(c);
t0.PMul(y.c.GetB());
t0.Times_I();
t1.Copy(t0);
t1.Neg();
c.Copy(z2);
c.Add(t1);
z3.Add(t1);
t0.Times_I();
b.Add(t0);
z3.Norm();
z3.Times_I();
a.Copy(z0);
a.Add(z3);
}
Norm();
//System.out.println("Out of smul");
}
/* FP12 full multiplication this=this*y */
public void mul(FP12 y)
{
//System.out.println("Into mul");
FP4 z0 = new FP4(a);
FP4 z1 = new FP4(0);
FP4 z2 = new FP4(b);
FP4 z3 = new FP4(0);
FP4 t0 = new FP4(a);
FP4 t1 = new FP4(y.a);
z0.Mul(y.a);
z2.Mul(y.b);
t0.Add(b);
t1.Add(y.b);
t0.Norm();
t1.Norm();
z1.Copy(t0);
z1.Mul(t1);
t0.Copy(b);
t0.Add(c);
t1.Copy(y.b);
t1.Add(y.c);
t0.Norm();
t1.Norm();
z3.Copy(t0);
z3.Mul(t1);
t0.Copy(z0);
t0.Neg();
t1.Copy(z2);
t1.Neg();
z1.Add(t0);
//z1.norm();
b.Copy(z1);
b.Add(t1);
z3.Add(t1);
z2.Add(t0);
t0.Copy(a);
t0.Add(c);
t1.Copy(y.a);
t1.Add(y.c);
t0.Norm();
t1.Norm();
t0.Mul(t1);
z2.Add(t0);
t0.Copy(c);
t0.Mul(y.c);
t1.Copy(t0);
t1.Neg();
// z2.norm();
// z3.norm();
// b.norm();
c.Copy(z2);
c.Add(t1);
z3.Add(t1);
t0.Times_I();
b.Add(t0);
z3.Norm();
z3.Times_I();
a.Copy(z0);
a.Add(z3);
Norm();
//System.out.println("Out of mul");
}
/* copy this=x */
public void Copy(FP12 x)
{
a.Copy(x.a);
b.Copy(x.b);
c.Copy(x.c);
}
