/* this=this^e */
public FP4 Pow(BIG e)
{
Norm();
e.Norm();
FP4 w = new FP4(this);
BIG z = new BIG(e);
FP4 r = new FP4(1);
while (true)
{
int bt = z.Parity();
z.FShr(1);
if (bt == 1)
{
r.Mul(w);
}
if (z.IsZilch())
{
break;
}
w.Sqr();
}
r.Reduce();
return(r);
}
/* this-=x */
public void Sub(FP4 x)
{
FP4 m = new FP4(x);
m.Neg();
Add(m);
}
/* this=this^e */
public FP4 pow(BIG e)
{
norm();
e.norm();
FP4 w = new FP4(this);
BIG z = new BIG(e);
FP4 r = new FP4(1);
while (true)
{
int bt = z.parity();
z.fshr(1);
if (bt == 1)
{
r.mul(w);
}
if (z.iszilch())
{
break;
}
w.sqr();
}
r.reduce();
return(r);
}
/* this-=x */
public void sub(FP4 x)
{
FP4 m = new FP4(x);
m.neg();
add(m);
}
/* this*=y */
public void mul(FP4 y)
{
norm();
FP2 t1 = new FP2(a);
FP2 t2 = new FP2(b);
FP2 t3 = new FP2(0);
FP2 t4 = new FP2(b);
t1.mul(y.a);
t2.mul(y.b);
t3.copy(y.b);
t3.add(y.a);
t4.add(a);
t4.mul(t3);
t4.sub(t1);
// t4.norm();
b.copy(t4);
b.sub(t2);
t2.mul_ip();
a.copy(t2);
a.add(t1);
norm();
}
/* 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);
}
/* 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);
}
/* trace function */
public FP4 Trace()
{
FP4 t = new FP4(0);
t.Copy(a);
t.IMul(3);
t.Reduce();
return(t);
}
/* trace function */
public FP4 trace()
{
FP4 t = new FP4(0);
t.copy(a);
t.imul(3);
t.reduce();
return(t);
}
/* XTR xtr_d function */
public void xtr_D()
{
FP4 w = new FP4(this);
sqr();
w.conj();
w.add(w);
sub(w);
reduce();
}
/* XTR xtr_d function */
public void Xtr_D()
{
FP4 w = new FP4(this);
Sqr();
w.Conj();
w.Add(w);
w.Norm();
Sub(w);
Reduce();
}
/* constant time powering by small integer of max length bts */
public void pinpow(int e, int bts)
{
int i, b;
FP12[] R = new FP12[2];
R[0] = new FP12(1);
R[1] = new FP12(this);
for (i = bts - 1; i >= 0; i--)
{
b = (e >> i) & 1;
R[1 - b].mul(R[b]);
R[b].usqr();
}
this.copy(R[0]);
}
/* XTR xtr_a function */
public void xtr_A(FP4 w, FP4 y, FP4 z)
{
FP4 r = new FP4(w);
FP4 t = new FP4(w);
r.sub(y);
r.pmul(a);
t.add(y);
t.pmul(b);
t.times_i();
copy(r);
add(t);
add(z);
norm();
}
/* 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);
}
public FP4 ComPow(BIG e, BIG r)
{
FP12 g1 = new FP12(0);
FP12 g2 = new FP12(0);
FP2 f = new FP2(new BIG(ROM.Fra), new BIG(ROM.Frb));
BIG q = new BIG(ROM.Modulus);
BIG m = new BIG(q);
m.Mod(r);
BIG a = new BIG(e);
a.Mod(m);
BIG b = new BIG(e);
b.Div(m);
g1.Copy(this);
g2.Copy(this);
FP4 c = g1.Trace();
if (b.IsZilch())
{
c = c.Xtr_Pow(e);
return(c);
}
g2.Frob(f);
FP4 cp = g2.Trace();
g1.Conj();
g2.mul(g1);
FP4 cpm1 = g2.Trace();
g2.mul(g1);
FP4 cpm2 = g2.Trace();
c = c.Xtr_Pow2(cp, cpm1, cpm2, a, b);
return(c);
}
/* 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");
}
/* 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);
f1.copy(c);
f1.sqr();
f1.times_i();
f2.mul(b);
f1.sub(f2);
f2.copy(b);
f2.sqr();
f3.copy(a);
f3.mul(c);
f2.sub(f3);
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.inverse();
a.copy(f0);
a.mul(f3);
b.copy(f1);
b.mul(f3);
c.copy(f2);
c.mul(f3);
}
/* this*=y */
public void Mul(FP4 y)
{
// norm();
FP2 t1 = new FP2(a);
FP2 t2 = new FP2(b);
FP2 t3 = new FP2(0);
FP2 t4 = new FP2(b);
t1.Mul(y.a);
t2.Mul(y.b);
t3.Copy(y.b);
t3.Add(y.a);
t4.Add(a);
t3.Norm();
t4.Norm();
t4.Mul(t3);
t3.Copy(t1);
t3.Neg();
t4.Add(t3);
t4.Norm();
// t4.sub(t1);
// t4.norm();
t3.Copy(t2);
t3.Neg();
b.Copy(t4);
b.Add(t3);
// b.copy(t4);
// b.sub(t2);
t2.Mul_Ip();
a.Copy(t2);
a.Add(t1);
Norm();
}
/* XTR xtr_a function */
public void Xtr_A(FP4 w, FP4 y, FP4 z)
{
FP4 r = new FP4(w);
FP4 t = new FP4(w);
//y.norm();
r.Sub(y);
r.Norm();
r.PMul(a);
t.Add(y);
t.Norm();
t.PMul(b);
t.Times_I();
Copy(r);
Add(t);
Add(z);
Norm();
}
/* Special case of multiplication arises from special form of ATE pairing line function */
public void smul(FP12 y)
{
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());
b.mul(t1);
z3.add(c);
z3.pmul(y.b.real());
t0.copy(z0);
t0.neg();
t1.copy(z2);
t1.neg();
b.add(t0);
// b.norm();
b.add(t1);
z3.add(t1);
z2.add(t0);
t0.copy(a);
t0.add(c);
t0.mul(y.a);
c.copy(z2);
c.add(t0);
z3.times_i();
a.copy(z0);
a.add(z3);
norm();
}
/* Chung-Hasan SQR2 method from http://cacr.uwaterloo.ca/techreports/2006/cacr2006-24.pdf */
public void Sqr()
{
//System.out.println("Into sqr");
FP4 A = new FP4(a);
FP4 B = new FP4(b);
FP4 C = new FP4(c);
FP4 D = new FP4(a);
A.Sqr();
B.Mul(c);
B.Add(B);
B.Norm();
C.Sqr();
D.Mul(b);
D.Add(D);
c.Add(a);
c.Add(b);
c.Norm();
c.Sqr();
a.Copy(A);
A.Add(B);
A.Norm();
A.Add(C);
A.Add(D);
A.Norm();
A.Neg();
B.Times_I();
C.Times_I();
a.Add(B);
b.Copy(C);
b.Add(D);
c.Add(A);
//System.out.println("Out of sqr");
Norm();
}
/* Granger-Scott Unitary Squaring */
public void 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);
reduce();
}
/* Chung-Hasan SQR2 method from http://cacr.uwaterloo.ca/techreports/2006/cacr2006-24.pdf */
public void sqr()
{
FP4 A = new FP4(a);
FP4 B = new FP4(b);
FP4 C = new FP4(c);
FP4 D = new FP4(a);
A.sqr();
B.mul(c);
B.add(B);
C.sqr();
D.mul(b);
D.add(D);
c.add(a);
c.add(b);
c.sqr();
a.copy(A);
A.add(B);
// A.norm();
A.add(C);
A.add(D);
// A.norm();
A.neg();
B.times_i();
C.times_i();
a.add(B);
b.copy(C);
b.add(D);
c.add(A);
norm();
}
/* test this=x? */
public bool Equals(FP4 x)
{
return(a.Equals(x.a) && b.Equals(x.b));
}
public void CMove(FP4 g, int d)
{
a.CMove(g.a, d);
b.CMove(g.b, d);
}
/* 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);
}
/* this=x-this */
public void RSub(FP4 x)
{
Neg();
Add(x);
}
/* this+=x */
public void Add(FP4 x)
{
a.Add(x.a);
b.Add(x.b);
}
/* copy this=x */
public void Copy(FP4 x)
{
a.Copy(x.a);
b.Copy(x.b);
}
public FP4(FP4 x)
{
a = new FP2(x.a);
b = new FP2(x.b);
}
