version3/go/FP48.go

/*
Licensed to the Apache Software Foundation (ASF) under one
or more contributor license agreements.  See the NOTICE file
distributed with this work for additional information
regarding copyright ownership.  The ASF licenses this file
to you under the Apache License, Version 2.0 (the
"License"); you may not use this file except in compliance
with the License.  You may obtain a copy of the License at

  http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing,
software distributed under the License is distributed on an
"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
KIND, either express or implied.  See the License for the
specific language governing permissions and limitations
under the License.
*/

/* MiotCL Fp^12 functions */
/* FP12 elements are of the form a+i.b+i^2.c */

package XXX

//import "fmt"

type FP48 struct {
	a *FP16
	b *FP16
	c *FP16
}

/* Constructors */
func NewFP48fp16(d *FP16) *FP48 {
	F:=new(FP48)
	F.a=NewFP16copy(d)
	F.b=NewFP16int(0)
	F.c=NewFP16int(0)
	return F
}

func NewFP48int(d int) *FP48 {
	F:=new(FP48)
	F.a=NewFP16int(d)
	F.b=NewFP16int(0)
	F.c=NewFP16int(0)
	return F
}

func NewFP48fp16s(d *FP16,e *FP16,f *FP16) *FP48 {
	F:=new(FP48)
	F.a=NewFP16copy(d)
	F.b=NewFP16copy(e)
	F.c=NewFP16copy(f)
	return F
}

func NewFP48copy(x *FP48) *FP48 {
	F:=new(FP48)
	F.a=NewFP16copy(x.a)
	F.b=NewFP16copy(x.b)
	F.c=NewFP16copy(x.c)
	return F
}

/* reduce all components of this mod Modulus */
func (F *FP48) reduce() {
	F.a.reduce()
	F.b.reduce()
	F.c.reduce()
}
/* normalise all components of this */
func (F *FP48) norm() {
	F.a.norm()
	F.b.norm()
	F.c.norm()
}
/* test x==0 ? */
func (F *FP48) iszilch() bool {
	//F.reduce()
	return (F.a.iszilch() && F.b.iszilch() && F.c.iszilch())
}

/* Conditional move */
func (F *FP48) cmove(g *FP48,d int) {
	F.a.cmove(g.a,d)
	F.b.cmove(g.b,d)
	F.c.cmove(g.c,d)
}

/* Constant time select from pre-computed table */
func (F *FP48) selector(g []*FP48,b int32) {

	m:=b>>31
	babs:=(b^m)-m

	babs=(babs-1)/2

	F.cmove(g[0],teq(babs,0))  // conditional move
	F.cmove(g[1],teq(babs,1))
	F.cmove(g[2],teq(babs,2))
	F.cmove(g[3],teq(babs,3))
	F.cmove(g[4],teq(babs,4))
	F.cmove(g[5],teq(babs,5))
	F.cmove(g[6],teq(babs,6))
	F.cmove(g[7],teq(babs,7))
 
 	invF:=NewFP48copy(F) 
	invF.conj()
	F.cmove(invF,int(m&1))
}

/* test x==1 ? */
func (F *FP48) Isunity() bool {
	one:=NewFP16int(1)
	return (F.a.Equals(one) && F.b.iszilch() && F.c.iszilch())
}
/* return 1 if x==y, else 0 */
func (F *FP48) Equals(x *FP48) bool {
	return (F.a.Equals(x.a) && F.b.Equals(x.b) && F.c.Equals(x.c))
}

/* extract a from this */
func (F *FP48) geta() *FP16 {
	return F.a
}
/* extract b */
func (F *FP48) getb() *FP16 {
	return F.b
}
/* extract c */
func (F *FP48) getc() *FP16 {
	return F.c
}
/* copy this=x */
func (F *FP48) Copy(x *FP48) {
	F.a.copy(x.a)
	F.b.copy(x.b)
	F.c.copy(x.c)
}
/* set this=1 */
func (F *FP48) one() {
	F.a.one()
	F.b.zero()
	F.c.zero()
}
/* this=conj(this) */
func (F *FP48) conj() {
	F.a.conj()
	F.b.nconj()
	F.c.conj()
}

/* Granger-Scott Unitary Squaring */
func (F *FP48) usqr() {
	A:=NewFP16copy(F.a)
	B:=NewFP16copy(F.c)
	C:=NewFP16copy(F.b)
	D:=NewFP16int(0)

	F.a.sqr()
	D.copy(F.a); D.add(F.a)
	F.a.add(D)

	F.a.norm();
	A.nconj()

	A.add(A)
	F.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();

	F.b.conj()
	F.b.add(F.b)
	F.c.nconj()

	F.c.add(F.c)
	F.b.add(B)
	F.c.add(C)
	F.reduce()

}

/* Chung-Hasan SQR2 method from http://cacr.uwaterloo.ca/techreports/2006/cacr2006-24.pdf */
func (F *FP48)  sqr() {
	A:=NewFP16copy(F.a)
	B:=NewFP16copy(F.b)
	C:=NewFP16copy(F.c)
	D:=NewFP16copy(F.a)

	A.sqr()
	B.mul(F.c)
	B.add(B); B.norm()
	C.sqr()
	D.mul(F.b)
	D.add(D)

	F.c.add(F.a)
	F.c.add(F.b); F.c.norm()
	F.c.sqr()

	F.a.copy(A)

	A.add(B)
	A.norm();
	A.add(C)
	A.add(D)
	A.norm();

	A.neg()
	B.times_i();
	C.times_i()

	F.a.add(B)

	F.b.copy(C); F.b.add(D)
	F.c.add(A)
	F.norm()
}

/* FP48 full multiplication this=this*y */
func (F *FP48) Mul(y *FP48) {
	z0:=NewFP16copy(F.a)
	z1:=NewFP16int(0)
	z2:=NewFP16copy(F.b)
	z3:=NewFP16int(0)
	t0:=NewFP16copy(F.a)
	t1:=NewFP16copy(y.a)

	z0.mul(y.a)
	z2.mul(y.b)

	t0.add(F.b); t0.norm()
	t1.add(y.b); t1.norm() 

	z1.copy(t0); z1.mul(t1)
	t0.copy(F.b); t0.add(F.c); t0.norm()

	t1.copy(y.b); t1.add(y.c); t1.norm()
	z3.copy(t0); z3.mul(t1)

	t0.copy(z0); t0.neg()
	t1.copy(z2); t1.neg()

	z1.add(t0)
	//z1.norm();
	F.b.copy(z1); F.b.add(t1)

	z3.add(t1)
	z2.add(t0)

	t0.copy(F.a); t0.add(F.c); t0.norm()
	t1.copy(y.a); t1.add(y.c); t1.norm()
	t0.mul(t1)
	z2.add(t0)

	t0.copy(F.c); t0.mul(y.c)
	t1.copy(t0); t1.neg()

	F.c.copy(z2); F.c.add(t1)
	z3.add(t1)
	t0.times_i()
	F.b.add(t0)
	z3.norm()
	z3.times_i()
	F.a.copy(z0); F.a.add(z3)
	F.norm()
}

/* Special case of multiplication arises from special form of ATE pairing line function */
func (F *FP48) smul(y *FP48,twist int ) {
	if twist==D_TYPE {
		z0:=NewFP16copy(F.a)
		z2:=NewFP16copy(F.b)
		z3:=NewFP16copy(F.b)
		t0:=NewFP16int(0)
		t1:=NewFP16copy(y.a)
		
		z0.mul(y.a)
		z2.pmul(y.b.real());
		F.b.add(F.a)
		t1.real().add(y.b.real())

		t1.norm(); F.b.norm()
		F.b.mul(t1)
		z3.add(F.c); z3.norm()
		z3.pmul(y.b.real())

		t0.copy(z0); t0.neg()
		t1.copy(z2); t1.neg()

		F.b.add(t0)
	//F.b.norm();

		F.b.add(t1)
		z3.add(t1); z3.norm()
		z2.add(t0)

		t0.copy(F.a); t0.add(F.c); t0.norm()
		t0.mul(y.a)
		F.c.copy(z2); F.c.add(t0)

		z3.times_i()
		F.a.copy(z0); F.a.add(z3)
	}
	if twist==M_TYPE {
		z0:=NewFP16copy(F.a)
		z1:=NewFP16int(0)
		z2:=NewFP16int(0)
		z3:=NewFP16int(0)
		t0:=NewFP16copy(F.a)
		t1:=NewFP16int(0)
		
		z0.mul(y.a)
		t0.add(F.b)
		t0.norm()

		z1.copy(t0); z1.mul(y.a)
		t0.copy(F.b); t0.add(F.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)
		F.b.copy(z1) 
		z2.copy(t0)

		t0.copy(F.a); t0.add(F.c)
		t1.copy(y.a); t1.add(y.c)

		t0.norm()
		t1.norm()
	
		t0.mul(t1)
		z2.add(t0)

		t0.copy(F.c)
			
		t0.pmul(y.c.getb())
		t0.times_i()

		t1.copy(t0); t1.neg()

		F.c.copy(z2); F.c.add(t1)
		z3.add(t1)
		t0.times_i()
		F.b.add(t0)
		z3.norm()
		z3.times_i()
		F.a.copy(z0); F.a.add(z3)
	}
	F.norm()
}

/* this=1/this */
func (F *FP48) Inverse() {
	f0:=NewFP16copy(F.a)
	f1:=NewFP16copy(F.b)
	f2:=NewFP16copy(F.a)
	f3:=NewFP16int(0)

	F.norm()
	f0.sqr()
	f1.mul(F.c)
	f1.times_i()
	f0.sub(f1); f0.norm()

	f1.copy(F.c); f1.sqr()
	f1.times_i()
	f2.mul(F.b)
	f1.sub(f2); f1.norm()

	f2.copy(F.b); f2.sqr()
	f3.copy(F.a); f3.mul(F.c)
	f2.sub(f3); f2.norm()

	f3.copy(F.b); f3.mul(f2)
	f3.times_i()
	F.a.mul(f0)
	f3.add(F.a)
	F.c.mul(f1)
	F.c.times_i()

	f3.add(F.c); f3.norm()
	f3.inverse()
	F.a.copy(f0); F.a.mul(f3)
	F.b.copy(f1); F.b.mul(f3)
	F.c.copy(f2); F.c.mul(f3)
}

/* this=this^p using Frobenius */
func (F *FP48) frob(f *FP2, n int) {
	f2:=NewFP2copy(f)
	f3:=NewFP2copy(f)

	f2.sqr()
	f3.mul(f2)

	f3.mul_ip(); f3.norm()
	f3.mul_ip(); f3.norm()

	for i:=0;i<n;i++ {
		F.a.frob(f3);
		F.b.frob(f3);
		F.c.frob(f3);

		F.b.qmul(f); F.b.times_i4(); F.b.times_i2(); 
		F.c.qmul(f2); F.c.times_i4(); F.c.times_i4(); F.c.times_i4()
	}
}

/* trace function */
func (F *FP48) trace() *FP16 {
	t:=NewFP16int(0)
	t.copy(F.a)
	t.imul(3)
	t.reduce()
	return t;
}

/* convert from byte array to FP48 */
func FP48_fromBytes(w []byte) *FP48 {
	var t [int(MODBYTES)]byte
	MB:=int(MODBYTES)

	for i:=0;i<MB;i++ {t[i]=w[i]}
	a:=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+MB]}
	b:=FromBytes(t[:])
	c:=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+2*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+3*MB]}
	b=FromBytes(t[:])
	d:=NewFP2bigs(a,b)

	ea:=NewFP4fp2s(c,d)

	for i:=0;i<MB;i++ {t[i]=w[i+4*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+5*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+6*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+7*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	eb:=NewFP4fp2s(c,d)

	e:=NewFP8fp4s(ea,eb)

	for i:=0;i<MB;i++ {t[i]=w[i+8*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+9*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+10*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+11*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	ea=NewFP4fp2s(c,d)

	for i:=0;i<MB;i++ {t[i]=w[i+12*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+13*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+14*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+15*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	eb=NewFP4fp2s(c,d)

	f:=NewFP8fp4s(ea,eb)

	g:=NewFP16fp8s(e,f)



	for i:=0;i<MB;i++ {t[i]=w[i+16*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+17*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+18*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+19*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	ea=NewFP4fp2s(c,d)

	for i:=0;i<MB;i++ {t[i]=w[i+20*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+21*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+22*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+23*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	eb=NewFP4fp2s(c,d)

	e=NewFP8fp4s(ea,eb)

	for i:=0;i<MB;i++ {t[i]=w[i+24*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+25*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+26*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+27*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	ea=NewFP4fp2s(c,d)

	for i:=0;i<MB;i++ {t[i]=w[i+28*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+29*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+30*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+31*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	eb=NewFP4fp2s(c,d)

	f=NewFP8fp4s(ea,eb)

	h:=NewFP16fp8s(e,f)

	for i:=0;i<MB;i++ {t[i]=w[i+32*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+33*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+34*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+35*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	ea=NewFP4fp2s(c,d)

	for i:=0;i<MB;i++ {t[i]=w[i+36*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+37*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+38*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+39*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	eb=NewFP4fp2s(c,d)

	e=NewFP8fp4s(ea,eb)

	for i:=0;i<MB;i++ {t[i]=w[i+40*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+41*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+42*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+43*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	ea=NewFP4fp2s(c,d)

	for i:=0;i<MB;i++ {t[i]=w[i+44*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+45*MB]}
	b=FromBytes(t[:])
	c=NewFP2bigs(a,b)

	for i:=0;i<MB;i++ {t[i]=w[i+46*MB]}
	a=FromBytes(t[:])
	for i:=0;i<MB;i++ {t[i]=w[i+47*MB]}
	b=FromBytes(t[:])
	d=NewFP2bigs(a,b)

	eb=NewFP4fp2s(c,d)

	f=NewFP8fp4s(ea,eb)

	i:=NewFP16fp8s(e,f)

	return NewFP48fp16s(g,h,i)
}

/* convert this to byte array */
func (F *FP48) ToBytes(w []byte) {
	var t [int(MODBYTES)]byte
	MB:=int(MODBYTES)
	F.a.a.a.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i]=t[i]}
	F.a.a.a.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+MB]=t[i]}
	F.a.a.a.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+2*MB]=t[i]}
	F.a.a.a.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+3*MB]=t[i]}
	F.a.a.b.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+4*MB]=t[i]}
	F.a.a.b.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+5*MB]=t[i]}
	F.a.a.b.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+6*MB]=t[i]}
	F.a.a.b.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+7*MB]=t[i]}

	F.a.b.a.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+8*MB]=t[i]}
	F.a.b.a.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+9*MB]=t[i]}
	F.a.b.a.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+10*MB]=t[i]}
	F.a.b.a.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+11*MB]=t[i]}
	F.a.b.b.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+12*MB]=t[i]}
	F.a.b.b.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+13*MB]=t[i]}
	F.a.b.b.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+14*MB]=t[i]}
	F.a.b.b.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+15*MB]=t[i]}


	F.b.a.a.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+16*MB]=t[i]}
	F.b.a.a.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+17*MB]=t[i]}
	F.b.a.a.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+18*MB]=t[i]}
	F.b.a.a.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+19*MB]=t[i]}
	F.b.a.b.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+20*MB]=t[i]}
	F.b.a.b.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+21*MB]=t[i]}
	F.b.a.b.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+22*MB]=t[i]}
	F.b.a.b.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+23*MB]=t[i]}

	F.b.b.a.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+24*MB]=t[i]}
	F.b.b.a.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+25*MB]=t[i]}
	F.b.b.a.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+26*MB]=t[i]}
	F.b.b.a.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+27*MB]=t[i]}
	F.b.b.b.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+28*MB]=t[i]}
	F.b.b.b.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+29*MB]=t[i]}
	F.b.b.b.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+30*MB]=t[i]}
	F.b.b.b.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+31*MB]=t[i]}



	F.c.a.a.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+32*MB]=t[i]}
	F.c.a.a.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+33*MB]=t[i]}
	F.c.a.a.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+34*MB]=t[i]}
	F.c.a.a.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+35*MB]=t[i]}
	F.c.a.b.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+36*MB]=t[i]}
	F.c.a.b.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+37*MB]=t[i]}
	F.c.a.b.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+38*MB]=t[i]}
	F.c.a.b.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+39*MB]=t[i]}

	F.c.b.a.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+40*MB]=t[i]}
	F.c.b.a.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+41*MB]=t[i]}
	F.c.b.a.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+42*MB]=t[i]}
	F.c.b.a.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+43*MB]=t[i]}
	F.c.b.b.geta().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+44*MB]=t[i]}
	F.c.b.b.geta().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+45*MB]=t[i]}
	F.c.b.b.getb().GetA().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+46*MB]=t[i]}
	F.c.b.b.getb().GetB().ToBytes(t[:])
	for i:=0;i<MB;i++ {w[i+47*MB]=t[i]}
}

/* convert to hex string */
func (F *FP48) ToString() string {
	return ("["+F.a.toString()+","+F.b.toString()+","+F.c.toString()+"]")
}

/* this=this^e */ 
func (F *FP48) Pow(e *BIG) *FP48 {
	sf:=NewFP48copy(F)
	sf.norm()
	e1:=NewBIGcopy(e)
	e1.norm()
	e3:=NewBIGcopy(e1)
	e3.pmul(3)
	e3.norm()

	w:=NewFP48copy(sf)

	nb:=e3.nbits()
	for i:=nb-2;i>=1;i-- {
		w.usqr()
		bt:=e3.bit(i)-e1.bit(i)
		if bt==1 {
			w.Mul(sf)
		}
		if bt==-1 {
			sf.conj()
			w.Mul(sf)
			sf.conj()	
		}
	}
	w.reduce()
	return w

}

/* constant time powering by small integer of max length bts */
func (F *FP48) pinpow(e int,bts int) {
	var R []*FP48
	R=append(R,NewFP48int(1))
	R=append(R,NewFP48copy(F))

	for i:=bts-1;i>=0;i-- {
		b:=(e>>uint(i))&1
		R[1-b].Mul(R[b])
		R[b].usqr()
	}
	F.Copy(R[0])
}

/* Fast compressed FP16 power of unitary FP48 */
func (F *FP48) Compow(e *BIG,r *BIG) *FP16 {
	q:=NewBIGints(Modulus)
	f:=NewFP2bigs(NewBIGints(Fra),NewBIGints(Frb))

	m:=NewBIGcopy(q)
	m.Mod(r)

	a:=NewBIGcopy(e)
	a.Mod(m)

	b:=NewBIGcopy(e)
	b.div(m)

	g1:=NewFP48copy(F);
	c:=g1.trace()

	if b.iszilch() {
		c=c.xtr_pow(e)
		return c
	}

	g2:=NewFP48copy(F)
	g2.frob(f,1)
	cp:=g2.trace()

	g1.conj()
	g2.Mul(g1)
	cpm1:=g2.trace()
	g2.Mul(g1)
	cpm2:=g2.trace()

	c=c.xtr_pow2(cp,cpm1,cpm2,a,b)
	return c
}


/* 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 

func pow16(q []*FP48,u []*BIG) *FP48 {
	var g1 []*FP48
	var g2 []*FP48
	var g3 []*FP48
	var g4 []*FP48
	var w1 [NLEN*int(BASEBITS)+1]int8
	var s1 [NLEN*int(BASEBITS)+1]int8
	var w2 [NLEN*int(BASEBITS)+1]int8
	var s2 [NLEN*int(BASEBITS)+1]int8
	var w3 [NLEN*int(BASEBITS)+1]int8
	var s3 [NLEN*int(BASEBITS)+1]int8
	var w4 [NLEN*int(BASEBITS)+1]int8
	var s4 [NLEN*int(BASEBITS)+1]int8
	var t []*BIG
	r:=NewFP48int(0)
	p:=NewFP48int(0)
	mt:=NewBIGint(0)
	var bt int8
	var k int

	for i:=0;i<16;i++ {
		t=append(t,NewBIGcopy(u[i]))
	}

	g1=append(g1,NewFP48copy(q[0]))	// q[0]
	g1=append(g1,NewFP48copy(g1[0])); g1[1].Mul(q[1])	// q[0].q[1]
	g1=append(g1,NewFP48copy(g1[0])); g1[2].Mul(q[2])	// q[0].q[2]
	g1=append(g1,NewFP48copy(g1[1])); g1[3].Mul(q[2])	// q[0].q[1].q[2]
	g1=append(g1,NewFP48copy(g1[0])); g1[4].Mul(q[3])	// q[0].q[3]
	g1=append(g1,NewFP48copy(g1[1])); g1[5].Mul(q[3])	// q[0].q[1].q[3]
	g1=append(g1,NewFP48copy(g1[2])); g1[6].Mul(q[3])	// q[0].q[2].q[3]
	g1=append(g1,NewFP48copy(g1[3])); g1[7].Mul(q[3])	// q[0].q[1].q[2].q[3]

	Fra:=NewBIGints(Fra)
	Frb:=NewBIGints(Frb)
	X:=NewFP2bigs(Fra,Frb)	

// Use Frobenius
	for i:=0;i<8;i++ {
		g2=append(g2,NewFP48copy(g1[i])); g2[i].frob(X,4)	
		g3=append(g3,NewFP48copy(g2[i])); g3[i].frob(X,4)	
		g4=append(g4,NewFP48copy(g3[i])); g4[i].frob(X,4)			
	}

// Make them odd
	pb1:=1-t[0].parity()
	t[0].inc(pb1)
//	t[0].norm();

	pb2:=1-t[4].parity()
	t[4].inc(pb2)
//	t[4].norm();

	pb3:=1-t[8].parity()
	t[8].inc(pb3)
//	t[8].norm();

	pb4:=1-t[12].parity()
	t[12].inc(pb4)
//	t[12].norm();

// Number of bits
	mt.zero()
	for i:=0;i<16;i++ {
		t[i].norm()
		mt.or(t[i])
	}

	nb:=1+mt.nbits();
	
// Sign pivot 
	s1[nb-1]=1
	s2[nb-1]=1
	s3[nb-1]=1
	s4[nb-1]=1
	for i:=0;i<nb-1;i++ {
		t[0].fshr(1)
		s1[i]=2*int8(t[0].parity())-1
		t[4].fshr(1)
		s2[i]=2*int8(t[4].parity())-1
		t[8].fshr(1)
		s3[i]=2*int8(t[8].parity())-1
		t[12].fshr(1)
		s4[i]=2*int8(t[12].parity())-1

	}

// Recoded exponents
	for i:=0; i<nb; i++ {
		w1[i]=0
		k=1
		for j:=1; j<4; j++ {
			bt=s1[i]*int8(t[j].parity())
			t[j].fshr(1)
			t[j].dec(int(bt)>>1)
			t[j].norm()
			w1[i]+=bt*int8(k)
			k*=2
		}
		w2[i]=0
		k=1
		for j:=5; j<8; j++ {
			bt=s2[i]*int8(t[j].parity())
			t[j].fshr(1)
			t[j].dec(int(bt)>>1)
			t[j].norm()
			w2[i]+=bt*int8(k)
			k*=2
		}
		w3[i]=0
		k=1
		for j:=9; j<12; j++ {
			bt=s3[i]*int8(t[j].parity())
			t[j].fshr(1)
			t[j].dec(int(bt)>>1)
			t[j].norm()
			w3[i]+=bt*int8(k)
			k*=2
		}
		w4[i]=0
		k=1
		for j:=13; j<16; j++ {
			bt=s4[i]*int8(t[j].parity())
			t[j].fshr(1)
			t[j].dec(int(bt)>>1)
			t[j].norm()
			w4[i]+=bt*int8(k)
			k*=2
		}
	}

// Main loop
	p.selector(g1,int32(2*w1[nb-1]+1))  
	r.selector(g2,int32(2*w2[nb-1]+1)) 
	p.Mul(r)
	r.selector(g3,int32(2*w3[nb-1]+1)) 
	p.Mul(r)
	r.selector(g4,int32(2*w4[nb-1]+1)) 
	p.Mul(r)
	for i:=nb-2;i>=0;i-- {
		p.usqr()
		r.selector(g1,int32(2*w1[i]+s1[i]))
		p.Mul(r)
		r.selector(g2,int32(2*w2[i]+s2[i]))
		p.Mul(r)
		r.selector(g3,int32(2*w3[i]+s3[i]))
		p.Mul(r)
		r.selector(g4,int32(2*w4[i]+s4[i]))
		p.Mul(r)
	}

// apply correction
	r.Copy(q[0]); r.conj()   
	r.Mul(p)
	p.cmove(r,pb1)
	r.Copy(q[4]); r.conj()   
	r.Mul(p)
	p.cmove(r,pb2)
	r.Copy(q[8]); r.conj()   
	r.Mul(p)
	p.cmove(r,pb3)
	r.Copy(q[12]); r.conj()   
	r.Mul(p)
	p.cmove(r,pb4)

	p.reduce()
	return p;
}