version3/rust/pair.rs - incubator-milagro-crypto - Git at Google

 /*
 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.
 */


 use xxx::fp::FP;
 use xxx::ecp::ECP;
 use xxx::fp2::FP2;
 use xxx::ecp2::ECP2;
 use xxx::fp4::FP4;
 use xxx::fp12::FP12;
 use xxx::big::BIG;
 use xxx::dbig::DBIG;
 use xxx::ecp;
 use xxx::rom;

 //use std::thread;


 #[allow(non_snake_case)]
 fn linedbl(A: &mut ECP2,qx: &FP,qy: &FP) -> FP12 {
 	let mut a=FP4::new();
 	let mut b=FP4::new();
 	let mut c=FP4::new();

 	let mut xx=FP2::new_copy(&A.getpx());  //X
 	let mut yy=FP2::new_copy(&A.getpy());  //Y
 	let mut zz=FP2::new_copy(&A.getpz());  //Z
 	let mut yz=FP2::new_copy(&yy);        //Y
 	yz.mul(&zz);                //YZ
 	xx.sqr();	               //X^2
 	yy.sqr();	               //Y^2
 	zz.sqr();			       //Z^2

 	yz.imul(4);
 	yz.neg(); yz.norm();       //-2YZ
 	yz.pmul(qy);               //-2YZ.Ys

 	xx.imul(6);                //3X^2
 	xx.pmul(qx);               //3X^2.Xs

 	let sb=3*rom::CURVE_B_I;
 	zz.imul(sb);
 	if ecp::SEXTIC_TWIST==ecp::D_TYPE {
 		zz.div_ip2();
 	}
 	if ecp::SEXTIC_TWIST==ecp::M_TYPE {
 		zz.mul_ip();
 		zz.dbl();
 		yz.mul_ip();
 		yz.norm();
 	}

 	zz.norm(); // 3b.Z^2

 	yy.dbl();
 	zz.sub(&yy); zz.norm();     // 3b.Z^2-Y^2

 	a.copy(&FP4::new_fp2s(&yz,&zz)); // -2YZ.Ys | 3b.Z^2-Y^2 | 3X^2.Xs
 	if ecp::SEXTIC_TWIST==ecp::D_TYPE {
 		b.copy(&FP4::new_fp2(&xx));       // L(0,1) | L(0,0) | L(1,0)
 	}
 	if ecp::SEXTIC_TWIST==ecp::M_TYPE {
 		c.copy(&FP4::new_fp2(&xx));
 		c.times_i();
 	}
 	A.dbl();
 	return FP12::new_fp4s(&a,&b,&c);
 }

 #[allow(non_snake_case)]
 fn lineadd(A: &mut ECP2,B: &ECP2,qx: &FP,qy: &FP) -> FP12 {

 	let mut a=FP4::new();
 	let mut b=FP4::new();
 	let mut c=FP4::new();

 	let mut x1=FP2::new_copy(&A.getpx());    // X1
 	let mut y1=FP2::new_copy(&A.getpy());    // Y1
 	let mut t1=FP2::new_copy(&A.getpz());    // Z1
 	let mut t2=FP2::new_copy(&A.getpz());    // Z1

 	t1.mul(&B.getpy());    // T1=Z1.Y2
 	t2.mul(&B.getpx());    // T2=Z1.X2

 	x1.sub(&t2); x1.norm();  // X1=X1-Z1.X2
 	y1.sub(&t1); y1.norm();  // Y1=Y1-Z1.Y2

 	t1.copy(&x1);            // T1=X1-Z1.X2
 	x1.pmul(qy);            // X1=(X1-Z1.X2).Ys
 	if ecp::SEXTIC_TWIST==ecp::M_TYPE {
 		x1.mul_ip();
 		x1.norm();
 	}

 	t1.mul(&B.getpy());       // T1=(X1-Z1.X2).Y2

 	t2.copy(&y1);            // T2=Y1-Z1.Y2
 	t2.mul(&B.getpx());       // T2=(Y1-Z1.Y2).X2
 	t2.sub(&t1); t2.norm();          // T2=(Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2
 	y1.pmul(qx); y1.neg(); y1.norm(); // Y1=-(Y1-Z1.Y2).Xs

 	a.copy(&FP4::new_fp2s(&x1,&t2)); // (X1-Z1.X2).Ys  |  (Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2  | - (Y1-Z1.Y2).Xs
 	if ecp::SEXTIC_TWIST==ecp::D_TYPE {
 		b.copy(&FP4::new_fp2(&y1));
 	}
 	if ecp::SEXTIC_TWIST==ecp::M_TYPE {
 		c.copy(&FP4::new_fp2(&y1));
 		c.times_i();
 	}

 	A.add(B);
 	return FP12::new_fp4s(&a,&b,&c);
 }

 #[allow(non_snake_case)]
 /* Optimal R-ate pairing */
 pub fn ate(P1: &ECP2,Q1: &ECP) -> FP12 {
 	let mut f = FP2::new_bigs(&BIG::new_ints(&rom::FRA),&BIG::new_ints(&rom::FRB));
 	let x = BIG::new_ints(&rom::CURVE_BNX);
 	let mut n = BIG::new_copy(&x);
 	let mut K = ECP2::new();

 	if ecp::CURVE_PAIRING_TYPE == ecp::BN {
 		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();
 	let mut n3 = BIG::new_copy(&n);
 	n3.pmul(3);
 	n3.norm();

 	let mut P=ECP2::new(); P.copy(P1); P.affine();
 	let mut Q=ECP::new(); Q.copy(Q1); Q.affine();


 	let qx=FP::new_copy(&Q.getpx());
 	let qy=FP::new_copy(&Q.getpy());

 	let mut A=ECP2::new();
 	let mut r=FP12::new_int(1);

 	A.copy(&P);
 	let mut NP=ECP2::new();
 	NP.copy(&P);
 	NP.neg();

 	let nb=n3.nbits();

 	for i in (1..nb-1).rev() {
 		r.sqr();
 		//let mut lv=FP12::new();
 		//let handler = thread::spawn(move || {
 		//	lv=linedbl(&mut A,&qx,&qy);
 		//});
 		//handler.join().unwrap();

 		let mut lv=linedbl(&mut A,&qx,&qy);
 		r.smul(&lv,ecp::SEXTIC_TWIST);
 		let bt=n3.bit(i)-n.bit(i);
 		if bt==1 {
 			lv=lineadd(&mut A,&P,&qx,&qy);
 			r.smul(&lv,ecp::SEXTIC_TWIST);
 		}
 		if bt == -1 {

 			lv=lineadd(&mut A,&NP,&qx,&qy);
 			r.smul(&lv,ecp::SEXTIC_TWIST);

 		}
 	}

 	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();
 		}

 		K.copy(&P);
 		K.frob(&f);

 		let mut lv=lineadd(&mut A,&K,&qx,&qy);
 		r.smul(&lv,ecp::SEXTIC_TWIST);
 		K.frob(&f);
 		K.neg();
 		lv=lineadd(&mut A,&K,&qx,&qy);
 		r.smul(&lv,ecp::SEXTIC_TWIST);
 	}

 	return r;
 }

 #[allow(non_snake_case)]
 /* Optimal R-ate double pairing e(P,Q).e(R,S) */
 pub fn ate2(P1: &ECP2,Q1: &ECP,R1: &ECP2,S1: &ECP) -> FP12 {
 	let mut f = FP2::new_bigs(&BIG::new_ints(&rom::FRA),&BIG::new_ints(&rom::FRB));
 	let x = BIG::new_ints(&rom::CURVE_BNX);
 	let mut n = BIG::new_copy(&x);
 	let mut K = ECP2::new();

 	if ecp::CURVE_PAIRING_TYPE == ecp::BN {
 		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();
 	let mut n3 = BIG::new_copy(&n);
 	n3.pmul(3);
 	n3.norm();

 	let mut P=ECP2::new(); P.copy(P1); P.affine();
 	let mut Q=ECP::new(); Q.copy(Q1); Q.affine();
 	let mut R=ECP2::new(); R.copy(R1); R.affine();
 	let mut S=ECP::new(); S.copy(S1); S.affine();


 	let qx=FP::new_copy(&Q.getpx());
 	let qy=FP::new_copy(&Q.getpy());

 	let sx=FP::new_copy(&S.getpx());
 	let sy=FP::new_copy(&S.getpy());

 	let mut A=ECP2::new();
 	let mut B=ECP2::new();
 	let mut r=FP12::new_int(1);

 	A.copy(&P);
 	B.copy(&R);

 	let mut NP=ECP2::new();
 	NP.copy(&P);
 	NP.neg();
 	let mut NR=ECP2::new();
 	NR.copy(&R);
 	NR.neg();

 	let nb=n3.nbits();

 	for i in (1..nb-1).rev() {
 		r.sqr();
 		let mut lv=linedbl(&mut A,&qx,&qy);
 		r.smul(&lv,ecp::SEXTIC_TWIST);
 		lv=linedbl(&mut B,&sx,&sy);
 		r.smul(&lv,ecp::SEXTIC_TWIST);
 		let bt=n3.bit(i)-n.bit(i);
 		if bt == 1 {
 			lv=lineadd(&mut A,&P,&qx,&qy);
 			r.smul(&lv,ecp::SEXTIC_TWIST);
 			lv=lineadd(&mut B,&R,&sx,&sy);
 			r.smul(&lv,ecp::SEXTIC_TWIST);
 		}
 		if bt == -1 {

 			lv=lineadd(&mut A,&NP,&qx,&qy);
 			r.smul(&lv,ecp::SEXTIC_TWIST);
 			lv=lineadd(&mut B,&NR,&sx,&sy);
 			r.smul(&lv,ecp::SEXTIC_TWIST);

 		}
 	}

 	if ecp::SIGN_OF_X == ecp::NEGATIVEX {
 		r.conj();
 	}

 /* R-ate fixup */
 	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);

 		let mut lv=lineadd(&mut A,&K,&qx,&qy);
 		r.smul(&lv,ecp::SEXTIC_TWIST);
 		K.frob(&f);
 		K.neg();
 		lv=lineadd(&mut A,&K,&qx,&qy);
 		r.smul(&lv,ecp::SEXTIC_TWIST);

 		K.copy(&R);
 		K.frob(&f);

 		lv=lineadd(&mut B,&K,&sx,&sy);
 		r.smul(&lv,ecp::SEXTIC_TWIST);
 		K.frob(&f);
 		K.neg();
 		lv=lineadd(&mut B,&K,&sx,&sy);
 		r.smul(&lv,ecp::SEXTIC_TWIST);
 	}

 	return r;
 }

 /* final exponentiation - keep separate for multi-pairings and to avoid thrashing stack */
 pub fn fexp(m: &FP12) -> FP12 {
 	let f = FP2::new_bigs(&BIG::new_ints(&rom::FRA),&BIG::new_ints(&rom::FRB));
 	let mut x = BIG::new_ints(&rom::CURVE_BNX);
 	let mut r=FP12::new_copy(m);

 /* Easy part of final exp */
 	let mut lv=FP12::new_copy(&r);
 	lv.inverse();
 	r.conj();

 	r.mul(&lv);
 	lv.copy(&r);
 	r.frob(&f);
 	r.frob(&f);
 	r.mul(&lv);
 /* Hard part of final exp */
 	if ecp::CURVE_PAIRING_TYPE == ecp::BN {
 		lv.copy(&r);
 		lv.frob(&f);
 		let mut x0=FP12::new_copy(&lv);
 		x0.frob(&f);
 		lv.mul(&r);
 		x0.mul(&lv);
 		x0.frob(&f);
 		let mut x1=FP12::new_copy(&r);
 		x1.conj();
 		let mut x4=r.pow(&mut x);
 		if ecp::SIGN_OF_X == ecp::POSITIVEX {
 			x4.conj();
 		}

 		let mut x3=FP12::new_copy(&x4);
 		x3.frob(&f);

 		let mut x2=x4.pow(&mut x);
 		if ecp::SIGN_OF_X == ecp::POSITIVEX {
 			x2.conj();
 		}
 		let mut x5=FP12::new_copy(&x2); x5.conj();
 		lv=x2.pow(&mut x);
 		if ecp::SIGN_OF_X == ecp::POSITIVEX {
 			lv.conj();
 		}
 		x2.frob(&f);
 		r.copy(&x2); r.conj();

 		x4.mul(&r);
 		x2.frob(&f);

 		r.copy(&lv);
 		r.frob(&f);
 		lv.mul(&r);

 		lv.usqr();
 		lv.mul(&x4);
 		lv.mul(&x5);
 		r.copy(&x3);
 		r.mul(&x5);
 		r.mul(&lv);
 		lv.mul(&x2);
 		r.usqr();
 		r.mul(&lv);
 		r.usqr();
 		lv.copy(&r);
 		lv.mul(&x1);
 		r.mul(&x0);
 		lv.usqr();
 		r.mul(&lv);
 		r.reduce();
 	} else {

 // Ghamman & Fouotsa Method

 		let mut y0=FP12::new_copy(&r); y0.usqr();
 		let mut y1=y0.pow(&mut x);
 		if ecp::SIGN_OF_X == ecp::NEGATIVEX {
 			y1.conj();
 		}
 		x.fshr(1); let mut y2=y1.pow(&mut x);
 		if ecp::SIGN_OF_X == ecp::NEGATIVEX {
 			y2.conj();
 		}
 		x.fshl(1);
 		let mut y3=FP12::new_copy(&r); y3.conj();
 		y1.mul(&y3);

 		y1.conj();
 		y1.mul(&y2);

 		y2=y1.pow(&mut x);
 		if ecp::SIGN_OF_X == ecp::NEGATIVEX {
 			y2.conj();
 		}
 		y3=y2.pow(&mut x);
 		if ecp::SIGN_OF_X == ecp::NEGATIVEX {
 			y3.conj();
 		}
 		y1.conj();
 		y3.mul(&y1);

 		y1.conj();
 		y1.frob(&f); y1.frob(&f); y1.frob(&f);
 		y2.frob(&f); y2.frob(&f);
 		y1.mul(&y2);

 		y2=y3.pow(&mut x);
 		if ecp::SIGN_OF_X == ecp::NEGATIVEX {
 			y2.conj();
 		}
 		y2.mul(&y0);
 		y2.mul(&r);

 		y1.mul(&y2);
 		y2.copy(&y3); y2.frob(&f);
 		y1.mul(&y2);
 		r.copy(&y1);
 		r.reduce();


 /*
 		let mut x0=FP12::new_copy(&r);
 		let mut x1=FP12::new_copy(&r);
 		lv.copy(&r); lv.frob(&mut f);
 		let mut x3=FP12::new_copy(&lv); x3.conj(); x1.mul(&mut x3);
 		lv.frob(&mut f); lv.frob(&mut f);
 		x1.mul(&mut lv);

 		r=r.pow(&mut x);  //r=r.pow(x);
 		x3.copy(&r); x3.conj(); x1.mul(&mut x3);
 		lv.copy(&r); lv.frob(&mut f);
 		x0.mul(&mut lv);
 		lv.frob(&mut f);
 		x1.mul(&mut lv);
 		lv.frob(&mut f);
 		x3.copy(&lv); x3.conj(); x0.mul(&mut x3);

 		r=r.pow(&mut x);
 		x0.mul(&mut r);
 		lv.copy(&r); lv.frob(&mut f); lv.frob(&mut f);
 		x3.copy(&lv); x3.conj(); x0.mul(&mut x3);
 		lv.frob(&mut f);
 		x1.mul(&mut lv);

 		r=r.pow(&mut x);
 		lv.copy(&r); lv.frob(&mut f);
 		x3.copy(&lv); x3.conj(); x0.mul(&mut x3);
 		lv.frob(&mut f);
 		x1.mul(&mut lv);

 		r=r.pow(&mut x);
 		x3.copy(&r); x3.conj(); x0.mul(&mut x3);
 		lv.copy(&r); lv.frob(&mut f);
 		x1.mul(&mut lv);

 		r=r.pow(&mut x);
 		x1.mul(&mut r);

 		x0.usqr();
 		x0.mul(&mut x1);
 		r.copy(&x0);
 		r.reduce();  */
 	}
 	return r;
 }

 #[allow(non_snake_case)]
 /* GLV method */
 fn glv(e: &BIG) -> [BIG;2] {
 	let mut u:[BIG;2]=[BIG::new(),BIG::new()];
 	if ecp::CURVE_PAIRING_TYPE == ecp::BN {
 		let mut t=BIG::new();
 		let q=BIG::new_ints(&rom::CURVE_ORDER);
 		let mut v:[BIG;2]=[BIG::new(),BIG::new()];

 		for i in 0..2 {
 			t.copy(&BIG::new_ints(&rom::CURVE_W[i]));  // why not just t=new BIG(ROM.CURVE_W[i]);
 			let mut d:DBIG = BIG::mul(&t,e);
 			v[i].copy(&d.div(&q));
 		}
 		u[0].copy(&e);
 		for i in 0..2 {
 			for j in 0..2 {
 				t=BIG::new_ints(&rom::CURVE_SB[j][i]);
 				t=BIG::modmul(&mut v[j],&mut t,&q);
 				u[i].add(&q);
 				u[i].sub(&t);
 				u[i].rmod(&q);
 			}
 		}
 	} else {
 		let q=BIG::new_ints(&rom::CURVE_ORDER);
 		let x=BIG::new_ints(&rom::CURVE_BNX);
 		let x2=BIG::smul(&x,&x);
 		u[0].copy(&e);
 		u[0].rmod(&x2);
 		u[1].copy(&e);
 		u[1].div(&x2);
 		u[1].rsub(&q);
 	}
 	return u;
 }

 #[allow(non_snake_case)]
 /* Galbraith & Scott Method */
 pub fn gs(e: &BIG) -> [BIG;4] {
 	let mut u:[BIG;4]=[BIG::new(),BIG::new(),BIG::new(),BIG::new()];
 	if ecp::CURVE_PAIRING_TYPE == ecp::BN {
 		let mut t=BIG::new();
 		let q=BIG::new_ints(&rom::CURVE_ORDER);

 		let mut v:[BIG;4]=[BIG::new(),BIG::new(),BIG::new(),BIG::new()];
 		for i in 0..4 {
 			t.copy(&BIG::new_ints(&rom::CURVE_WB[i]));
 			let mut d:DBIG=BIG::mul(&t,e);
 			v[i].copy(&d.div(&q));
 		}
 		u[0].copy(&e);
 		for i in 0..4 {
 			for j in 0..4 {
 				t=BIG::new_ints(&rom::CURVE_BB[j][i]);
 				t=BIG::modmul(&mut v[j],&mut t,&q);
 				u[i].add(&q);
 				u[i].sub(&t);
 				u[i].rmod(&q);
 			}
 		}
 	} else {
 		let q=BIG::new_ints(&rom::CURVE_ORDER);
 		let x=BIG::new_ints(&rom::CURVE_BNX);
 		let mut w=BIG::new_copy(&e);
 		for i in 0..3 {
 			u[i].copy(&w);
 			u[i].rmod(&x);
 			w.div(&x);
 		}
 		u[3].copy(&w);
 		if ecp::SIGN_OF_X == ecp::NEGATIVEX {
 			let mut t=BIG::new();
 			t.copy(&BIG::modneg(&mut u[1],&q));
 			u[1].copy(&t);
 			t.copy(&BIG::modneg(&mut u[3],&q));
 			u[3].copy(&t);
 		}
 	}
 	return u;
 }

 #[allow(non_snake_case)]
 /* Multiply P by e in group G1 */
 pub fn g1mul(P: &ECP,e: &mut BIG) -> ECP {
 	let mut R=ECP::new();
 	if rom::USE_GLV {
 	//	P.affine();
 		R.copy(P);
 		let mut Q=ECP::new();
 		Q.copy(P); Q.affine();
 		let q=BIG::new_ints(&rom::CURVE_ORDER);
 		let mut cru=FP::new_big(&BIG::new_ints(&rom::CURVE_CRU));
 		let mut u=glv(e);
 		Q.mulx(&mut cru);

 		let mut np=u[0].nbits();
 		let mut t:BIG=BIG::modneg(&mut u[0],&q);
 		let mut nn=t.nbits();
 		if nn<np {
 			u[0].copy(&t);
 			R.neg();
 		}

 		np=u[1].nbits();
 		t=BIG::modneg(&mut u[1],&q);
 		nn=t.nbits();
 		if nn<np {
 			u[1].copy(&t);
 			Q.neg();
 		}
 		u[0].norm();
 		u[1].norm();
 		R=R.mul2(&u[0],&mut Q,&u[1]);

 	} else {
 		R=P.mul(e);
 	}
 	return R;
 }

 #[allow(non_snake_case)]
 /* Multiply P by e in group G2 */
 pub fn g2mul(P: &ECP2,e: &BIG) -> ECP2 {
 	let mut R=ECP2::new();
 	if rom::USE_GS_G2 {
 		let mut Q:[ECP2;4]=[ECP2::new(),ECP2::new(),ECP2::new(),ECP2::new()];
 		let mut f = FP2::new_bigs(&BIG::new_ints(&rom::FRA),&BIG::new_ints(&rom::FRB));
 		let q=BIG::new_ints(&rom::CURVE_ORDER);
 		let mut u=gs(e);
 		let mut T=ECP2::new();

 		if ecp::SEXTIC_TWIST==ecp::M_TYPE {
 			f.inverse();
 			f.norm();
 		}

 		let mut t=BIG::new();
 	//	P.affine();
 		Q[0].copy(&P);
 		for i in 1..4 {
 			T.copy(&Q[i-1]);
 			Q[i].copy(&T);
 			Q[i].frob(&f);
 		}
 		for i in 0..4 {
 			let np=u[i].nbits();
 			t.copy(&BIG::modneg(&mut u[i],&q));
 			let nn=t.nbits();
 			if nn<np {
 				u[i].copy(&t);
 				Q[i].neg();
 			}
 			u[i].norm();
 		}

 		R.copy(&ECP2::mul4(&mut Q,&u));

 	} else {
 		R.copy(&P.mul(e));
 	}
 	return R;
 }

 /* f=f^e */
 /* Note that this method requires a lot of RAM! Better to use compressed XTR method, see FP4.java */
 pub fn gtpow(d: &FP12,e: &BIG) -> FP12 {
 	let mut r=FP12::new();
 	if rom::USE_GS_GT {
 		let mut g:[FP12;4]=[FP12::new(),FP12::new(),FP12::new(),FP12::new()];
 		let f = FP2::new_bigs(&BIG::new_ints(&rom::FRA),&BIG::new_ints(&rom::FRB));
 		let q=BIG::new_ints(&rom::CURVE_ORDER);
 		let mut t=BIG::new();
 		let mut u=gs(e);
 		let mut w=FP12::new();

 		g[0].copy(&d);
 		for i in 1..4 {
 			w.copy(&g[i-1]);
 			g[i].copy(&w);
 			g[i].frob(&f);
 		}
 		for i in 0..4 {
 			let np=u[i].nbits();
 			t.copy(&BIG::modneg(&mut u[i],&q));
 			let nn=t.nbits();
 			if nn<np {
 				u[i].copy(&t);
 				g[i].conj();
 			}
 			u[i].norm();
 		}
 		r.copy(&FP12::pow4(&mut g,&u));
 	} else {
 		r.copy(&d.pow(e));
 	}
 	return r;
 }

 /*
 #[allow(non_snake_case)]
 fn main()
 {
 	let mut Q=ECP::new_bigs(&BIG::new_ints(&rom::CURVE_GX),&BIG::new_ints(&rom::CURVE_GY));
 	let mut P=ECP2::new_fp2s(&FP2::new_bigs(&BIG::new_ints(&rom::CURVE_PXA),&BIG::new_ints(&rom::CURVE_PXB)),&FP2::new_bigs(&BIG::new_ints(&rom::CURVE_PYA),&BIG::new_ints(&rom::CURVE_PYB)));

 	let mut r=BIG::new_ints(&rom::CURVE_ORDER);

 	println!("P= {}",P.tostring());
 	println!("Q= {}",Q.tostring());

 	//m:=NewBIGint(17)

 	let mut e=ate(&mut P,&mut Q);
 	println!("\ne= {}",e.tostring());

 	e=fexp(&e);

 	for i in 1..10 {
 		e=ate(&mut P,&mut Q);
 		e=fexp(&e);
 	}


 	//	e=GTpow(e,m);

 	println!("\ne= {}",e.tostring());


 	fmt.Printf("\n");
 	GLV:=glv(r)

 	fmt.Printf("GLV[0]= "+GLV[0].toString())
 	fmt.Printf("\n")

 	fmt.Printf("GLV[0]= "+GLV[1].toString())
 	fmt.Printf("\n")

 	G:=NewECP(); G.copy(Q)
 	R:=NewECP2(); R.copy(P)


 	e=ate(R,Q)
 	e=fexp(e)

 	e=GTpow(e,xa)
 	fmt.Printf("\ne= "+e.toString());
 	fmt.Printf("\n")

 	R=G2mul(R,xa)
 	e=ate(R,G)
 	e=fexp(e)

 	fmt.Printf("\ne= "+e.toString())
 	fmt.Printf("\n")

 	G=G1mul(G,xa)
 	e=ate(P,G)
 	e=fexp(e)
 	fmt.Printf("\ne= "+e.toString())
 	fmt.Printf("\n")
 }*/
	/*
	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.
	*/


	use xxx::fp::FP;
	use xxx::ecp::ECP;
	use xxx::fp2::FP2;
	use xxx::ecp2::ECP2;
	use xxx::fp4::FP4;
	use xxx::fp12::FP12;
	use xxx::big::BIG;
	use xxx::dbig::DBIG;
	use xxx::ecp;
	use xxx::rom;

	//use std::thread;


	#[allow(non_snake_case)]
	fn linedbl(A: &mut ECP2,qx: &FP,qy: &FP) -> FP12 {
	let mut a=FP4::new();
	let mut b=FP4::new();
	let mut c=FP4::new();

	let mut xx=FP2::new_copy(&A.getpx()); //X
	let mut yy=FP2::new_copy(&A.getpy()); //Y
	let mut zz=FP2::new_copy(&A.getpz()); //Z
	let mut yz=FP2::new_copy(&yy); //Y
	yz.mul(&zz); //YZ
	xx.sqr(); //X^2
	yy.sqr(); //Y^2
	zz.sqr(); //Z^2

	yz.imul(4);
	yz.neg(); yz.norm(); //-2YZ
	yz.pmul(qy); //-2YZ.Ys

	xx.imul(6); //3X^2
	xx.pmul(qx); //3X^2.Xs

	let sb=3*rom::CURVE_B_I;
	zz.imul(sb);
	if ecp::SEXTIC_TWIST==ecp::D_TYPE {
	zz.div_ip2();
	}
	if ecp::SEXTIC_TWIST==ecp::M_TYPE {
	zz.mul_ip();
	zz.dbl();
	yz.mul_ip();
	yz.norm();
	}

	zz.norm(); // 3b.Z^2

	yy.dbl();
	zz.sub(&yy); zz.norm(); // 3b.Z^2-Y^2

	a.copy(&FP4::new_fp2s(&yz,&zz)); // -2YZ.Ys \| 3b.Z^2-Y^2 \| 3X^2.Xs
	if ecp::SEXTIC_TWIST==ecp::D_TYPE {
	b.copy(&FP4::new_fp2(&xx)); // L(0,1) \| L(0,0) \| L(1,0)
	}
	if ecp::SEXTIC_TWIST==ecp::M_TYPE {
	c.copy(&FP4::new_fp2(&xx));
	c.times_i();
	}
	A.dbl();
	return FP12::new_fp4s(&a,&b,&c);
	}

	#[allow(non_snake_case)]
	fn lineadd(A: &mut ECP2,B: &ECP2,qx: &FP,qy: &FP) -> FP12 {

	let mut a=FP4::new();
	let mut b=FP4::new();
	let mut c=FP4::new();

	let mut x1=FP2::new_copy(&A.getpx()); // X1
	let mut y1=FP2::new_copy(&A.getpy()); // Y1
	let mut t1=FP2::new_copy(&A.getpz()); // Z1
	let mut t2=FP2::new_copy(&A.getpz()); // Z1

	t1.mul(&B.getpy()); // T1=Z1.Y2
	t2.mul(&B.getpx()); // T2=Z1.X2

	x1.sub(&t2); x1.norm(); // X1=X1-Z1.X2
	y1.sub(&t1); y1.norm(); // Y1=Y1-Z1.Y2

	t1.copy(&x1); // T1=X1-Z1.X2
	x1.pmul(qy); // X1=(X1-Z1.X2).Ys
	if ecp::SEXTIC_TWIST==ecp::M_TYPE {
	x1.mul_ip();
	x1.norm();
	}

	t1.mul(&B.getpy()); // T1=(X1-Z1.X2).Y2

	t2.copy(&y1); // T2=Y1-Z1.Y2
	t2.mul(&B.getpx()); // T2=(Y1-Z1.Y2).X2
	t2.sub(&t1); t2.norm(); // T2=(Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2
	y1.pmul(qx); y1.neg(); y1.norm(); // Y1=-(Y1-Z1.Y2).Xs

	a.copy(&FP4::new_fp2s(&x1,&t2)); // (X1-Z1.X2).Ys \| (Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2 \| - (Y1-Z1.Y2).Xs
	if ecp::SEXTIC_TWIST==ecp::D_TYPE {
	b.copy(&FP4::new_fp2(&y1));
	}
	if ecp::SEXTIC_TWIST==ecp::M_TYPE {
	c.copy(&FP4::new_fp2(&y1));
	c.times_i();
	}

	A.add(B);
	return FP12::new_fp4s(&a,&b,&c);
	}

	#[allow(non_snake_case)]
	/* Optimal R-ate pairing */
	pub fn ate(P1: &ECP2,Q1: &ECP) -> FP12 {
	let mut f = FP2::new_bigs(&BIG::new_ints(&rom::FRA),&BIG::new_ints(&rom::FRB));
	let x = BIG::new_ints(&rom::CURVE_BNX);
	let mut n = BIG::new_copy(&x);
	let mut K = ECP2::new();

	if ecp::CURVE_PAIRING_TYPE == ecp::BN {
	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();
	let mut n3 = BIG::new_copy(&n);
	n3.pmul(3);
	n3.norm();

	let mut P=ECP2::new(); P.copy(P1); P.affine();
	let mut Q=ECP::new(); Q.copy(Q1); Q.affine();


	let qx=FP::new_copy(&Q.getpx());
	let qy=FP::new_copy(&Q.getpy());

	let mut A=ECP2::new();
	let mut r=FP12::new_int(1);

	A.copy(&P);
	let mut NP=ECP2::new();
	NP.copy(&P);
	NP.neg();

	let nb=n3.nbits();

	for i in (1..nb-1).rev() {
	r.sqr();
	//let mut lv=FP12::new();
	//let handler = thread::spawn(move \|\| {
	// lv=linedbl(&mut A,&qx,&qy);
	//});
	//handler.join().unwrap();

	let mut lv=linedbl(&mut A,&qx,&qy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	let bt=n3.bit(i)-n.bit(i);
	if bt==1 {
	lv=lineadd(&mut A,&P,&qx,&qy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	}
	if bt == -1 {

	lv=lineadd(&mut A,&NP,&qx,&qy);
	r.smul(&lv,ecp::SEXTIC_TWIST);

	}
	}

	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();
	}

	K.copy(&P);
	K.frob(&f);

	let mut lv=lineadd(&mut A,&K,&qx,&qy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	K.frob(&f);
	K.neg();
	lv=lineadd(&mut A,&K,&qx,&qy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	}

	return r;
	}

	#[allow(non_snake_case)]
	/* Optimal R-ate double pairing e(P,Q).e(R,S) */
	pub fn ate2(P1: &ECP2,Q1: &ECP,R1: &ECP2,S1: &ECP) -> FP12 {
	let mut f = FP2::new_bigs(&BIG::new_ints(&rom::FRA),&BIG::new_ints(&rom::FRB));
	let x = BIG::new_ints(&rom::CURVE_BNX);
	let mut n = BIG::new_copy(&x);
	let mut K = ECP2::new();

	if ecp::CURVE_PAIRING_TYPE == ecp::BN {
	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();
	let mut n3 = BIG::new_copy(&n);
	n3.pmul(3);
	n3.norm();

	let mut P=ECP2::new(); P.copy(P1); P.affine();
	let mut Q=ECP::new(); Q.copy(Q1); Q.affine();
	let mut R=ECP2::new(); R.copy(R1); R.affine();
	let mut S=ECP::new(); S.copy(S1); S.affine();


	let qx=FP::new_copy(&Q.getpx());
	let qy=FP::new_copy(&Q.getpy());

	let sx=FP::new_copy(&S.getpx());
	let sy=FP::new_copy(&S.getpy());

	let mut A=ECP2::new();
	let mut B=ECP2::new();
	let mut r=FP12::new_int(1);

	A.copy(&P);
	B.copy(&R);

	let mut NP=ECP2::new();
	NP.copy(&P);
	NP.neg();
	let mut NR=ECP2::new();
	NR.copy(&R);
	NR.neg();

	let nb=n3.nbits();

	for i in (1..nb-1).rev() {
	r.sqr();
	let mut lv=linedbl(&mut A,&qx,&qy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	lv=linedbl(&mut B,&sx,&sy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	let bt=n3.bit(i)-n.bit(i);
	if bt == 1 {
	lv=lineadd(&mut A,&P,&qx,&qy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	lv=lineadd(&mut B,&R,&sx,&sy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	}
	if bt == -1 {

	lv=lineadd(&mut A,&NP,&qx,&qy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	lv=lineadd(&mut B,&NR,&sx,&sy);
	r.smul(&lv,ecp::SEXTIC_TWIST);

	}
	}

	if ecp::SIGN_OF_X == ecp::NEGATIVEX {
	r.conj();
	}

	/* R-ate fixup */
	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);

	let mut lv=lineadd(&mut A,&K,&qx,&qy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	K.frob(&f);
	K.neg();
	lv=lineadd(&mut A,&K,&qx,&qy);
	r.smul(&lv,ecp::SEXTIC_TWIST);

	K.copy(&R);
	K.frob(&f);

	lv=lineadd(&mut B,&K,&sx,&sy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	K.frob(&f);
	K.neg();
	lv=lineadd(&mut B,&K,&sx,&sy);
	r.smul(&lv,ecp::SEXTIC_TWIST);
	}

	return r;
	}

	/* final exponentiation - keep separate for multi-pairings and to avoid thrashing stack */
	pub fn fexp(m: &FP12) -> FP12 {
	let f = FP2::new_bigs(&BIG::new_ints(&rom::FRA),&BIG::new_ints(&rom::FRB));
	let mut x = BIG::new_ints(&rom::CURVE_BNX);
	let mut r=FP12::new_copy(m);

	/* Easy part of final exp */
	let mut lv=FP12::new_copy(&r);
	lv.inverse();
	r.conj();

	r.mul(&lv);
	lv.copy(&r);
	r.frob(&f);
	r.frob(&f);
	r.mul(&lv);
	/* Hard part of final exp */
	if ecp::CURVE_PAIRING_TYPE == ecp::BN {
	lv.copy(&r);
	lv.frob(&f);
	let mut x0=FP12::new_copy(&lv);
	x0.frob(&f);
	lv.mul(&r);
	x0.mul(&lv);
	x0.frob(&f);
	let mut x1=FP12::new_copy(&r);
	x1.conj();
	let mut x4=r.pow(&mut x);
	if ecp::SIGN_OF_X == ecp::POSITIVEX {
	x4.conj();
	}

	let mut x3=FP12::new_copy(&x4);
	x3.frob(&f);

	let mut x2=x4.pow(&mut x);
	if ecp::SIGN_OF_X == ecp::POSITIVEX {
	x2.conj();
	}
	let mut x5=FP12::new_copy(&x2); x5.conj();
	lv=x2.pow(&mut x);
	if ecp::SIGN_OF_X == ecp::POSITIVEX {
	lv.conj();
	}
	x2.frob(&f);
	r.copy(&x2); r.conj();

	x4.mul(&r);
	x2.frob(&f);

	r.copy(&lv);
	r.frob(&f);
	lv.mul(&r);

	lv.usqr();
	lv.mul(&x4);
	lv.mul(&x5);
	r.copy(&x3);
	r.mul(&x5);
	r.mul(&lv);
	lv.mul(&x2);
	r.usqr();
	r.mul(&lv);
	r.usqr();
	lv.copy(&r);
	lv.mul(&x1);
	r.mul(&x0);
	lv.usqr();
	r.mul(&lv);
	r.reduce();
	} else {

	// Ghamman & Fouotsa Method

	let mut y0=FP12::new_copy(&r); y0.usqr();
	let mut y1=y0.pow(&mut x);
	if ecp::SIGN_OF_X == ecp::NEGATIVEX {
	y1.conj();
	}
	x.fshr(1); let mut y2=y1.pow(&mut x);
	if ecp::SIGN_OF_X == ecp::NEGATIVEX {
	y2.conj();
	}
	x.fshl(1);
	let mut y3=FP12::new_copy(&r); y3.conj();
	y1.mul(&y3);

	y1.conj();
	y1.mul(&y2);

	y2=y1.pow(&mut x);
	if ecp::SIGN_OF_X == ecp::NEGATIVEX {
	y2.conj();
	}
	y3=y2.pow(&mut x);
	if ecp::SIGN_OF_X == ecp::NEGATIVEX {
	y3.conj();
	}
	y1.conj();
	y3.mul(&y1);

	y1.conj();
	y1.frob(&f); y1.frob(&f); y1.frob(&f);
	y2.frob(&f); y2.frob(&f);
	y1.mul(&y2);

	y2=y3.pow(&mut x);
	if ecp::SIGN_OF_X == ecp::NEGATIVEX {
	y2.conj();
	}
	y2.mul(&y0);
	y2.mul(&r);

	y1.mul(&y2);
	y2.copy(&y3); y2.frob(&f);
	y1.mul(&y2);
	r.copy(&y1);
	r.reduce();


	/*
	let mut x0=FP12::new_copy(&r);
	let mut x1=FP12::new_copy(&r);
	lv.copy(&r); lv.frob(&mut f);
	let mut x3=FP12::new_copy(&lv); x3.conj(); x1.mul(&mut x3);
	lv.frob(&mut f); lv.frob(&mut f);
	x1.mul(&mut lv);

	r=r.pow(&mut x); //r=r.pow(x);
	x3.copy(&r); x3.conj(); x1.mul(&mut x3);
	lv.copy(&r); lv.frob(&mut f);
	x0.mul(&mut lv);
	lv.frob(&mut f);
	x1.mul(&mut lv);
	lv.frob(&mut f);
	x3.copy(&lv); x3.conj(); x0.mul(&mut x3);

	r=r.pow(&mut x);
	x0.mul(&mut r);
	lv.copy(&r); lv.frob(&mut f); lv.frob(&mut f);
	x3.copy(&lv); x3.conj(); x0.mul(&mut x3);
	lv.frob(&mut f);
	x1.mul(&mut lv);

	r=r.pow(&mut x);
	lv.copy(&r); lv.frob(&mut f);
	x3.copy(&lv); x3.conj(); x0.mul(&mut x3);
	lv.frob(&mut f);
	x1.mul(&mut lv);

	r=r.pow(&mut x);
	x3.copy(&r); x3.conj(); x0.mul(&mut x3);
	lv.copy(&r); lv.frob(&mut f);
	x1.mul(&mut lv);

	r=r.pow(&mut x);
	x1.mul(&mut r);

	x0.usqr();
	x0.mul(&mut x1);
	r.copy(&x0);
	r.reduce(); */
	}
	return r;
	}

	#[allow(non_snake_case)]
	/* GLV method */
	fn glv(e: &BIG) -> [BIG;2] {
	let mut u:[BIG;2]=[BIG::new(),BIG::new()];
	if ecp::CURVE_PAIRING_TYPE == ecp::BN {
	let mut t=BIG::new();
	let q=BIG::new_ints(&rom::CURVE_ORDER);
	let mut v:[BIG;2]=[BIG::new(),BIG::new()];

	for i in 0..2 {
	t.copy(&BIG::new_ints(&rom::CURVE_W[i])); // why not just t=new BIG(ROM.CURVE_W[i]);
	let mut d:DBIG = BIG::mul(&t,e);
	v[i].copy(&d.div(&q));
	}
	u[0].copy(&e);
	for i in 0..2 {
	for j in 0..2 {
	t=BIG::new_ints(&rom::CURVE_SB[j][i]);
	t=BIG::modmul(&mut v[j],&mut t,&q);
	u[i].add(&q);
	u[i].sub(&t);
	u[i].rmod(&q);
	}
	}
	} else {
	let q=BIG::new_ints(&rom::CURVE_ORDER);
	let x=BIG::new_ints(&rom::CURVE_BNX);
	let x2=BIG::smul(&x,&x);
	u[0].copy(&e);
	u[0].rmod(&x2);
	u[1].copy(&e);
	u[1].div(&x2);
	u[1].rsub(&q);
	}
	return u;
	}

	#[allow(non_snake_case)]
	/* Galbraith & Scott Method */
	pub fn gs(e: &BIG) -> [BIG;4] {
	let mut u:[BIG;4]=[BIG::new(),BIG::new(),BIG::new(),BIG::new()];
	if ecp::CURVE_PAIRING_TYPE == ecp::BN {
	let mut t=BIG::new();
	let q=BIG::new_ints(&rom::CURVE_ORDER);

	let mut v:[BIG;4]=[BIG::new(),BIG::new(),BIG::new(),BIG::new()];
	for i in 0..4 {
	t.copy(&BIG::new_ints(&rom::CURVE_WB[i]));
	let mut d:DBIG=BIG::mul(&t,e);
	v[i].copy(&d.div(&q));
	}
	u[0].copy(&e);
	for i in 0..4 {
	for j in 0..4 {
	t=BIG::new_ints(&rom::CURVE_BB[j][i]);
	t=BIG::modmul(&mut v[j],&mut t,&q);
	u[i].add(&q);
	u[i].sub(&t);
	u[i].rmod(&q);
	}
	}
	} else {
	let q=BIG::new_ints(&rom::CURVE_ORDER);
	let x=BIG::new_ints(&rom::CURVE_BNX);
	let mut w=BIG::new_copy(&e);
	for i in 0..3 {
	u[i].copy(&w);
	u[i].rmod(&x);
	w.div(&x);
	}
	u[3].copy(&w);
	if ecp::SIGN_OF_X == ecp::NEGATIVEX {
	let mut t=BIG::new();
	t.copy(&BIG::modneg(&mut u[1],&q));
	u[1].copy(&t);
	t.copy(&BIG::modneg(&mut u[3],&q));
	u[3].copy(&t);
	}
	}
	return u;
	}

	#[allow(non_snake_case)]
	/* Multiply P by e in group G1 */
	pub fn g1mul(P: &ECP,e: &mut BIG) -> ECP {
	let mut R=ECP::new();
	if rom::USE_GLV {
	// P.affine();
	R.copy(P);
	let mut Q=ECP::new();
	Q.copy(P); Q.affine();
	let q=BIG::new_ints(&rom::CURVE_ORDER);
	let mut cru=FP::new_big(&BIG::new_ints(&rom::CURVE_CRU));
	let mut u=glv(e);
	Q.mulx(&mut cru);

	let mut np=u[0].nbits();
	let mut t:BIG=BIG::modneg(&mut u[0],&q);
	let mut nn=t.nbits();
	if nn<np {
	u[0].copy(&t);
	R.neg();
	}

	np=u[1].nbits();
	t=BIG::modneg(&mut u[1],&q);
	nn=t.nbits();
	if nn<np {
	u[1].copy(&t);
	Q.neg();
	}
	u[0].norm();
	u[1].norm();
	R=R.mul2(&u[0],&mut Q,&u[1]);

	} else {
	R=P.mul(e);
	}
	return R;
	}

	#[allow(non_snake_case)]
	/* Multiply P by e in group G2 */
	pub fn g2mul(P: &ECP2,e: &BIG) -> ECP2 {
	let mut R=ECP2::new();
	if rom::USE_GS_G2 {
	let mut Q:[ECP2;4]=[ECP2::new(),ECP2::new(),ECP2::new(),ECP2::new()];
	let mut f = FP2::new_bigs(&BIG::new_ints(&rom::FRA),&BIG::new_ints(&rom::FRB));
	let q=BIG::new_ints(&rom::CURVE_ORDER);
	let mut u=gs(e);
	let mut T=ECP2::new();

	if ecp::SEXTIC_TWIST==ecp::M_TYPE {
	f.inverse();
	f.norm();
	}

	let mut t=BIG::new();
	// P.affine();
	Q[0].copy(&P);
	for i in 1..4 {
	T.copy(&Q[i-1]);
	Q[i].copy(&T);
	Q[i].frob(&f);
	}
	for i in 0..4 {
	let np=u[i].nbits();
	t.copy(&BIG::modneg(&mut u[i],&q));
	let nn=t.nbits();
	if nn<np {
	u[i].copy(&t);
	Q[i].neg();
	}
	u[i].norm();
	}

	R.copy(&ECP2::mul4(&mut Q,&u));

	} else {
	R.copy(&P.mul(e));
	}
	return R;
	}

	/* f=f^e */
	/* Note that this method requires a lot of RAM! Better to use compressed XTR method, see FP4.java */
	pub fn gtpow(d: &FP12,e: &BIG) -> FP12 {
	let mut r=FP12::new();
	if rom::USE_GS_GT {
	let mut g:[FP12;4]=[FP12::new(),FP12::new(),FP12::new(),FP12::new()];
	let f = FP2::new_bigs(&BIG::new_ints(&rom::FRA),&BIG::new_ints(&rom::FRB));
	let q=BIG::new_ints(&rom::CURVE_ORDER);
	let mut t=BIG::new();
	let mut u=gs(e);
	let mut w=FP12::new();

	g[0].copy(&d);
	for i in 1..4 {
	w.copy(&g[i-1]);
	g[i].copy(&w);
	g[i].frob(&f);
	}
	for i in 0..4 {
	let np=u[i].nbits();
	t.copy(&BIG::modneg(&mut u[i],&q));
	let nn=t.nbits();
	if nn<np {
	u[i].copy(&t);
	g[i].conj();
	}
	u[i].norm();
	}
	r.copy(&FP12::pow4(&mut g,&u));
	} else {
	r.copy(&d.pow(e));
	}
	return r;
	}

	/*
	#[allow(non_snake_case)]
	fn main()
	{
	let mut Q=ECP::new_bigs(&BIG::new_ints(&rom::CURVE_GX),&BIG::new_ints(&rom::CURVE_GY));
	let mut P=ECP2::new_fp2s(&FP2::new_bigs(&BIG::new_ints(&rom::CURVE_PXA),&BIG::new_ints(&rom::CURVE_PXB)),&FP2::new_bigs(&BIG::new_ints(&rom::CURVE_PYA),&BIG::new_ints(&rom::CURVE_PYB)));

	let mut r=BIG::new_ints(&rom::CURVE_ORDER);

	println!("P= {}",P.tostring());
	println!("Q= {}",Q.tostring());

	//m:=NewBIGint(17)

	let mut e=ate(&mut P,&mut Q);
	println!("\ne= {}",e.tostring());

	e=fexp(&e);

	for i in 1..10 {
	e=ate(&mut P,&mut Q);
	e=fexp(&e);
	}


	// e=GTpow(e,m);

	println!("\ne= {}",e.tostring());


	fmt.Printf("\n");
	GLV:=glv(r)

	fmt.Printf("GLV[0]= "+GLV[0].toString())
	fmt.Printf("\n")

	fmt.Printf("GLV[0]= "+GLV[1].toString())
	fmt.Printf("\n")

	G:=NewECP(); G.copy(Q)
	R:=NewECP2(); R.copy(P)


	e=ate(R,Q)
	e=fexp(e)

	e=GTpow(e,xa)
	fmt.Printf("\ne= "+e.toString());
	fmt.Printf("\n")

	R=G2mul(R,xa)
	e=ate(R,G)
	e=fexp(e)

	fmt.Printf("\ne= "+e.toString())
	fmt.Printf("\n")

	G=G1mul(G,xa)
	e=ate(P,G)
	e=fexp(e)
	fmt.Printf("\ne= "+e.toString())
	fmt.Printf("\n")
	}*/