version22/rust/src/fp4.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 std::fmt;
 use std::str::SplitWhitespace;

 #[derive(Copy, Clone)]
 pub struct FP4 {
 	a:FP2,
 	b:FP2,
 }

 use rom::BIG_HEX_STRING_LEN;
 //mod fp;
 //use fp::FP;
 //mod fp2;
 use fp2::FP2;
 //mod big;
 use big::BIG;
 //mod dbig;
 //use dbig::DBIG;
 //mod rand;
 //mod hash256;
 //mod rom;
 //use rom;

 impl PartialEq for FP4 {
 	fn eq(&self, other: &FP4) -> bool {
 		return (self.a == other.a) &&
 			(self.b == other.b);
 	}
 }

 impl fmt::Display for FP4 {
 	fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
 		write!(f, "FP4: [ {}, {} ]", self.a, self.b)
 	}
 }

 impl fmt::Debug for FP4 {
 	fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
 		write!(f, "FP4: [ {}, {} ]", self.a, self.b)
 	}
 }

 impl FP4 {

 	pub fn new() -> FP4 {
 		FP4 {
 				a: FP2::new(),
 				b: FP2::new(),
 		}
 	}

 	pub fn new_int(a: isize) -> FP4 {
 		let mut f=FP4::new();
 		f.a.copy(&FP2::new_int(a));
 		f.b.zero();
 		return f;
 	}

 	pub fn new_copy(x: &FP4) -> FP4 {
 		let mut f=FP4::new();
 		f.a.copy(&x.a);
 		f.b.copy(&x.b);
 		return f;
 	}

 	pub fn new_fp2s(c: &FP2,d: &FP2) -> FP4 {
 		let mut f=FP4::new();
 		f.a.copy(c);
 		f.b.copy(d);
 		return f;
 	}

 	pub fn new_fp2(c: &FP2) -> FP4 {
 		let mut f=FP4::new();
 		f.a.copy(c);
 		f.b.zero();
 		return f;
 	}

 /* reduce components mod Modulus */
 	pub fn reduce(&mut self) {
 		self.a.reduce();
 		self.b.reduce();
 	}

 /* normalise components of w */
 	pub fn norm(&mut self) {
 		self.a.norm();
 		self.b.norm();
 	}

 /* test self=0 ? */
 	pub fn iszilch(&mut self) -> bool {
 		self.reduce();
 		return self.a.iszilch() && self.b.iszilch();
 	}

 /* test self=1 ? */
 	pub fn isunity(&mut self) -> bool {
 		let mut one=FP2::new_int(1);
 		return self.a.equals(&mut one) && self.b.iszilch();
 	}

 /* test is w real? That is in a+ib test b is zero */
 	pub fn isreal(&mut self) -> bool {
 		return self.b.iszilch();
 	}
 /* extract real part a */
 	pub fn real(&mut self) -> FP2 {
 		let f=FP2::new_copy(&self.a);
 		return f;
 	}

 	pub fn geta(&mut self) -> FP2 {
 		let f=FP2::new_copy(&self.a);
 		return f;
 	}
 /* extract imaginary part b */
 	pub fn getb(&mut self) -> FP2 {
 		let f=FP2::new_copy(&self.b);
 		return f;
 	}

 /* test self=x */
 	pub fn equals(&mut self,x:&mut FP4) -> bool {
 		return self.a.equals(&mut x.a) && self.b.equals(&mut x.b);
 	}
 /* copy self=x */
 	pub fn copy(&mut self,x :&FP4) {
 		self.a.copy(&x.a);
 		self.b.copy(&x.b);
 	}

 /* set self=0 */
 	pub fn zero(&mut self) {
 		self.a.zero();
 		self.b.zero();
 	}

 /* set self=1 */
 	pub fn one(&mut self) {
 		self.a.one();
 		self.b.zero();
 	}

 /* negate self mod Modulus */
 	pub fn neg(&mut self) {
 		self.norm();
 		let mut m=FP2::new_copy(&self.a);
 		let mut t=FP2::new();

 		m.add(&self.b);
 		m.neg();
 		m.norm();
 		t.copy(&m); t.add(&self.b);
 		self.b.copy(&m);
 		self.b.add(&self.a);
 		self.a.copy(&t);
 	}

 /* set to a-ib */
 	pub fn conj(&mut self) {
 		self.b.neg();
 		self.b.norm();
 	}

 /* self=-conjugate(self) */
 	pub fn nconj(&mut self) {
 		self.a.neg(); self.a.norm();
 	}

 /* self+=a */
 	pub fn add(&mut self,x:&FP4) {
 		self.a.add(&x.a);
 		self.b.add(&x.b);
 	}

 	pub fn padd(&mut self,x:&FP2) {
 		self.a.add(x);
 	}

 	pub fn dbl(&mut self) {
 		self.a.dbl();
 		self.b.dbl();
 	}

 /* self-=a */
 	pub fn sub(&mut self,x:&FP4) {
 		let mut m=FP4::new_copy(x);
 		m.neg();
 		self.add(&m);
 	}

 /* self*=s, where s is an FP */
 	pub fn pmul(&mut self,s:&mut FP2) {
 		self.a.mul(s);
 		self.b.mul(s);
 	}

 /* self*=i, where i is an int */
 	pub fn imul(&mut self,c: isize) {
 		self.a.imul(c);
 		self.b.imul(c);
 	}

 /* self*=self */
 	pub fn sqr(&mut self) {
 		self.norm();

 		let mut t1=FP2::new_copy(&self.a);
 		let mut t2=FP2::new_copy(&self.b);
 		let mut t3=FP2::new_copy(&self.a);


 		t3.mul(&mut self.b);
 		t1.add(&self.b);
 		t2.mul_ip();

 		t2.add(&mut self.a);
 		self.a.copy(&t1);

 		self.a.mul(&mut t2);

 		t2.copy(&t3);
 		t2.mul_ip();
 		t2.add(&mut t3);
 		t2.neg();
 		self.a.add(&t2);

 		t3.dbl();
 		self.b.copy(&t3);

 		self.norm();
 	}

 /* self*=y */
 	pub fn mul(&mut self,y :&mut FP4) {
 		self.norm();

 		let mut t1=FP2::new_copy(&self.a);
 		let mut t2=FP2::new_copy(&self.b);
 		let mut t3=FP2::new();
 		let mut t4=FP2::new_copy(&self.b);

 		t1.mul(&mut y.a);
 		t2.mul(&mut y.b);
 		t3.copy(&y.b);
 		t3.add(&y.a);
 		t4.add(&self.a);

 		t4.mul(&mut t3);
 		t4.sub(&t1);
 		t4.norm();

 		self.b.copy(&t4);
 		self.b.sub(&t2);
 		t2.mul_ip();
 		self.a.copy(&t2);
 		self.a.add(&t1);

 		self.norm();
 	}

 /* output to hex string */
 	pub fn tostring(&mut self) -> String {
 		return format!("[{},{}]",self.a.tostring(),self.b.tostring());
 	}

 	pub fn to_hex(&self) -> String {
 		let mut ret: String = String::with_capacity(4 * BIG_HEX_STRING_LEN);
 		ret.push_str(&format!("{} {}", self.a.to_hex(), self.b.to_hex()));
 		return ret;
 	}

 	pub fn from_hex_iter(iter: &mut SplitWhitespace) -> FP4 {
 		let mut ret:FP4 = FP4::new();
 		ret.a = FP2::from_hex_iter(iter);
 		ret.b = FP2::from_hex_iter(iter);
 		return ret;
 	}

 	pub fn from_hex(val: String) -> FP4 {
 		let mut iter = val.split_whitespace();
 		return FP4::from_hex_iter(&mut iter);
 	}

 /* self=1/self */
 	pub fn inverse(&mut self) {
 		self.norm();

 		let mut t1=FP2::new_copy(&self.a);
 		let mut t2=FP2::new_copy(&self.b);

 		t1.sqr();
 		t2.sqr();
 		t2.mul_ip();
 		t1.sub(&t2);
 		t1.inverse();
 		self.a.mul(&mut t1);
 		t1.neg();
 		self.b.mul(&mut t1);
 	}

 /* self*=i where i = sqrt(-1+sqrt(-1)) */
 	pub fn times_i(&mut self) {
 		self.norm();
 		let mut s=FP2::new_copy(&self.b);
 		let mut t=FP2::new_copy(&self.b);
 		s.times_i();
 		t.add(&s);
 		t.norm();
 		self.b.copy(&self.a);
 		self.a.copy(&t);
 	}

 /* self=self^p using Frobenius */
 	pub fn frob(&mut self,f: &mut FP2) {
 		self.a.conj();
 		self.b.conj();
 		self.b.mul(f);
 	}

 /* self=self^e */
 	pub fn pow(&mut self,e: &mut BIG) -> FP4 {
 		self.norm();
 		e.norm();
 		let mut w=FP4::new_copy(self);
 		let mut z=BIG::new_copy(&e);
 		let mut r=FP4::new_int(1);
 		loop {
 			let bt=z.parity();
 			z.fshr(1);
 			if bt==1 {r.mul(&mut w)};
 			if z.iszilch() {break}
 			w.sqr();
 		}
 		r.reduce();
 		return r;
 	}

 /* XTR xtr_a function */
 	pub fn xtr_a(&mut self,w:&FP4,y:&FP4,z:&FP4) {
 		let mut r=FP4::new_copy(w);
 		let mut t=FP4::new_copy(w);
 		r.sub(y);
 		r.pmul(&mut self.a);
 		t.add(y);
 		t.pmul(&mut self.b);
 		t.times_i();

 		self.copy(&r);
 		self.add(&t);
 		self.add(z);

 		self.norm();
 	}

 /* XTR xtr_d function */
 	pub fn xtr_d(&mut self) {
 		let mut w=FP4::new_copy(self);
 		self.sqr(); w.conj();
 		w.dbl();
 		self.sub(&w);
 		self.reduce();
 	}

 /* r=x^n using XTR method on traces of FP12s */
 	pub fn xtr_pow(&mut self,n: &mut BIG) -> FP4 {
 		let mut a=FP4::new_int(3);
 		let mut b=FP4::new_copy(self);
 		let mut c=FP4::new_copy(&b);
 		c.xtr_d();
 		let mut t=FP4::new();
 		let mut r=FP4::new();

 		n.norm();
 		let par=n.parity();
 		let mut v=BIG::new_copy(n); v.fshr(1);
 		if par==0 {v.dec(1); v.norm(); }

 		let nb=v.nbits();
 		for i in (0..nb).rev() {
 			if v.bit(i)!=1 {
 				t.copy(&b);
 				self.conj();
 				c.conj();
 				b.xtr_a(&a,self,&c);
 				self.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,self,&t);
 				c.xtr_d();
 			}
 		}
 		if par==0 {
 			r.copy(&c)
 		} else {r.copy(&b)}
 		r.reduce();
 		return r;
 	}

 /* r=ck^a.cl^n using XTR double exponentiation method on traces of FP12s. See Stam thesis. */
 	pub fn xtr_pow2(&mut self,ck: &FP4,ckml: &FP4,ckm2l: &FP4,a: &mut BIG,b: &mut BIG) -> FP4 {
 		a.norm(); b.norm();
 		let mut e=BIG::new_copy(a);
 		let mut d=BIG::new_copy(b);
 		let mut w=BIG::new();

 		let mut cu=FP4::new_copy(ck);  // can probably be passed in w/o copying
 		let mut cv=FP4::new_copy(self);
 		let mut cumv=FP4::new_copy(ckml);
 		let mut cum2v=FP4::new_copy(ckm2l);
 		let mut r=FP4::new();
 		let mut t=FP4::new();

 		let mut f2:usize=0;
 		while d.parity()==0 && e.parity()==0 {
 			d.fshr(1);
 			e.fshr(1);
 			f2+=1;
 		}

 		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 _ in 0..f2 {r.xtr_d()}
 		r=r.xtr_pow(&mut d);
 		return r;
 	}


 }
 /*
 fn main()
 {
 	let mut w=FP4::new();
 }
 */
	/*
	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 std::fmt;
	use std::str::SplitWhitespace;

	#[derive(Copy, Clone)]
	pub struct FP4 {
	a:FP2,
	b:FP2,
	}

	use rom::BIG_HEX_STRING_LEN;
	//mod fp;
	//use fp::FP;
	//mod fp2;
	use fp2::FP2;
	//mod big;
	use big::BIG;
	//mod dbig;
	//use dbig::DBIG;
	//mod rand;
	//mod hash256;
	//mod rom;
	//use rom;

	impl PartialEq for FP4 {
	fn eq(&self, other: &FP4) -> bool {
	return (self.a == other.a) &&
	(self.b == other.b);
	}
	}

	impl fmt::Display for FP4 {
	fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
	write!(f, "FP4: [ {}, {} ]", self.a, self.b)
	}
	}

	impl fmt::Debug for FP4 {
	fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
	write!(f, "FP4: [ {}, {} ]", self.a, self.b)
	}
	}

	impl FP4 {

	pub fn new() -> FP4 {
	FP4 {
	a: FP2::new(),
	b: FP2::new(),
	}
	}

	pub fn new_int(a: isize) -> FP4 {
	let mut f=FP4::new();
	f.a.copy(&FP2::new_int(a));
	f.b.zero();
	return f;
	}

	pub fn new_copy(x: &FP4) -> FP4 {
	let mut f=FP4::new();
	f.a.copy(&x.a);
	f.b.copy(&x.b);
	return f;
	}

	pub fn new_fp2s(c: &FP2,d: &FP2) -> FP4 {
	let mut f=FP4::new();
	f.a.copy(c);
	f.b.copy(d);
	return f;
	}

	pub fn new_fp2(c: &FP2) -> FP4 {
	let mut f=FP4::new();
	f.a.copy(c);
	f.b.zero();
	return f;
	}

	/* reduce components mod Modulus */
	pub fn reduce(&mut self) {
	self.a.reduce();
	self.b.reduce();
	}

	/* normalise components of w */
	pub fn norm(&mut self) {
	self.a.norm();
	self.b.norm();
	}

	/* test self=0 ? */
	pub fn iszilch(&mut self) -> bool {
	self.reduce();
	return self.a.iszilch() && self.b.iszilch();
	}

	/* test self=1 ? */
	pub fn isunity(&mut self) -> bool {
	let mut one=FP2::new_int(1);
	return self.a.equals(&mut one) && self.b.iszilch();
	}

	/* test is w real? That is in a+ib test b is zero */
	pub fn isreal(&mut self) -> bool {
	return self.b.iszilch();
	}
	/* extract real part a */
	pub fn real(&mut self) -> FP2 {
	let f=FP2::new_copy(&self.a);
	return f;
	}

	pub fn geta(&mut self) -> FP2 {
	let f=FP2::new_copy(&self.a);
	return f;
	}
	/* extract imaginary part b */
	pub fn getb(&mut self) -> FP2 {
	let f=FP2::new_copy(&self.b);
	return f;
	}

	/* test self=x */
	pub fn equals(&mut self,x:&mut FP4) -> bool {
	return self.a.equals(&mut x.a) && self.b.equals(&mut x.b);
	}
	/* copy self=x */
	pub fn copy(&mut self,x :&FP4) {
	self.a.copy(&x.a);
	self.b.copy(&x.b);
	}

	/* set self=0 */
	pub fn zero(&mut self) {
	self.a.zero();
	self.b.zero();
	}

	/* set self=1 */
	pub fn one(&mut self) {
	self.a.one();
	self.b.zero();
	}

	/* negate self mod Modulus */
	pub fn neg(&mut self) {
	self.norm();
	let mut m=FP2::new_copy(&self.a);
	let mut t=FP2::new();

	m.add(&self.b);
	m.neg();
	m.norm();
	t.copy(&m); t.add(&self.b);
	self.b.copy(&m);
	self.b.add(&self.a);
	self.a.copy(&t);
	}

	/* set to a-ib */
	pub fn conj(&mut self) {
	self.b.neg();
	self.b.norm();
	}

	/* self=-conjugate(self) */
	pub fn nconj(&mut self) {
	self.a.neg(); self.a.norm();
	}

	/* self+=a */
	pub fn add(&mut self,x:&FP4) {
	self.a.add(&x.a);
	self.b.add(&x.b);
	}

	pub fn padd(&mut self,x:&FP2) {
	self.a.add(x);
	}

	pub fn dbl(&mut self) {
	self.a.dbl();
	self.b.dbl();
	}

	/* self-=a */
	pub fn sub(&mut self,x:&FP4) {
	let mut m=FP4::new_copy(x);
	m.neg();
	self.add(&m);
	}

	/* self=s, where s is an FP /
	pub fn pmul(&mut self,s:&mut FP2) {
	self.a.mul(s);
	self.b.mul(s);
	}

	/* self=i, where i is an int /
	pub fn imul(&mut self,c: isize) {
	self.a.imul(c);
	self.b.imul(c);
	}

	/* self=self /
	pub fn sqr(&mut self) {
	self.norm();

	let mut t1=FP2::new_copy(&self.a);
	let mut t2=FP2::new_copy(&self.b);
	let mut t3=FP2::new_copy(&self.a);


	t3.mul(&mut self.b);
	t1.add(&self.b);
	t2.mul_ip();

	t2.add(&mut self.a);
	self.a.copy(&t1);

	self.a.mul(&mut t2);

	t2.copy(&t3);
	t2.mul_ip();
	t2.add(&mut t3);
	t2.neg();
	self.a.add(&t2);

	t3.dbl();
	self.b.copy(&t3);

	self.norm();
	}

	/* self=y /
	pub fn mul(&mut self,y :&mut FP4) {
	self.norm();

	let mut t1=FP2::new_copy(&self.a);
	let mut t2=FP2::new_copy(&self.b);
	let mut t3=FP2::new();
	let mut t4=FP2::new_copy(&self.b);

	t1.mul(&mut y.a);
	t2.mul(&mut y.b);
	t3.copy(&y.b);
	t3.add(&y.a);
	t4.add(&self.a);

	t4.mul(&mut t3);
	t4.sub(&t1);
	t4.norm();

	self.b.copy(&t4);
	self.b.sub(&t2);
	t2.mul_ip();
	self.a.copy(&t2);
	self.a.add(&t1);

	self.norm();
	}

	/* output to hex string */
	pub fn tostring(&mut self) -> String {
	return format!("[{},{}]",self.a.tostring(),self.b.tostring());
	}

	pub fn to_hex(&self) -> String {
	let mut ret: String = String::with_capacity(4 * BIG_HEX_STRING_LEN);
	ret.push_str(&format!("{} {}", self.a.to_hex(), self.b.to_hex()));
	return ret;
	}

	pub fn from_hex_iter(iter: &mut SplitWhitespace) -> FP4 {
	let mut ret:FP4 = FP4::new();
	ret.a = FP2::from_hex_iter(iter);
	ret.b = FP2::from_hex_iter(iter);
	return ret;
	}

	pub fn from_hex(val: String) -> FP4 {
	let mut iter = val.split_whitespace();
	return FP4::from_hex_iter(&mut iter);
	}

	/* self=1/self */
	pub fn inverse(&mut self) {
	self.norm();

	let mut t1=FP2::new_copy(&self.a);
	let mut t2=FP2::new_copy(&self.b);

	t1.sqr();
	t2.sqr();
	t2.mul_ip();
	t1.sub(&t2);
	t1.inverse();
	self.a.mul(&mut t1);
	t1.neg();
	self.b.mul(&mut t1);
	}

	/* self=i where i = sqrt(-1+sqrt(-1)) /
	pub fn times_i(&mut self) {
	self.norm();
	let mut s=FP2::new_copy(&self.b);
	let mut t=FP2::new_copy(&self.b);
	s.times_i();
	t.add(&s);
	t.norm();
	self.b.copy(&self.a);
	self.a.copy(&t);
	}

	/* self=self^p using Frobenius */
	pub fn frob(&mut self,f: &mut FP2) {
	self.a.conj();
	self.b.conj();
	self.b.mul(f);
	}

	/* self=self^e */
	pub fn pow(&mut self,e: &mut BIG) -> FP4 {
	self.norm();
	e.norm();
	let mut w=FP4::new_copy(self);
	let mut z=BIG::new_copy(&e);
	let mut r=FP4::new_int(1);
	loop {
	let bt=z.parity();
	z.fshr(1);
	if bt==1 {r.mul(&mut w)};
	if z.iszilch() {break}
	w.sqr();
	}
	r.reduce();
	return r;
	}

	/* XTR xtr_a function */
	pub fn xtr_a(&mut self,w:&FP4,y:&FP4,z:&FP4) {
	let mut r=FP4::new_copy(w);
	let mut t=FP4::new_copy(w);
	r.sub(y);
	r.pmul(&mut self.a);
	t.add(y);
	t.pmul(&mut self.b);
	t.times_i();

	self.copy(&r);
	self.add(&t);
	self.add(z);

	self.norm();
	}

	/* XTR xtr_d function */
	pub fn xtr_d(&mut self) {
	let mut w=FP4::new_copy(self);
	self.sqr(); w.conj();
	w.dbl();
	self.sub(&w);
	self.reduce();
	}

	/* r=x^n using XTR method on traces of FP12s */
	pub fn xtr_pow(&mut self,n: &mut BIG) -> FP4 {
	let mut a=FP4::new_int(3);
	let mut b=FP4::new_copy(self);
	let mut c=FP4::new_copy(&b);
	c.xtr_d();
	let mut t=FP4::new();
	let mut r=FP4::new();

	n.norm();
	let par=n.parity();
	let mut v=BIG::new_copy(n); v.fshr(1);
	if par==0 {v.dec(1); v.norm(); }

	let nb=v.nbits();
	for i in (0..nb).rev() {
	if v.bit(i)!=1 {
	t.copy(&b);
	self.conj();
	c.conj();
	b.xtr_a(&a,self,&c);
	self.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,self,&t);
	c.xtr_d();
	}
	}
	if par==0 {
	r.copy(&c)
	} else {r.copy(&b)}
	r.reduce();
	return r;
	}

	/* r=ck^a.cl^n using XTR double exponentiation method on traces of FP12s. See Stam thesis. */
	pub fn xtr_pow2(&mut self,ck: &FP4,ckml: &FP4,ckm2l: &FP4,a: &mut BIG,b: &mut BIG) -> FP4 {
	a.norm(); b.norm();
	let mut e=BIG::new_copy(a);
	let mut d=BIG::new_copy(b);
	let mut w=BIG::new();

	let mut cu=FP4::new_copy(ck); // can probably be passed in w/o copying
	let mut cv=FP4::new_copy(self);
	let mut cumv=FP4::new_copy(ckml);
	let mut cum2v=FP4::new_copy(ckm2l);
	let mut r=FP4::new();
	let mut t=FP4::new();

	let mut f2:usize=0;
	while d.parity()==0 && e.parity()==0 {
	d.fshr(1);
	e.fshr(1);
	f2+=1;
	}

	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 _ in 0..f2 {r.xtr_d()}
	r=r.xtr_pow(&mut d);
	return r;
	}


	}
	/*
	fn main()
	{
	let mut w=FP4::new();
	}
	*/