version3/go/FP4.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.
*/

/* Finite Field arithmetic  Fp^4 functions */

/* FP4 elements are of the form a+ib, where i is sqrt(-1+sqrt(-1)) */

package XXX

//import "fmt"

type FP4 struct {
	a *FP2
	b *FP2
}

/* Constructors */
func NewFP4() *FP4 {
	F := new(FP4)
	F.a = NewFP2()
	F.b = NewFP2()
	return F
}

func NewFP4int(a int) *FP4 {
	F := new(FP4)
	F.a = NewFP2int(a)
	F.b = NewFP2()
	return F
}

func NewFP4copy(x *FP4) *FP4 {
	F := new(FP4)
	F.a = NewFP2copy(x.a)
	F.b = NewFP2copy(x.b)
	return F
}

func NewFP4fp2s(c *FP2, d *FP2) *FP4 {
	F := new(FP4)
	F.a = NewFP2copy(c)
	F.b = NewFP2copy(d)
	return F
}

func NewFP4fp2(c *FP2) *FP4 {
	F := new(FP4)
	F.a = NewFP2copy(c)
	F.b = NewFP2()
	return F
}

/* reduce all components of this mod Modulus */
func (F *FP4) reduce() {
	F.a.reduce()
	F.b.reduce()
}

/* normalise all components of this mod Modulus */
func (F *FP4) norm() {
	F.a.norm()
	F.b.norm()
}

/* test this==0 ? */
func (F *FP4) iszilch() bool {
	return F.a.iszilch() && F.b.iszilch()
}

/* Conditional move */
func (F *FP4) cmove(g *FP4, d int) {
	F.a.cmove(g.a, d)
	F.b.cmove(g.b, d)
}

/* test this==1 ? */
func (F *FP4) isunity() bool {
	one := NewFP2int(1)
	return F.a.Equals(one) && F.b.iszilch()
}

/* test is w real? That is in a+ib test b is zero */
func (F *FP4) isreal() bool {
	return F.b.iszilch()
}

/* extract real part a */
func (F *FP4) real() *FP2 {
	return F.a
}

func (F *FP4) geta() *FP2 {
	return F.a
}

/* extract imaginary part b */
func (F *FP4) getb() *FP2 {
	return F.b
}

/* test this=x? */
func (F *FP4) Equals(x *FP4) bool {
	return (F.a.Equals(x.a) && F.b.Equals(x.b))
}

/* copy this=x */
func (F *FP4) copy(x *FP4) {
	F.a.copy(x.a)
	F.b.copy(x.b)
}

/* set this=0 */
func (F *FP4) zero() {
	F.a.zero()
	F.b.zero()
}

/* set this=1 */
func (F *FP4) one() {
	F.a.one()
	F.b.zero()
}

/* set this=-this */
func (F *FP4) neg() {
	F.norm()
	m := NewFP2copy(F.a)
	t := NewFP2()
	m.add(F.b)
	m.neg()
	t.copy(m)
	t.add(F.b)
	F.b.copy(m)
	F.b.add(F.a)
	F.a.copy(t)
	F.norm()
}

/* this=conjugate(this) */
func (F *FP4) conj() {
	F.b.neg()
	F.norm()
}

/* this=-conjugate(this) */
func (F *FP4) nconj() {
	F.a.neg()
	F.norm()
}

/* this+=x */
func (F *FP4) add(x *FP4) {
	F.a.add(x.a)
	F.b.add(x.b)
}

/* this-=x */
func (F *FP4) sub(x *FP4) {
	m := NewFP4copy(x)
	m.neg()
	F.add(m)
}

/* this-=x */
func (F *FP4) rsub(x *FP4) {
	F.neg()
	F.add(x)
}

/* this*=s where s is FP2 */
func (F *FP4) pmul(s *FP2) {
	F.a.mul(s)
	F.b.mul(s)
}

/* this*=s where s is FP2 */
func (F *FP4) qmul(s *FP) {
	F.a.pmul(s)
	F.b.pmul(s)
}

/* this*=c where c is int */
func (F *FP4) imul(c int) {
	F.a.imul(c)
	F.b.imul(c)
}

/* this*=this */
func (F *FP4) sqr() {
	t1 := NewFP2copy(F.a)
	t2 := NewFP2copy(F.b)
	t3 := NewFP2copy(F.a)

	t3.mul(F.b)
	t1.add(F.b)
	t2.mul_ip()

	t2.add(F.a)

	t1.norm()
	t2.norm()

	F.a.copy(t1)

	F.a.mul(t2)

	t2.copy(t3)
	t2.mul_ip()
	t2.add(t3)
	t2.norm()
	t2.neg()
	F.a.add(t2)

	F.b.copy(t3)
	F.b.add(t3)

	F.norm()
}

/* this*=y */
func (F *FP4) mul(y *FP4) {
	t1 := NewFP2copy(F.a)
	t2 := NewFP2copy(F.b)
	t3 := NewFP2()
	t4 := NewFP2copy(F.b)

	t1.mul(y.a)
	t2.mul(y.b)
	t3.copy(y.b)
	t3.add(y.a)
	t4.add(F.a)

	t3.norm()
	t4.norm()

	t4.mul(t3)

	t3.copy(t1)
	t3.neg()
	t4.add(t3)
	t4.norm()

	t3.copy(t2)
	t3.neg()
	F.b.copy(t4)
	F.b.add(t3)

	t2.mul_ip()
	F.a.copy(t2)
	F.a.add(t1)

	F.norm()
}

/* convert this to hex string */
func (F *FP4) toString() string {
	return ("[" + F.a.toString() + "," + F.b.toString() + "]")
}

/* this=1/this */
func (F *FP4) inverse() {
	t1 := NewFP2copy(F.a)
	t2 := NewFP2copy(F.b)

	t1.sqr()
	t2.sqr()
	t2.mul_ip()
	t2.norm()
	t1.sub(t2)
	t1.inverse()
	F.a.mul(t1)
	t1.neg()
	t1.norm()
	F.b.mul(t1)
}

/* this*=i where i = sqrt(-1+sqrt(-1)) */
func (F *FP4) times_i() {
	s := NewFP2copy(F.b)
	t := NewFP2copy(F.b)
	s.times_i()
	t.add(s)
	F.b.copy(F.a)
	F.a.copy(t)
	F.norm()
}

/* this=this^p using Frobenius */
func (F *FP4) frob(f *FP2) {
	F.a.conj()
	F.b.conj()
	F.b.mul(f)
}

/* this=this^e */
func (F *FP4) pow(e *BIG) *FP4 {
	w := NewFP4copy(F)
	w.norm()
	z := NewBIGcopy(e)
	r := NewFP4int(1)
	z.norm()
	for true {
		bt := z.parity()
		z.fshr(1)
		if bt == 1 {
			r.mul(w)
		}
		if z.iszilch() {
			break
		}
		w.sqr()
	}
	r.reduce()
	return r
}

/* XTR xtr_a function */
func (F *FP4) xtr_A(w *FP4, y *FP4, z *FP4) {
	r := NewFP4copy(w)
	t := NewFP4copy(w)
	r.sub(y)
	r.norm()
	r.pmul(F.a)
	t.add(y)
	t.norm()
	t.pmul(F.b)
	t.times_i()

	F.copy(r)
	F.add(t)
	F.add(z)

	F.norm()
}

/* XTR xtr_d function */
func (F *FP4) xtr_D() {
	w := NewFP4copy(F)
	F.sqr()
	w.conj()
	w.add(w)
	w.norm()
	F.sub(w)
	F.reduce()
}

/* r=x^n using XTR method on traces of FP12s */
func (F *FP4) xtr_pow(n *BIG) *FP4 {
	a := NewFP4int(3)
	b := NewFP4copy(F)
	c := NewFP4copy(b)
	c.xtr_D()
	t := NewFP4()
	r := NewFP4()
	sf := NewFP4copy(F)
	sf.norm()

	par := n.parity()
	v := NewBIGcopy(n)
	v.norm()
	v.fshr(1)
	if par == 0 {
		v.dec(1)
		v.norm()
	}

	nb := v.nbits()
	for i := nb - 1; i >= 0; i-- {
		if v.bit(i) != 1 {
			t.copy(b)
			sf.conj()
			c.conj()
			b.xtr_A(a, sf, c)
			sf.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, sf, 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. */
func (F *FP4) xtr_pow2(ck *FP4, ckml *FP4, ckm2l *FP4, a *BIG, b *BIG) *FP4 {

	e := NewBIGcopy(a)
	d := NewBIGcopy(b)
	w := NewBIGint(0)
	e.norm()
	d.norm()

	cu := NewFP4copy(ck) // can probably be passed in w/o copying
	cv := NewFP4copy(F)
	cumv := NewFP4copy(ckml)
	cum2v := NewFP4copy(ckm2l)
	r := NewFP4()
	t := NewFP4()

	f2 := 0
	for d.parity() == 0 && e.parity() == 0 {
		d.fshr(1)
		e.fshr(1)
		f2++
	}

	for Comp(d, e) != 0 {
		if Comp(d, e) > 0 {
			w.copy(e)
			w.imul(4)
			w.norm()
			if 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 Comp(d, e) < 0 {
			w.copy(d)
			w.imul(4)
			w.norm()
			if 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 i := 0; i < f2; i++ {
		r.xtr_D()
	}
	r = r.xtr_pow(d)
	return r
}

/* this/=2 */
func (F *FP4) div2() {
	F.a.div2()
	F.b.div2()
}

func (F *FP4) div_i() {
	u := NewFP2copy(F.a)
	v := NewFP2copy(F.b)
	u.div_ip()
	F.a.copy(v)
	F.b.copy(u)
}

func (F *FP4) div_2i() {
	u := NewFP2copy(F.a)
	v := NewFP2copy(F.b)
	u.div_ip2()
	v.add(v)
	v.norm()
	F.a.copy(v)
	F.b.copy(u)
}

/* sqrt(a+ib) = sqrt(a+sqrt(a*a-n*b*b)/2)+ib/(2*sqrt(a+sqrt(a*a-n*b*b)/2)) */
/* returns true if this is QR */
func (F *FP4) sqrt() bool {
	if F.iszilch() {
		return true
	}

	a := NewFP2copy(F.a)
	s := NewFP2copy(F.b)
	t := NewFP2copy(F.a)

	if s.iszilch() {
		if t.sqrt() {
			F.a.copy(t)
			F.b.zero()
		} else {
			t.div_ip()
			t.sqrt()
			F.b.copy(t)
			F.a.zero()
		}
		return true
	}
	s.sqr()
	a.sqr()
	s.mul_ip()
	s.norm()
	a.sub(s)

	s.copy(a)
	if !s.sqrt() {
		return false
	}

	a.copy(t)
	a.add(s)
	a.norm()
	a.div2()

	if !a.sqrt() {
		a.copy(t)
		a.sub(s)
		a.norm()
		a.div2()
		if !a.sqrt() {
			return false
		}
	}
	t.copy(F.b)
	s.copy(a)
	s.add(a)
	s.inverse()

	t.mul(s)
	F.a.copy(a)
	F.b.copy(t)

	return true
}