/*
    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.
*/

/* AMCL Fp^24 functions */

/* FP24 elements are of the form a+i.b+i^2.c */

var FP24 = function(ctx) {
    "use strict";

    /**
      * Creates an instance of FP24.
      *
      * @constructor
      * @this {FP24}
      */
    var FP24 = function(d, e, f) {
		if (!isNaN(d))
		{
			this.a = new ctx.FP8(d);
			this.b = new ctx.FP8(0);
			this.c = new ctx.FP8(0);
			if (d==1) this.stype=ctx.FP.ONE;
			else this.stype=ctx.FP.SPARSER;
		}
		else
		{
			if (d instanceof FP24) {
				this.a = new ctx.FP8(d.a);
				this.b = new ctx.FP8(d.b);
				this.c = new ctx.FP8(d.c);
			} else {
				this.a = new ctx.FP8(d);
				this.b = new ctx.FP8(e);
				this.c = new ctx.FP8(f);
			}
			this.stype=ctx.FP.DENSE;
		}
    };

    FP24.prototype = {

	/**
         * Reduces all components of possibly unreduced FP24 mod Modulus
         *
         * @this {FP24}
         */
        reduce: function() {
            this.a.reduce();
            this.b.reduce();
            this.c.reduce();
        },

	/**
         * Normalises the components of an FP24
         *
         * @this {FP24}
         */
        norm: function() {
            this.a.norm();
            this.b.norm();
            this.c.norm();
        },

	/**
         * Tests for FP24 equal to zero
         *
         * @this {FP24}
         */
        iszilch: function() {
            return (this.a.iszilch() && this.b.iszilch() && this.c.iszilch());
        },

	/**
         * Tests for FP24 equal to unity
         *
         * @this {FP24}
         */
        isunity: function() {
            var one = new ctx.FP8(1);
            return (this.a.equals(one) && this.b.iszilch() && this.c.iszilch());
        },

	/**
         * Conditional copy of FP24 number
         *
         * @this {FP24}
         * @param g FP24 instance
         * @param d copy depends on this value
         */
        cmove: function(g, d) {
            this.a.cmove(g.a, d);
            this.b.cmove(g.b, d);
            this.c.cmove(g.c, d);
			d=~(d-1);
			this.stype^=(this.stype^g.stype)&d;
        },

	/**
         * Constant time select from pre-computed table 
         *
         * @this {FP24}
         */
        select: function(g, b) {
            var invf = new FP24(0),
                m, babs;

            m = b >> 31;
            babs = (b ^ m) - m;
            babs = (babs - 1) / 2;

            this.cmove(g[0], FP24.teq(babs, 0)); // conditional move
            this.cmove(g[1], FP24.teq(babs, 1));
            this.cmove(g[2], FP24.teq(babs, 2));
            this.cmove(g[3], FP24.teq(babs, 3));
            this.cmove(g[4], FP24.teq(babs, 4));
            this.cmove(g[5], FP24.teq(babs, 5));
            this.cmove(g[6], FP24.teq(babs, 6));
            this.cmove(g[7], FP24.teq(babs, 7));

            invf.copy(this);
            invf.conj();
            this.cmove(invf, (m & 1));
        },
		
		settype: function(w) {
			this.stype=w;
		},

		gettype: function() {
			return this.stype;
		},
	
	/**
         * extract a from this
         *
         * @this {FP24}
         */	
        geta: function() {
            return this.a;
        },

	/**
         * extract b from this
         *
         * @this {FP24}
         */
        getb: function() {
            return this.b;
        },

	/**
         * extract c from this
         *
         * @this {FP24}
         */
        getc: function() {
            return this.c;
        },

	/**
         * Tests for equality of two FP24s
         *
         * @this {FP24}
         * @param x FP24 instance to compare
         */
        equals: function(x) {
            return (this.a.equals(x.a) && this.b.equals(x.b) && this.c.equals(x.c));
        },

	/**
         * Copy FP24 to another FP24
         *
         * @this {FP24}
         * @param x FP24 instance to be copied
         */
        copy: function(x) {
            this.a.copy(x.a);
            this.b.copy(x.b);
            this.c.copy(x.c);
			this.stype=x.stype;
        },

	/**
         * Set FP24 to unity
         *
         * @this {FP24}
         * @param x FP24 instance to be set to one
         */
        one: function() {
            this.a.one();
            this.b.zero();
            this.c.zero();
			this.stype=ctx.FP.ONE;
        },

	/**
         * Set FP24 to zero
         *
         * @this {FP24}
         */
        zero: function() {
            this.a.zero();
            this.b.zero();
            this.c.zero();
			this.stype=ctx.FP.ZERO;
        },

	/**
         * Conjugation of FP24
         *
         * @this {FP24}
         */
        conj: function() {
            this.a.conj();
            this.b.nconj();
            this.c.conj();
        },

	/**
         * Set FP24 from three FP8 values
         *
         * @this {FP24}
         * @param d FP8 instance
         * @param e FP8 instance
         * @param f FP8 instance
         */
        set: function(d, e, f) {
            this.a.copy(d);
            this.b.copy(e);
            this.c.copy(f);
			this.stype=ctx.FP.DENSE;
        },

	/**
         * Set FP24 from one FP8 value
         *
         * @this {FP24}
         * @param c FP8 instance
         */
        seta: function(d) {
            this.a.copy(d);
            this.b.zero();
            this.c.zero();
			this.stype=ctx.FP.SPARSER
        },

	/**
         * Fast Squaring of an FP24 in "unitary" form
         *
         * @this {FP24}
         */
        usqr: function() {
            var A = new ctx.FP8(this.a), 
                B = new ctx.FP8(this.c), 
                C = new ctx.FP8(this.b), 
                D = new ctx.FP8(0);

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

            A.nconj();

            A.add(A);
            this.a.add(A);
            B.sqr();
            B.times_i();

            D.copy(B);
            D.add(B);
            B.add(D);

            C.sqr();
            D.copy(C);
            D.add(C);
            C.add(D);

            this.b.conj();
            this.b.add(this.b);
            this.c.nconj();

            this.c.add(this.c);
            this.b.add(B);
            this.c.add(C);
			this.stype=ctx.FP.DENSE;
            this.reduce();
        },

	/**
         * Fast Squaring of an FP24
         *
         * @this {FP24}
         */
        sqr: function() {
			if (this.stype==ctx.FP.ONE)
				return;

            var A = new ctx.FP8(this.a), 
                B = new ctx.FP8(this.b), 
                C = new ctx.FP8(this.c), 
                D = new ctx.FP8(this.a); 

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

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

            this.a.copy(A);

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

            this.a.add(B);
            this.b.copy(C);
            this.b.add(D);
            this.c.add(A);
			if (this.stype==ctx.FP.SPARSER)
				this.stype=ctx.FP.SPARSE;
			else
				this.stype=ctx.FP.DENSE;
            this.norm();
        },

	/**
         * Full unconditional Multiplication of two FP24s
         *
         * @this {FP24}
         * @param y FP24 instance, the multiplier
         */
        mul: function(y) {
            var z0 = new ctx.FP8(this.a), 
                z1 = new ctx.FP8(0),
                z2 = new ctx.FP8(this.b), 
                z3 = new ctx.FP8(0),
                t0 = new ctx.FP8(this.a), 
                t1 = new ctx.FP8(y.a); 

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

            t0.add(this.b);
            t1.add(y.b);

            t0.norm();
            t1.norm();

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

            t1.copy(y.b);
            t1.add(y.c);

            t0.norm();
            t1.norm();
            z3.copy(t0);
            z3.mul(t1);

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

            z1.add(t0);
            this.b.copy(z1);
            this.b.add(t1);

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

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

            t0.norm();
            t1.norm();

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

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

            this.c.copy(z2);
            this.c.add(t1);
            z3.add(t1);
            t0.times_i();
            this.b.add(t0);
            // z3.norm();
            z3.times_i();
            this.a.copy(z0);
            this.a.add(z3);
			this.stype=ctx.FP.DENSE;
            this.norm();
        },

/* FP24 multiplication w=w*y */
/* catering for special case that arises from special form of ATE pairing line function */
	/* w and y are both sparser line functions - cost = 6m */

	/**
         * Fast multiplication of two sparse FP24s that arises from ATE pairing line functions
         *
         * @this {FP24}
         * @param y FP24 instance, the multiplier
         */	
	smul: function(y) {
			if (ctx.ECP.SEXTIC_TWIST==ctx.ECP.D_TYPE)
			{	
				var w1=new ctx.FP4(this.a.geta());
				var w2=new ctx.FP4(this.a.getb());
				var w3=new ctx.FP4(this.b.geta());

				w1.mul(y.a.geta());
				w2.mul(y.a.getb());
				w3.mul(y.b.geta());

				var ta=new ctx.FP4(this.a.geta());
				var tb=new ctx.FP4(y.a.geta());
				ta.add(this.a.getb()); ta.norm();
				tb.add(y.a.getb()); tb.norm();
				var tc=new ctx.FP4(ta);
				tc.mul(tb);
				var t=new ctx.FP4(w1);
				t.add(w2);
				t.neg();
				tc.add(t);

				ta.copy(this.a.geta()); ta.add(this.b.geta()); ta.norm();
				tb.copy(y.a.geta()); tb.add(y.b.geta()); tb.norm();
				var td=new ctx.FP4(ta);
				td.mul(tb);
				t.copy(w1);
				t.add(w3);
				t.neg();
				td.add(t);

				ta.copy(this.a.getb()); ta.add(this.b.geta()); ta.norm();
				tb.copy(y.a.getb()); tb.add(y.b.geta()); tb.norm();
				var te=new ctx.FP4(ta);
				te.mul(tb);
				t.copy(w2);
				t.add(w3);
				t.neg();
				te.add(t);

				w2.times_i();
				w1.add(w2);

				this.a.geta().copy(w1); this.a.getb().copy(tc);
				this.b.geta().copy(td); this.b.getb().copy(te);
				this.c.geta().copy(w3); this.c.getb().zero();

				this.a.norm();
				this.b.norm();

			} else {
				var w1=new ctx.FP4(this.a.geta());
				var w2=new ctx.FP4(this.a.getb());
				var w3=new ctx.FP4(this.c.getb());

				w1.mul(y.a.geta());
				w2.mul(y.a.getb());
				w3.mul(y.c.getb());

				var ta=new ctx.FP4(this.a.geta());
				var tb=new ctx.FP4(y.a.geta());
				ta.add(this.a.getb()); ta.norm();
				tb.add(y.a.getb()); tb.norm();
				var tc=new ctx.FP4(ta);
				tc.mul(tb);
				var t=new ctx.FP4(w1);
				t.add(w2);
				t.neg();
				tc.add(t);

				ta.copy(this.a.geta()); ta.add(this.c.getb()); ta.norm();
				tb.copy(y.a.geta()); tb.add(y.c.getb()); tb.norm();
				var td=new ctx.FP4(ta);
				td.mul(tb);
				t.copy(w1);
				t.add(w3);
				t.neg();
				td.add(t);

				ta.copy(this.a.getb()); ta.add(this.c.getb()); ta.norm();
				tb.copy(y.a.getb()); tb.add(y.c.getb()); tb.norm();
				var te=new ctx.FP4(ta);
				te.mul(tb);
				t.copy(w2);
				t.add(w3);
				t.neg();
				te.add(t);

				w2.times_i();
				w1.add(w2);
				this.a.geta().copy(w1); this.a.getb().copy(tc);

				w3.times_i();
				w3.norm();
				this.b.geta().zero(); this.b.getb().copy(w3);

				te.norm();
				te.times_i();
				this.c.geta().copy(te);
				this.c.getb().copy(td);

				this.a.norm();
				this.c.norm();

			}
			this.stype=ctx.FP.SPARSE;
		},

/* FP24 full multiplication w=w*y */
/* Supports sparse multiplicands */
	/* Usually w is denser than y */

	/**
         * Fast multiplication of what may be sparse multiplicands
         *
         * @this {FP24}
         * @param y FP24 instance, the multiplier
         */
	ssmul: function(y) {
			if (this.stype==ctx.FP.ONE)
			{
				this.copy(y);
				return;
			}
			if (y.stype==ctx.FP.ONE)
				return;

			if (y.stype>=ctx.FP.SPARSE)
			{
				var z0=new ctx.FP8(this.a);
				var z1=new ctx.FP8(0);
				var z2=new ctx.FP8(0);
				var z3=new ctx.FP8(0);
				z0.mul(y.a);

				if (ctx.ECP.SEXTIC_TWIST==ctx.ECP.M_TYPE)
				{
					if (y.stype==ctx.FP.SPARSE || this.stype==ctx.FP.SPARSE)
					{
						z2.getb().copy(this.b.getb());
						z2.getb().mul(y.b.getb());
						z2.geta().zero();
						if (y.stype!=ctx.FP.SPARSE)
						{
							z2.geta().copy(this.b.getb());
							z2.geta().mul(y.b.geta());
						}
						if (this.stype!=ctx.FP.SPARSE)
						{
							z2.geta().copy(this.b.geta());
							z2.geta().mul(y.b.getb());
						}
						z2.times_i();
					} else {
						z2.copy(this.b);
						z2.mul(y.b);
					}
				} else {
					z2.copy(this.b);
					z2.mul(y.b);
				}
				var t0=new ctx.FP8(this.a);
				var t1=new ctx.FP8(y.a);
				t0.add(this.b); t0.norm();
				t1.add(y.b); t1.norm();

				z1.copy(t0); z1.mul(t1);
				t0.copy(this.b); t0.add(this.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);
				this.b.copy(z1); this.b.add(t1);

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

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

				if (ctx.ECP.SEXTIC_TWIST==ctx.ECP.D_TYPE)
				{
					if (y.stype==ctx.FP.SPARSE || this.stype==ctx.FP.SPARSE)
					{
						t0.geta().copy(this.c.geta());
						t0.geta().mul(y.c.geta());
						t0.getb().zero();
						if (y.stype!=ctx.FP.SPARSE)
						{
							t0.getb().copy(this.c.geta());
							t0.getb().mul(y.c.getb());
						}
						if (this.stype!=ctx.FP.SPARSE)
						{
							t0.getb().copy(this.c.getb());
							t0.getb().mul(y.c.geta());
						}
					} else {
						t0.copy(this.c);
						t0.mul(y.c);
					}
				} else {
					t0.copy(this.c);
					t0.mul(y.c);
				}
				t1.copy(t0); t1.neg();

				this.c.copy(z2); this.c.add(t1);
				z3.add(t1);
				t0.times_i();
				this.b.add(t0);
				z3.norm();
				z3.times_i();
				this.a.copy(z0); this.a.add(z3);
			} else {
				if (this.stype==ctx.FP.SPARSER)
				{
					this.smul(y);
					return;
				}
				if (ctx.ECP.SEXTIC_TWIST==ctx.ECP.D_TYPE)
				{ // dense by sparser - 13m 
					var z0=new ctx.FP8(this.a);
					var z2=new ctx.FP8(this.b);
					var z3=new ctx.FP8(this.b);
					var t0=new ctx.FP8(0);
					var t1=new ctx.FP8(y.a);
					z0.mul(y.a);
					z2.pmul(y.b.real());
					this.b.add(this.a);
					t1.real().add(y.b.real());

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

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

					this.b.add(t0);

					this.b.add(t1);
					z3.add(t1);
					z2.add(t0);

					t0.copy(this.a); t0.add(this.c); t0.norm();
					z3.norm();
					t0.mul(y.a);
					this.c.copy(z2); this.c.add(t0);

					z3.times_i();
					this.a.copy(z0); this.a.add(z3);
				}
				if (ctx.ECP.SEXTIC_TWIST==ctx.ECP.M_TYPE)
				{
					var z0=new ctx.FP8(this.a);
					var z1=new ctx.FP8(0);
					var z2=new ctx.FP8(0);
					var z3=new ctx.FP8(0);
					var t0=new ctx.FP8(this.a);
					var t1=new ctx.FP8(0);
		
					z0.mul(y.a);
					t0.add(this.b); t0.norm();

					z1.copy(t0); z1.mul(y.a);
					t0.copy(this.b); t0.add(this.c);
					t0.norm();

					z3.copy(t0); 
					z3.pmul(y.c.getb());
					z3.times_i();

					t0.copy(z0); t0.neg();
					z1.add(t0);
					this.b.copy(z1); 
					z2.copy(t0);

					t0.copy(this.a); t0.add(this.c); t0.norm();
					t1.copy(y.a); t1.add(y.c); t1.norm();

					t0.mul(t1);
					z2.add(t0);
					t0.copy(this.c); 
			
					t0.pmul(y.c.getb());
					t0.times_i();
					t1.copy(t0); t1.neg();

					this.c.copy(z2); this.c.add(t1);
					z3.add(t1);
					t0.times_i();
					this.b.add(t0);
					z3.norm();
					z3.times_i();
					this.a.copy(z0); this.a.add(z3);
				}	
			}
			this.stype=ctx.FP.DENSE;
			this.norm();
		},

	/**
         * Inverting an FP24
         *
         * @this {FP24}
         */
        inverse: function() {
            var f0 = new ctx.FP8(this.a), 
                f1 = new ctx.FP8(this.b), 
                f2 = new ctx.FP8(this.a), 
                f3 = new ctx.FP8(0);

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

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

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

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

            f3.add(this.c);
            f3.norm();
            f3.inverse();
            this.a.copy(f0);
            this.a.mul(f3);
            this.b.copy(f1);
            this.b.mul(f3);
            this.c.copy(f2);
            this.c.mul(f3);
			this.stype=ctx.FP.DENSE;
        },

	/**
         * Raises an FP24 to the power of the internal modulus p, using the Frobenius
         *
         * @this {FP24}
         * @param f Modulus
         */
        frob: function(f,n) {
            var f2 = new ctx.FP2(f),
                f3 = new ctx.FP2(f),
                i;

            f2.sqr();
            f3.mul(f2);

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

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

                this.b.qmul(f); this.b.times_i2();
                this.c.qmul(f2); this.c.times_i2(); this.c.times_i2();
            }
			this.stype=ctx.FP.DENSE;
        },

	/**
         * Calculate the trace of an FP24
         *
         * @this {FP24}
         */
        trace: function() {
            var t = new ctx.FP8(0);

            t.copy(this.a);
            t.imul(3);
            t.reduce();

            return t;
        },

	/**
         * convert this to hex string
         *
         * @this {FP24}
         */
        toString: function() {
            return ("[" + this.a.toString() + "," + this.b.toString() + "," + this.c.toString() + "]");
        },

	/**
         * convert this to byte array
         *
         * @this {FP24}
         * @param w Byte array
         */
        toBytes: function(w) {
            var t = [],
                i;

            this.a.geta().geta().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i] = t[i];
            }
            this.a.geta().geta().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + ctx.BIG.MODBYTES] = t[i];
            }
            this.a.geta().getb().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 2 * ctx.BIG.MODBYTES] = t[i];
            }
            this.a.geta().getb().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 3 * ctx.BIG.MODBYTES] = t[i];
            }

            this.a.getb().geta().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 4 * ctx.BIG.MODBYTES] = t[i];
            }
            this.a.getb().geta().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 5 * ctx.BIG.MODBYTES] = t[i];
            }
            this.a.getb().getb().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 6 * ctx.BIG.MODBYTES] = t[i];
            }
            this.a.getb().getb().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 7 * ctx.BIG.MODBYTES] = t[i];
            }

            this.b.geta().geta().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 8 * ctx.BIG.MODBYTES] = t[i];
            }
            this.b.geta().geta().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 9 * ctx.BIG.MODBYTES] = t[i];
            }
            this.b.geta().getb().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 10 * ctx.BIG.MODBYTES] = t[i];
            }
            this.b.geta().getb().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 11 * ctx.BIG.MODBYTES] = t[i];
            }

            this.b.getb().geta().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 12 * ctx.BIG.MODBYTES] = t[i];
            }
            this.b.getb().geta().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 13 * ctx.BIG.MODBYTES] = t[i];
            }
            this.b.getb().getb().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 14 * ctx.BIG.MODBYTES] = t[i];
            }
            this.b.getb().getb().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 15 * ctx.BIG.MODBYTES] = t[i];
            }

            this.c.geta().geta().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 16 * ctx.BIG.MODBYTES] = t[i];
            }
            this.c.geta().geta().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 17 * ctx.BIG.MODBYTES] = t[i];
            }
            this.c.geta().getb().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 18 * ctx.BIG.MODBYTES] = t[i];
            }
            this.c.geta().getb().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 19 * ctx.BIG.MODBYTES] = t[i];
            }

            this.c.getb().geta().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 20 * ctx.BIG.MODBYTES] = t[i];
            }
            this.c.getb().geta().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 21 * ctx.BIG.MODBYTES] = t[i];
            }
            this.c.getb().getb().getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 22 * ctx.BIG.MODBYTES] = t[i];
            }
            this.c.getb().getb().getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                w[i + 23 * ctx.BIG.MODBYTES] = t[i];
            }
        },

	/**
         * Raises an FP24 to the power of a BIG
         *
         * @this {FP24}
         * @param e BIG instance exponent
         */
        pow: function(e) {
            var e1, e3, w, nb, i, bt, sf;

			sf = new FP24(this);
            sf.norm();
			e1 = new ctx.BIG(e);
            e1.norm();

            e3 = new ctx.BIG(e1);
            e3.pmul(3);
            e3.norm();

            w = new FP24(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;
        },

	/**
         * Raises an FP24 instance x to a small integer power, side-channel resistant
         *
         * @this {FP24}
         * @param e small integer exponent
         * @param bts maximum number of bits in exponent
         */
        pinpow: function(e, bts) {
            var R = [],
                i, b;

            R[0] = new FP24(1);
            R[1] = new FP24(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]);
        },

	/**
         * Raises an FP24 instance to a BIG power, compressed to FP4
         *
         * @this {FP24}
         * @param e BIG exponent
         * @param r BIG group order
         */
        compow: function(e, r) {
            var fa, fb, f, q, m, a, b, g1, g2, c, cp, cpm1, cpm2;

            fa = new ctx.BIG(0);
            fa.rcopy(ctx.ROM_FIELD.Fra);
            fb = new ctx.BIG(0);
            fb.rcopy(ctx.ROM_FIELD.Frb);
            f = new ctx.FP2(fa, fb);

            q = new ctx.BIG(0);
            q.rcopy(ctx.ROM_FIELD.Modulus);

            m = new ctx.BIG(q);
            m.mod(r);

            a = new ctx.BIG(e);
            a.mod(m);

            b = new ctx.BIG(e);
            b.div(m);

            g1 = new FP24(0);
            g2 = new FP24(0);
            g1.copy(this);

            c = g1.trace();

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

            g2.copy(g1);
            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;
        }
    };

    /**
      * convert from byte array to FP24 
      *
      * @this {FP24}
      * @param w Byte array
      */    
    FP24.fromBytes = function(w) {
        var t = [],
            i, a, b, c, d, e, f, g, r, ea, eb;

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        c = new ctx.FP2(a, b); //c.bset(a,b);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 2 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 3 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        d = new ctx.FP2(a, b); //d.bset(a,b);

        ea = new ctx.FP4(c, d); //e.set(c,d);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 4 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 5 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        c = new ctx.FP2(a, b); //c.bset(a,b);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 6 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 7 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        d = new ctx.FP2(a, b); //d.bset(a,b);

        eb = new ctx.FP4(c, d); //e.set(c,d);

        e = new ctx.FP8(ea,eb);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 8 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 9 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        c = new ctx.FP2(a, b); //c.bset(a,b);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 10 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 11 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        d = new ctx.FP2(a, b);

        ea = new ctx.FP4(c, d); //e.set(c,d);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 12 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 13 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        c = new ctx.FP2(a, b); //c.bset(a,b);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 14 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 15 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        d = new ctx.FP2(a, b);

        eb = new ctx.FP4(c, d); //e.set(c,d);

        f = new ctx.FP8(ea, eb); //f.set(c,d);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 16 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 17 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        c = new ctx.FP2(a, b); //c.bset(a,b);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 18 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 19 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        d = new ctx.FP2(a, b); //d.bset(a,b);

        ea = new ctx.FP4(c, d); //e.set(c,d);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 20 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 21 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        c = new ctx.FP2(a, b); //c.bset(a,b);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 22 * ctx.BIG.MODBYTES];
        }
        a = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = w[i + 23 * ctx.BIG.MODBYTES];
        }
        b = ctx.BIG.fromBytes(t);
        d = new ctx.FP2(a, b); //d.bset(a,b);

        eb = new ctx.FP4(c, d); //e.set(c,d);

        g = new ctx.FP8(ea, eb); //g.set(c,d);

        r = new FP24(e, f, g); //r.set(e,f,g);

        return r;
    };

    /**
      * return 1 if b==c, no branching 
      *
      * @this {FP24}
      */    
    FP24.teq = function(b, c) {
        var x = b ^ c;
        x -= 1; // if x=0, x now -1
        return ((x >> 31) & 1);
    };

    /* 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

    /**
      * p=q0^u0.q1^u1.q2^u2.q3^u3... 
      *
      * @this {FP24}
      */    
    FP24.pow8 = function(q, u) {
        var g1 = [],
            g2 = [],
            r = new FP24(0),
            p = new FP24(0),
            t = [],
            mt = new ctx.BIG(0),
            fa = new ctx.BIG(0),
            fb = new ctx.BIG(0),
            w1 = [],
            s1 = [],
            w2 = [],
            s2 = [],
            i, j, k, nb, bt, pb1, pb2, f;

        for (i = 0; i < 8; i++) {
            t[i] = new ctx.BIG(u[i]); t[i].norm();
        }

        g1[0] = new FP24(q[0]);  // q[0]
        g1[1] = new FP24(g1[0]); g1[1].mul(q[1]);   // q[0].q[1]
        g1[2] = new FP24(g1[0]); g1[2].mul(q[2]);   // q[0].q[2]
        g1[3] = new FP24(g1[1]); g1[3].mul(q[2]);   // q[0].q[1].q[2]
        g1[4] = new FP24(q[0]);  g1[4].mul(q[3]);   // q[0].q[3]
        g1[5] = new FP24(g1[1]); g1[5].mul(q[3]);   // q[0].q[1].q[3]
        g1[6] = new FP24(g1[2]); g1[6].mul(q[3]);   // q[0].q[2].q[3]
        g1[7] = new FP24(g1[3]); g1[7].mul(q[3]);   // q[0].q[1].q[2].q[3]

        //  Use Frobenius
        fa.rcopy(ctx.ROM_FIELD.Fra);
        fb.rcopy(ctx.ROM_FIELD.Frb);
        f = new ctx.FP2(fa, fb);

        for (i=0;i<8;i++) {
            g2[i]=new FP24(g1[i]);
            g2[i].frob(f,4);
        }

        // Make it 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();

        // Number of bits
        mt.zero();
        for (i=0;i<8;i++) {
            mt.or(t[i]);
        }

        nb=1+mt.nbits();

        // Sign pivot
        s1[nb-1]=1;
        s2[nb-1]=1;
        for (i=0;i<nb-1;i++) {
            t[0].fshr(1);
            s1[i]=2*t[0].parity()-1;
            t[4].fshr(1);
            s2[i]=2*t[4].parity()-1;

        }

        // Recoded exponent
        for (i=0; i<nb; i++) {
            w1[i]=0;
            k=1;
            for (j=1; j<4; j++) {
                bt=s1[i]*t[j].parity();
                t[j].fshr(1);
                t[j].dec(bt>>1);
                t[j].norm();
                w1[i]+=bt*k;
                k*=2;
            }
            w2[i]=0;
            k=1;
            for (j=5; j<8; j++) {
                bt=s2[i]*t[j].parity();
                t[j].fshr(1);
                t[j].dec(bt>>1);
                t[j].norm();
                w2[i]+=bt*k;
                k*=2;
            }
        }

        // Main loop
        p.select(g1,2*w1[nb-1]+1);
        r.select(g2,2*w2[nb-1]+1);
        p.mul(r);
        for (i=nb-2;i>=0;i--) {
            p.usqr();
            r.select(g1,2*w1[i]+s1[i]);
            p.mul(r);
            r.select(g2,2*w2[i]+s2[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);

        p.reduce();
        return p;
    };

    return FP24;
};

if (typeof module !== "undefined" && typeof module.exports !== "undefined") {
    module.exports = {
        FP24: FP24
    };
}