/*
    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 Weierstrass elliptic curve functions over ctx.FP2 */

var ECP2 = function(ctx) {
    "use strict";

    /**
     * Creates an instance of ECP2
     *
     * @constructor
     * @this {ECP2}
     */    
    var ECP2 = function(input) {
        if (input instanceof ECP2) {
            // copy constructor
            this.x = new ctx.FP2(input.x);
            this.y = new ctx.FP2(input.y);
            this.z = new ctx.FP2(input.z);
        } else {
            // default constructor (point at infinity)
            this.x = new ctx.FP2(0);
            this.y = new ctx.FP2(1);
            this.z = new ctx.FP2(0);
        }
    };

    ECP2.prototype = {
	
	/**
         * Tests for ECP2 point equal to infinity
         *
         * @this {ECP2}
         * @param 1 if infinity, else returns 0
         */	
        is_infinity: function() {

            this.x.reduce();
            this.y.reduce();
            this.z.reduce();
            return (this.x.iszilch() && this.z.iszilch());
        },

	/**
         * Copy ECP2 point to another ECP2 point
         *
         * @this {ECP2}
         * @param P ECP2 instance
         */	
        copy: function(P) {
            this.x.copy(P.x);
            this.y.copy(P.y);
            this.z.copy(P.z);
        },

	/**
         * Set ECP2 to point-at-infinity
         *
         * @this {ECP2}
         */	
        inf: function() {
            this.x.zero();
            this.y.one();
            this.z.zero();
        },

	/**
         * conditional move of Q to P dependant on d 
         *
         * @this {ECP2}
         */	
        cmove: function(Q, d) {
            this.x.cmove(Q.x, d);
            this.y.cmove(Q.y, d);
            this.z.cmove(Q.z, d);
        },

	/**
         * Constant time select from pre-computed table 
         *
         * @this {ECP2}
         */	
        select: function(W, b) {
            var MP = new ECP2(),
                m, babs;

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

            this.cmove(W[0], ECP2.teq(babs, 0)); // conditional move
            this.cmove(W[1], ECP2.teq(babs, 1));
            this.cmove(W[2], ECP2.teq(babs, 2));
            this.cmove(W[3], ECP2.teq(babs, 3));
            this.cmove(W[4], ECP2.teq(babs, 4));
            this.cmove(W[5], ECP2.teq(babs, 5));
            this.cmove(W[6], ECP2.teq(babs, 6));
            this.cmove(W[7], ECP2.teq(babs, 7));

            MP.copy(this);
            MP.neg();
            this.cmove(MP, (m & 1));
        },

	/**
         * Test P == Q 
         *
         * @this {ECP2}
         * @param Q ECP2 instance 
         */	
        equals: function(Q) {
            var a, b;

            a = new ctx.FP2(0);
            a.copy(this.x);
            b = new ctx.FP2(0);
            b.copy(Q.x);

            a.copy(this.x);
            a.mul(Q.z);
            a.reduce();
            b.copy(Q.x);
            b.mul(this.z);
            b.reduce();
            if (!a.equals(b)) {
                return false;
            }

            a.copy(this.y);
            a.mul(Q.z);
            a.reduce();
            b.copy(Q.y);
            b.mul(this.z);
            b.reduce();
            if (!a.equals(b)) {
                return false;
            }

            return true;
        },

	/**
         * set this=-this 
         *
         * @this {ECP2}
         */	
        neg: function() {
            this.y.norm();
            this.y.neg();
            this.y.norm();
            return;
        },

	/**
         * convert this to affine, from (x,y,z) to (x,y) 
         *
         * @this {ECP2}
         */	
        affine: function() {
            var one;

            if (this.is_infinity()) {
                return;
            }

            one = new ctx.FP2(1);

            if (this.z.equals(one)) {
                this.x.reduce();
                this.y.reduce();
                return;
            }

            this.z.inverse();

            this.x.mul(this.z);
            this.x.reduce();
            this.y.mul(this.z);
            this.y.reduce();
            this.z.copy(one);
        },

	/**
         * extract affine x as ctx.FP2 
         *
         * @this {ECP2}
         */	
        getX: function() {
			var W=new ECP2(); W.copy(this); W.affine();
            return W.x;
        },

  
	/**
         * extract affine y as ctx.FP2
         *
         * @this {ECP2}
         */	
        getY: function() {
			var W=new ECP2(); W.copy(this); W.affine();
            return W.y;
        },

	/**
         * extract projective x
         *
         * @this {ECP2}
         */	
        getx: function() {
            return this.x;
        },

	/**
         * extract projective y
         *
         * @this {ECP2}
         */	
        gety: function() {
            return this.y;
        },

	/**
         * extract projective z
         *
         * @this {ECP2}
         */	
        getz: function() {
            return this.z;
        },

	/**
         * convert this to byte arrayextract projective x
         *
         * @this {ECP2}
         * @param b byte array output
         */	
        toBytes: function(b) {
            var t = [],
                i;
			var W=new ECP2(); W.copy(this);
            W.affine();
            W.x.getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                b[i] = t[i];
            }
            W.x.getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                b[i + ctx.BIG.MODBYTES] = t[i];
            }

            W.y.getA().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                b[i + 2 * ctx.BIG.MODBYTES] = t[i];
            }
            W.y.getB().toBytes(t);
            for (i = 0; i < ctx.BIG.MODBYTES; i++) {
                b[i + 3 * ctx.BIG.MODBYTES] = t[i];
            }
        },

	/**
         * convert this to hex string 
         *
         * @this {ECP2}
         * @return hex string
         */	
        toString: function() {
			var W=new ECP2(); W.copy(this);
            if (W.is_infinity()) {
                return "infinity";
            }
            W.affine();
            return "(" + W.x.toString() + "," + W.y.toString() + ")";
        },

 
	/**
         * set this=(x,y)
         *
         * @this {ECP2}
         * @param ix x-value
         * @param iy y-value
         */	
        setxy: function(ix, iy) {
            var rhs, y2;

            this.x.copy(ix);
            this.y.copy(iy);
            this.z.one();
			this.x.norm();

            rhs = ECP2.RHS(this.x);

            y2 = new ctx.FP2(this.y); 
            y2.sqr();

            if (!y2.equals(rhs)) {
                this.inf();
            }
        },

	/**
         * set this=(x,.) 
         *
         * @this {ECP2}
         * @param ix x-value
         */	
        setx: function(ix) {
            var rhs;

            this.x.copy(ix);
            this.z.one();
			this.x.norm();

            rhs = ECP2.RHS(this.x);

            if (rhs.sqrt()) {
                this.y.copy(rhs);
            } else {
                this.inf();
            }
        },

	/**
         * set this*=q, where q is Modulus, using Frobenius 
         *
         * @this {ECP2}
         */	
        frob: function(X) {
            var X2;

            X2 = new ctx.FP2(X); //X2.copy(X);
            X2.sqr();
            this.x.conj();
            this.y.conj();
            this.z.conj();
            this.z.reduce();
            this.x.mul(X2);
            this.y.mul(X2);
            this.y.mul(X);
        },

	/**
         * this+=this 
         *
         * @this {ECP2}
         */	
        dbl: function() {
            var iy, t0, t1, t2, x3, y3;

            iy = new ctx.FP2(0);
            iy.copy(this.y); 
            if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.D_TYPE) {
                iy.mul_ip();
                iy.norm();
            }

            t0 = new ctx.FP2(0);
            t0.copy(this.y); 
            t0.sqr();
            if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.D_TYPE) {
                t0.mul_ip();
            }
            t1 = new ctx.FP2(0);
            t1.copy(iy); 
            t1.mul(this.z);
            t2 = new ctx.FP2(0);
            t2.copy(this.z);
            t2.sqr();

            this.z.copy(t0);
            this.z.add(t0);
            this.z.norm();
            this.z.add(this.z);
            this.z.add(this.z);
            this.z.norm();

            t2.imul(3 * ctx.ROM_CURVE.CURVE_B_I);
            if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.M_TYPE) {
                t2.mul_ip();
                t2.norm();
            }

            x3 = new ctx.FP2(0);
            x3.copy(t2); 
            x3.mul(this.z);

            y3 = new ctx.FP2(0);
            y3.copy(t0); 

            y3.add(t2);
            y3.norm();
            this.z.mul(t1);
            t1.copy(t2);
            t1.add(t2);
            t2.add(t1);
            t2.norm();
            t0.sub(t2);
            t0.norm(); //y^2-9bz^2
            y3.mul(t0);
            y3.add(x3); //(y^2+3z*2)(y^2-9z^2)+3b.z^2.8y^2
            t1.copy(this.x);
            t1.mul(iy); //
            this.x.copy(t0);
            this.x.norm();
            this.x.mul(t1);
            this.x.add(this.x); //(y^2-9bz^2)xy2

            this.x.norm();
            this.y.copy(y3);
            this.y.norm();

            return 1;
        },

	/**
         * Adds ECP2 instances
         *
         * param Q ECP2 instance
         * @this {ECP2}
         */		
        add: function(Q) {
            var b, t0, t1, t2, t3, t4, x3, y3, z3;

            b = 3 * ctx.ROM_CURVE.CURVE_B_I;
            t0 = new ctx.FP2(0);
            t0.copy(this.x); 
            t0.mul(Q.x); // x.Q.x
            t1 = new ctx.FP2(0);
            t1.copy(this.y); 
            t1.mul(Q.y); // y.Q.y

            t2 = new ctx.FP2(0);
            t2.copy(this.z); 
            t2.mul(Q.z);
            t3 = new ctx.FP2(0);
            t3.copy(this.x); 
            t3.add(this.y);
            t3.norm(); //t3=X1+Y1
            t4 = new ctx.FP2(0);
            t4.copy(Q.x); 
            t4.add(Q.y);
            t4.norm(); //t4=X2+Y2
            t3.mul(t4); //t3=(X1+Y1)(X2+Y2)
            t4.copy(t0);
            t4.add(t1); //t4=X1.X2+Y1.Y2

            t3.sub(t4);
            t3.norm();
            if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.D_TYPE) {
                t3.mul_ip();
                t3.norm(); //t3=(X1+Y1)(X2+Y2)-(X1.X2+Y1.Y2) = X1.Y2+X2.Y1
            }

            t4.copy(this.y);
            t4.add(this.z);
            t4.norm(); //t4=Y1+Z1
            x3 = new ctx.FP2(0);
            x3.copy(Q.y); 
            x3.add(Q.z);
            x3.norm(); //x3=Y2+Z2

            t4.mul(x3); //t4=(Y1+Z1)(Y2+Z2)
            x3.copy(t1); //
            x3.add(t2); //X3=Y1.Y2+Z1.Z2

            t4.sub(x3);
            t4.norm();
            if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.D_TYPE) {
                t4.mul_ip();
                t4.norm(); //t4=(Y1+Z1)(Y2+Z2) - (Y1.Y2+Z1.Z2) = Y1.Z2+Y2.Z1
            }

            x3.copy(this.x);
            x3.add(this.z);
            x3.norm(); // x3=X1+Z1
            y3 = new ctx.FP2(0);
            y3.copy(Q.x); 
            y3.add(Q.z);
            y3.norm(); // y3=X2+Z2
            x3.mul(y3); // x3=(X1+Z1)(X2+Z2)
            y3.copy(t0);
            y3.add(t2); // y3=X1.X2+Z1+Z2
            y3.rsub(x3);
            y3.norm(); // y3=(X1+Z1)(X2+Z2) - (X1.X2+Z1.Z2) = X1.Z2+X2.Z1

            if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.D_TYPE) {
                t0.mul_ip();
                t0.norm(); // x.Q.x
                t1.mul_ip();
                t1.norm(); // y.Q.y
            }

            x3.copy(t0);
            x3.add(t0);
            t0.add(x3);
            t0.norm();
            t2.imul(b);
            if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.M_TYPE) {
                t2.mul_ip(); t2.norm();
            }

            z3 = new ctx.FP2(0);
            z3.copy(t1); 
            z3.add(t2);
            z3.norm();
            t1.sub(t2);
            t1.norm();
            y3.imul(b);
            if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.M_TYPE) {
                y3.mul_ip();
                y3.norm();
            }

            x3.copy(y3);
            x3.mul(t4);
            t2.copy(t3);
            t2.mul(t1);
            x3.rsub(t2);
            y3.mul(t0);
            t1.mul(z3);
            y3.add(t1);
            t0.mul(t3);
            z3.mul(t4);
            z3.add(t0);

            this.x.copy(x3);
            this.x.norm();
            this.y.copy(y3);
            this.y.norm();
            this.z.copy(z3);
            this.z.norm();

            return 0;
        },

	/**
         * Subtracts ECP instance Q  from this
         *
         * @this {ECP2}
         * @param Q ECP2 instance
         */	
        sub: function(Q) {
            var D;
			var NQ=new ECP2(); NQ.copy(Q);
            NQ.neg();
            D = this.add(NQ);
            return D;
        },

	/**
         * Multiplies an ECP2 instance P by a BIG, side-channel resistant
         *
         * @this {ECP2}
         * @param e BIG number multiplier
         */		
        mul: function(e) {
            /* fixed size windows */
            var mt = new ctx.BIG(),
                t = new ctx.BIG(),
                C = new ECP2(),
                P = new ECP2(),
                Q = new ECP2(),
                W = [],
                w = [],
                i, nb, s, ns;

            if (this.is_infinity()) {
                return new ECP2();
            }

            // precompute table
            Q.copy(this);
            Q.dbl();
            W[0] = new ECP2();
            W[0].copy(this);

            for (i = 1; i < 8; i++) {
                W[i] = new ECP2();
                W[i].copy(W[i - 1]);
                W[i].add(Q);
            }

            // make exponent odd - add 2P if even, P if odd
            t.copy(e);
            s = t.parity();
            t.inc(1);
            t.norm();
            ns = t.parity();
            mt.copy(t);
            mt.inc(1);
            mt.norm();
            t.cmove(mt, s);
            Q.cmove(this, ns);
            C.copy(Q);

            nb = 1 + Math.floor((t.nbits() + 3) / 4);

            // convert exponent to signed 4-bit window
            for (i = 0; i < nb; i++) {
                w[i] = (t.lastbits(5) - 16);
                t.dec(w[i]);
                t.norm();
                t.fshr(4);
            }
            w[nb] = t.lastbits(5);

            P.copy(W[Math.floor((w[nb] - 1) / 2)]);
            for (i = nb - 1; i >= 0; i--) {
                Q.select(W, w[i]);
                P.dbl();
                P.dbl();
                P.dbl();
                P.dbl();
                P.add(Q);
            }
            P.sub(C);
            P.affine();

            return P;
        }
    };

    /**
      * Set group generator
      *
      * @this {ECP2}
      */	
    ECP2.generator = function() {
        var G=new ECP2(),
            A = new ctx.BIG(0),
            B = new ctx.BIG(0),
            QX, QY;

        A.rcopy(ctx.ROM_CURVE.CURVE_Pxa);
        B.rcopy(ctx.ROM_CURVE.CURVE_Pxb);
        QX = new ctx.FP2(0);
        QX.bset(A, B);
        A.rcopy(ctx.ROM_CURVE.CURVE_Pya);
        B.rcopy(ctx.ROM_CURVE.CURVE_Pyb);
        QY = new ctx.FP2(0);
        QY.bset(A, B);
        G.setxy(QX, QY);
        return G;
    };

    /**
      * convert from byte array to point 
      *
      * @this {ECP2}
      * @param b input byte array
      */	    
    ECP2.fromBytes = function(b) {
        var t = [],
            ra, rb, i, rx, ry, P;

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = b[i];
        }
        ra = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = b[i + ctx.BIG.MODBYTES];
        }
        rb = ctx.BIG.fromBytes(t);

        rx = new ctx.FP2(ra, rb); //rx.bset(ra,rb);

        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = b[i + 2 * ctx.BIG.MODBYTES];
        }
        ra = ctx.BIG.fromBytes(t);
        for (i = 0; i < ctx.BIG.MODBYTES; i++) {
            t[i] = b[i + 3 * ctx.BIG.MODBYTES];
        }
        rb = ctx.BIG.fromBytes(t);

        ry = new ctx.FP2(ra, rb); //ry.bset(ra,rb);

        P = new ECP2();
        P.setxy(rx, ry);

        return P;
    };

    /**
      * Calculate RHS of curve equation x^3+B
      *
      * @this {ECP2}
      * @param x x-value
      */	    
    ECP2.RHS = function(x) {
        var r, c, b;

        //x.norm();
        r = new ctx.FP2(x); //r.copy(x);
        r.sqr();

        c = new ctx.BIG(0);
        c.rcopy(ctx.ROM_CURVE.CURVE_B);
        b = new ctx.FP2(c); //b.bseta(c);

        if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.D_TYPE) {
            b.div_ip();
        }
        if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.M_TYPE) {
            b.norm();
            b.mul_ip();
            b.norm();
        }

        r.mul(x);
        r.add(b);

        r.reduce();

        return r;
    };

    /* P=u0.Q0+u1*Q1+u2*Q2+u3*Q3 */
    // Bos & Costello https://eprint.iacr.org/2013/458.pdf
    // Faz-Hernandez & Longa & Sanchez  https://eprint.iacr.org/2013/158.pdf
    // Side channel attack secure

    /**
      * Calculate P=u0.Q0+u1*Q1+u2*Q2+u3*Q3 
      *
      * @this {ECP2}
      */ 
    ECP2.mul4 = function(Q, u) {
        var W = new ECP2(),
            P = new ECP2(),
            T = [],
            mt = new ctx.BIG(),
            t = [],
            w = [],
            s = [],
            i, j, k, nb, bt, pb;

        for (i = 0; i < 4; i++) {
            t[i] = new ctx.BIG(u[i]); t[i].norm();
            //Q[i].affine();
        }

        T[0] = new ECP2(); T[0].copy(Q[0]); // Q[0]
        T[1] = new ECP2(); T[1].copy(T[0]); T[1].add(Q[1]); // Q[0]+Q[1]
        T[2] = new ECP2(); T[2].copy(T[0]); T[2].add(Q[2]); // Q[0]+Q[2]
        T[3] = new ECP2(); T[3].copy(T[1]); T[3].add(Q[2]); // Q[0]+Q[1]+Q[2]
        T[4] = new ECP2(); T[4].copy(T[0]); T[4].add(Q[3]); // Q[0]+Q[3]
        T[5] = new ECP2(); T[5].copy(T[1]); T[5].add(Q[3]); // Q[0]+Q[1]+Q[3]
        T[6] = new ECP2(); T[6].copy(T[2]); T[6].add(Q[3]); // Q[0]+Q[2]+Q[3]
        T[7] = new ECP2(); T[7].copy(T[3]); T[7].add(Q[3]); // Q[0]+Q[1]+Q[2]+Q[3]

        // Make it odd
        pb=1-t[0].parity();
        t[0].inc(pb);
        t[0].norm();

        // Number of bits
        mt.zero();
        for (i=0;i<4;i++) {
            mt.or(t[i]);
        }

        nb=1+mt.nbits();

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

        // Recoded exponent
        for (i=0; i<nb; i++) {
            w[i]=0;
            k=1;
            for (j=1; j<4; j++) {
                bt=s[i]*t[j].parity();
                t[j].fshr(1);
                t[j].dec(bt>>1);
                t[j].norm();
                w[i]+=bt*k;
                k*=2;
            }
        }

        // Main loop
        P.select(T,2*w[nb-1]+1);
        for (i=nb-2;i>=0;i--) {
            P.dbl();
            W.select(T,2*w[i]+s[i]);
            P.add(W);
        }

        // apply correction
        W.copy(P);
        W.sub(Q[0]);
        P.cmove(W,pb);
        P.affine();
        return P;
    };


    /* return 1 if b==c, no branching */
    ECP2.teq = function(b, c) {
        var x = b ^ c;
        x -= 1; // if x=0, x now -1
        return ((x >> 31) & 1);
    };

    /* needed for SOK */
    ECP2.mapit = function(h) {
        var fa = new ctx.BIG(0),
            fb = new ctx.BIG(0),
            q, x, one, Q, T, K, X, xQ, x2Q;

        q = new ctx.BIG(0);
        q.rcopy(ctx.ROM_FIELD.Modulus);
        x = ctx.BIG.fromBytes(h);
        one = new ctx.BIG(1);
        x.mod(q);

        for (;;) {
            X = new ctx.FP2(one, x);
            Q = new ECP2();
            Q.setx(X);
            if (!Q.is_infinity()) {
                break;
            }
            x.inc(1);
            x.norm();
        }
        /* Fast Hashing to G2 - Fuentes-Castaneda, Knapp and Rodriguez-Henriquez */
        fa.rcopy(ctx.ROM_FIELD.Fra);
        fb.rcopy(ctx.ROM_FIELD.Frb);
        X = new ctx.FP2(fa, fb);
        if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.M_TYPE) {
            X.inverse();
            X.norm();
        }

        x = new ctx.BIG(0);
        x.rcopy(ctx.ROM_CURVE.CURVE_Bnx);

        if (ctx.ECP.CURVE_PAIRING_TYPE == ctx.ECP.BN) {
            T = new ECP2();
            T.copy(Q);
            T = T.mul(x);
            if (ctx.ECP.SIGN_OF_X == ctx.ECP.NEGATIVEX) {
                T.neg();
            }
            K = new ECP2();
            K.copy(T);
            K.dbl();
            K.add(T); //K.affine();

            K.frob(X);
            Q.frob(X);
            Q.frob(X);
            Q.frob(X);
            Q.add(T);
            Q.add(K);
            T.frob(X);
            T.frob(X);
            Q.add(T);
        }

        if (ctx.ECP.CURVE_PAIRING_TYPE == ctx.ECP.BLS) {

            xQ = Q.mul(x);
            x2Q = xQ.mul(x);

            if (ctx.ECP.SIGN_OF_X == ctx.ECP.NEGATIVEX) {
                xQ.neg();
            }

            x2Q.sub(xQ);
            x2Q.sub(Q);

            xQ.sub(Q);
            xQ.frob(X);

            Q.dbl();
            Q.frob(X);
            Q.frob(X);

            Q.add(x2Q);
            Q.add(xQ);
        }

        Q.affine();

        return Q;
    };

    return ECP2;
};

// CommonJS module exports
if (typeof module !== "undefined" && typeof module.exports !== "undefined") {
  module.exports.ECP2 = ECP2;
}