1const fUtils = require("./futils.js");
  2
  3class GCurve {
  4
  5    constructor(F, g) {
  6        this.F = F;
  7        this.g = [F.copy(g[0]), F.copy(g[1])];
  8        if (this.g.length == 2) this.g[2] = this.F.one;
  9        this.zero = [this.F.zero, this.F.one, this.F.zero];
 10    }
 11
 12    isZero(p) {
 13        return this.F.isZero(p[2]);
 14    }
 15
 16    add(p1, p2) {
 17
 18        if (this.isZero(p1)) return p2;
 19        if (this.isZero(p2)) return p1;
 20
 21        const res = new Array(3);
 22
 23        const Z1Z1 = this.F.square( p1[2] );
 24        const Z2Z2 = this.F.square( p2[2] );
 25
 26        const U1 = this.F.mul( p1[0] , Z2Z2 );     // U1 = X1  * Z2Z2
 27        const U2 = this.F.mul( p2[0] , Z1Z1 );     // U2 = X2  * Z1Z1
 28
 29        const Z1_cubed = this.F.mul( p1[2] , Z1Z1);
 30        const Z2_cubed = this.F.mul( p2[2] , Z2Z2);
 31
 32        const S1 = this.F.mul( p1[1] , Z2_cubed);  // S1 = Y1 * Z2 * Z2Z2
 33        const S2 = this.F.mul( p2[1] , Z1_cubed);  // S2 = Y2 * Z1 * Z1Z1
 34
 35        if (this.F.equals(U1,U2) && this.F.equals(S1,S2)) {
 36            return this.double(p1);
 37        }
 38
 39        const H = this.F.sub( U2 , U1 );                    // H = U2-U1
 40
 41        const S2_minus_S1 = this.F.sub( S2 , S1 );
 42
 43        const I = this.F.square( this.F.add(H,H) );         // I = (2 * H)^2
 44        const J = this.F.mul( H , I );                      // J = H * I
 45
 46        const r = this.F.add( S2_minus_S1 , S2_minus_S1 );  // r = 2 * (S2-S1)
 47        const V = this.F.mul( U1 , I );                     // V = U1 * I
 48
 49        res[0] =
 50            this.F.sub(
 51                this.F.sub( this.F.square(r) , J ),
 52                this.F.add( V , V ));                       // X3 = r^2 - J - 2 * V
 53
 54        const S1_J = this.F.mul( S1 , J );
 55
 56        res[1] =
 57            this.F.sub(
 58                this.F.mul( r , this.F.sub(V,res[0])),
 59                this.F.add( S1_J,S1_J ));                   // Y3 = r * (V-X3)-2 S1 J
 60
 61        res[2] =
 62            this.F.mul(
 63                H,
 64                this.F.sub(
 65                    this.F.square( this.F.add(p1[2],p2[2]) ),
 66                    this.F.add( Z1Z1 , Z2Z2 )));            // Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2) * H
 67
 68        return res;
 69    }
 70
 71    neg(p) {
 72        return [p[0], this.F.neg(p[1]), p[2]];
 73    }
 74
 75    sub(a, b) {
 76        return this.add(a, this.neg(b));
 77    }
 78
 79    double(p) {
 80        const res = new Array(3);
 81
 82        if (this.isZero(p)) return p;
 83
 84        const A = this.F.square( p[0] );                    // A = X1^2
 85        const B = this.F.square( p[1] );                    // B = Y1^2
 86        const C = this.F.square( B );                       // C = B^2
 87
 88        let D =
 89            this.F.sub(
 90                this.F.square( this.F.add(p[0] , B )),
 91                this.F.add( A , C));
 92        D = this.F.add(D,D);                    // D = 2 * ((X1 + B)^2 - A - C)
 93
 94        const E = this.F.add( this.F.add(A,A), A);          // E = 3 * A
 95        const F = this.F.square( E );                       // F = E^2
 96
 97        res[0] = this.F.sub( F , this.F.add(D,D) );         // X3 = F - 2 D
 98
 99        let eightC = this.F.add( C , C );
100        eightC = this.F.add( eightC , eightC );
101        eightC = this.F.add( eightC , eightC );
102
103        res[1] =
104            this.F.sub(
105                this.F.mul(
106                    E,
107                    this.F.sub( D, res[0] )),
108                eightC);                                    // Y3 = E * (D - X3) - 8 * C
109
110        const Y1Z1 = this.F.mul( p[1] , p[2] );
111        res[2] = this.F.add( Y1Z1 , Y1Z1 );                 // Z3 = 2 * Y1 * Z1
112
113        return res;
114    }
115
116    mulScalar(base, e) {
117        return fUtils.mulScalar(this, base, e);
118    }
119
120    affine(p) {
121        if (this.isZero(p)) {
122            return this.zero;
123        } else {
124            const Z_inv = this.F.inverse(p[2]);
125            const Z2_inv = this.F.square(Z_inv);
126            const Z3_inv = this.F.mul(Z2_inv, Z_inv);
127
128            const res = new Array(3);
129            res[0] = this.F.affine( this.F.mul(p[0],Z2_inv));
130            res[1] = this.F.affine( this.F.mul(p[1],Z3_inv));
131            res[2] = this.F.one;
132
133            return res;
134        }
135    }
136
137    equals(p1, p2) {
138        if (this.isZero(p1)) return this.isZero(p2);
139        if (this.isZero(p2)) return this.isZero(p1);
140
141        const Z1Z1 = this.F.square( p1[2] );
142        const Z2Z2 = this.F.square( p2[2] );
143
144        const U1 = this.F.mul( p1[0] , Z2Z2 );
145        const U2 = this.F.mul( p2[0] , Z1Z1 );
146
147        const Z1_cubed = this.F.mul( p1[2] , Z1Z1);
148        const Z2_cubed = this.F.mul( p2[2] , Z2Z2);
149
150        const S1 = this.F.mul( p1[1] , Z2_cubed);
151        const S2 = this.F.mul( p2[1] , Z1_cubed);
152
153        return (this.F.equals(U1,U2) && this.F.equals(S1,S2));
154    }
155
156    toString(p) {
157        const cp = this.affine(p);
158        return `[ ${this.F.toString(cp[0])} , ${this.F.toString(cp[1])} ]`;
159    }
160
161}
162
163module.exports = GCurve;
164