| /* |
| 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"; |
| |
| /* Constructor */ |
| 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 = { |
| /* Test this=O? */ |
| is_infinity: function() { |
| |
| this.x.reduce(); |
| this.y.reduce(); |
| this.z.reduce(); |
| return (this.x.iszilch() && this.z.iszilch()); |
| }, |
| |
| /* copy this=P */ |
| copy: function(P) { |
| this.x.copy(P.x); |
| this.y.copy(P.y); |
| this.z.copy(P.z); |
| }, |
| |
| /* set this=O */ |
| inf: function() { |
| this.x.zero(); |
| this.y.one(); |
| this.z.zero(); |
| }, |
| |
| /* conditional move of Q to P dependant on d */ |
| 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 */ |
| 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 */ |
| 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 */ |
| neg: function() { |
| this.y.norm(); |
| this.y.neg(); |
| this.y.norm(); |
| return; |
| }, |
| |
| /* convert this to affine, from (x,y,z) to (x,y) */ |
| 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 */ |
| getX: function() { |
| var W=new ECP2(); W.copy(this); W.affine(); |
| return W.x; |
| }, |
| |
| /* extract affine y as ctx.FP2 */ |
| getY: function() { |
| var W=new ECP2(); W.copy(this); W.affine(); |
| return W.y; |
| }, |
| |
| /* extract projective x */ |
| getx: function() { |
| return this.x; |
| }, |
| |
| /* extract projective y */ |
| gety: function() { |
| return this.y; |
| }, |
| |
| /* extract projective z */ |
| getz: function() { |
| return this.z; |
| }, |
| |
| /* convert this to byte array */ |
| 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 */ |
| 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) */ |
| 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,.) */ |
| 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 */ |
| 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 */ |
| 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; |
| }, |
| |
| /* this+=Q - return 0 for add, 1 for double, -1 for O */ |
| /* this+=Q */ |
| 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; |
| }, |
| |
| /* this-=Q */ |
| sub: function(Q) { |
| var D; |
| var NQ=new ECP2(); NQ.copy(Q); |
| NQ.neg(); |
| D = this.add(NQ); |
| return D; |
| }, |
| |
| /* P*=e */ |
| 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 to group generator |
| 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 */ |
| 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 */ |
| 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 |
| 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; |
| } |
