| /* |
| 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. |
| */ |
| |
| var PAIR192 = function(ctx) { |
| "use strict"; |
| |
| var PAIR192 = { |
| /* Line function */ |
| line: function(A, B, Qx, Qy) { |
| var r = new ctx.FP24(1), |
| XX, YY, ZZ, YZ, sb, |
| X1, Y1, T1, T2, |
| a, b, c; |
| |
| if (A == B) { /* Doubling */ |
| XX = new ctx.FP4(A.getx()); |
| YY = new ctx.FP4(A.gety()); |
| ZZ = new ctx.FP4(A.getz()); |
| YZ = new ctx.FP4(YY); |
| |
| YZ.mul(ZZ); //YZ |
| XX.sqr(); //X^2 |
| YY.sqr(); //Y^2 |
| ZZ.sqr(); //Z^2 |
| |
| YZ.imul(4); |
| YZ.neg(); |
| YZ.norm(); //-2YZ |
| YZ.qmul(Qy); //-2YZ.Ys |
| |
| XX.imul(6); //3X^2 |
| XX.qmul(Qx); //3X^2.Xs |
| |
| sb = 3 * ctx.ROM_CURVE.CURVE_B_I; |
| ZZ.imul(sb); |
| if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.D_TYPE) { |
| ZZ.div_2i(); |
| } |
| if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.M_TYPE) { |
| ZZ.times_i(); |
| ZZ.add(ZZ); |
| YZ.times_i(); |
| YZ.norm(); |
| } |
| ZZ.norm(); // 3b.Z^2 |
| |
| YY.add(YY); |
| ZZ.sub(YY); |
| ZZ.norm(); // 3b.Z^2-Y^2 |
| |
| a = new ctx.FP8(YZ, ZZ); // -2YZ.Ys | 3b.Z^2-Y^2 | 3X^2.Xs |
| if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.D_TYPE) { |
| b = new ctx.FP8(XX); // L(0,1) | L(0,0) | L(1,0) |
| c = new ctx.FP8(0); |
| } |
| if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.M_TYPE) { |
| b = new ctx.FP8(0); |
| c = new ctx.FP8(XX); c.times_i(); |
| } |
| |
| A.dbl(); |
| } else { /* Addition */ |
| X1 = new ctx.FP4(A.getx()); // X1 |
| Y1 = new ctx.FP4(A.gety()); // Y1 |
| T1 = new ctx.FP4(A.getz()); // Z1 |
| T2 = new ctx.FP4(A.getz()); // Z1 |
| |
| T1.mul(B.gety()); // T1=Z1.Y2 |
| T2.mul(B.getx()); // T2=Z1.X2 |
| |
| X1.sub(T2); |
| X1.norm(); // X1=X1-Z1.X2 |
| Y1.sub(T1); |
| Y1.norm(); // Y1=Y1-Z1.Y2 |
| |
| T1.copy(X1); // T1=X1-Z1.X2 |
| X1.qmul(Qy); // X1=(X1-Z1.X2).Ys |
| |
| if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.M_TYPE) { |
| X1.times_i(); |
| X1.norm(); |
| } |
| |
| T1.mul(B.gety()); // T1=(X1-Z1.X2).Y2 |
| |
| T2.copy(Y1); // T2=Y1-Z1.Y2 |
| T2.mul(B.getx()); // T2=(Y1-Z1.Y2).X2 |
| T2.sub(T1); |
| T2.norm(); // T2=(Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2 |
| Y1.qmul(Qx); |
| Y1.neg(); |
| Y1.norm(); // Y1=-(Y1-Z1.Y2).Xs |
| |
| a = new ctx.FP8(X1, T2); // (X1-Z1.X2).Ys | (Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2 | - (Y1-Z1.Y2).Xs |
| if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.D_TYPE) { |
| b = new ctx.FP8(Y1); |
| c = new ctx.FP8(0); |
| } |
| if (ctx.ECP.SEXTIC_TWIST == ctx.ECP.M_TYPE) { |
| b = new ctx.FP8(0); |
| c = new ctx.FP8(Y1); c.times_i(); |
| } |
| |
| A.add(B); |
| } |
| |
| r.set(a, b, c); |
| |
| return r; |
| }, |
| |
| /* Optimal R-ate pairing */ |
| ate: function(P1, Q1) { |
| var x, n, n3, lv, |
| Qx, Qy, A, NP, r, nb, bt, |
| i; |
| |
| x = new ctx.BIG(0); |
| x.rcopy(ctx.ROM_CURVE.CURVE_Bnx); |
| n = new ctx.BIG(x); //n.copy(x); |
| |
| n3 = new ctx.BIG(n); |
| n3.pmul(3); |
| n3.norm(); |
| |
| var P=new ctx.ECP4(); P.copy(P1); P.affine(); |
| var Q=new ctx.ECP(); Q.copy(Q1); Q.affine(); |
| |
| // P.affine(); |
| // Q.affine(); |
| Qx = new ctx.FP(Q.getx()); //Qx.copy(Q.getx()); |
| Qy = new ctx.FP(Q.gety()); //Qy.copy(Q.gety()); |
| |
| A = new ctx.ECP4(); |
| r = new ctx.FP24(1); |
| |
| A.copy(P); |
| NP = new ctx.ECP4(); |
| NP.copy(P); |
| NP.neg(); |
| |
| |
| nb = n3.nbits(); |
| |
| for (i = nb - 2; i >= 1; i--) { |
| r.sqr(); |
| lv = PAIR192.line(A, A, Qx, Qy); |
| |
| r.smul(lv,ctx.ECP.SEXTIC_TWIST); |
| |
| bt=n3.bit(i)-n.bit(i); |
| |
| if (bt == 1) { |
| lv = PAIR192.line(A, P, Qx, Qy); |
| r.smul(lv,ctx.ECP.SEXTIC_TWIST); |
| } |
| if (bt == -1) { |
| //P.neg(); |
| lv = PAIR192.line(A, NP, Qx, Qy); |
| r.smul(lv,ctx.ECP.SEXTIC_TWIST); |
| //P.neg(); |
| } |
| } |
| |
| if (ctx.ECP.SIGN_OF_X == ctx.ECP.NEGATIVEX) { |
| r.conj(); |
| } |
| |
| return r; |
| }, |
| |
| /* Optimal R-ate double pairing e(P,Q).e(R,S) */ |
| ate2: function(P1, Q1, R1, S1) { |
| var x, n, n3, lv, |
| Qx, Qy, Sx, Sy, A, B, NP, NR, r, nb, bt, |
| i; |
| |
| |
| x = new ctx.BIG(0); |
| x.rcopy(ctx.ROM_CURVE.CURVE_Bnx); |
| |
| n = new ctx.BIG(x); //n.copy(x); |
| n3 = new ctx.BIG(n); |
| n3.pmul(3); |
| n3.norm(); |
| |
| var P=new ctx.ECP4(); P.copy(P1); P.affine(); |
| var Q=new ctx.ECP(); Q.copy(Q1); Q.affine(); |
| var R=new ctx.ECP4(); R.copy(R1); R.affine(); |
| var S=new ctx.ECP(); S.copy(S1); S.affine(); |
| |
| |
| Qx = new ctx.FP(Q.getx()); //Qx.copy(Q.getx()); |
| Qy = new ctx.FP(Q.gety()); //Qy.copy(Q.gety()); |
| |
| Sx = new ctx.FP(S.getx()); //Sx.copy(S.getx()); |
| Sy = new ctx.FP(S.gety()); //Sy.copy(S.gety()); |
| |
| A = new ctx.ECP4(); |
| B = new ctx.ECP4(); |
| r = new ctx.FP24(1); |
| |
| A.copy(P); |
| B.copy(R); |
| NP = new ctx.ECP4(); |
| NP.copy(P); |
| NP.neg(); |
| NR = new ctx.ECP4(); |
| NR.copy(R); |
| NR.neg(); |
| |
| |
| nb = n3.nbits(); |
| |
| for (i = nb - 2; i >= 1; i--) { |
| r.sqr(); |
| lv = PAIR192.line(A, A, Qx, Qy); |
| r.smul(lv,ctx.ECP.SEXTIC_TWIST); |
| lv = PAIR192.line(B, B, Sx, Sy); |
| r.smul(lv,ctx.ECP.SEXTIC_TWIST); |
| |
| bt=n3.bit(i)-n.bit(i); |
| |
| if (bt == 1) { |
| lv = PAIR192.line(A, P, Qx, Qy); |
| r.smul(lv,ctx.ECP.SEXTIC_TWIST); |
| lv = PAIR192.line(B, R, Sx, Sy); |
| r.smul(lv,ctx.ECP.SEXTIC_TWIST); |
| } |
| if (bt == -1) { |
| //P.neg(); |
| lv = PAIR192.line(A, NP, Qx, Qy); |
| r.smul(lv,ctx.ECP.SEXTIC_TWIST); |
| //P.neg(); |
| //R.neg(); |
| lv = PAIR192.line(B, NR, Sx, Sy); |
| r.smul(lv,ctx.ECP.SEXTIC_TWIST); |
| //R.neg(); |
| } |
| } |
| |
| if (ctx.ECP.SIGN_OF_X == ctx.ECP.NEGATIVEX) { |
| r.conj(); |
| } |
| |
| return r; |
| }, |
| |
| /* final exponentiation - keep separate for multi-pairings and to avoid thrashing stack */ |
| fexp: function(m) { |
| var fa, fb, f, x, r, lv, |
| t0,t1,t2,t3,t4,t5,t6,t7; |
| |
| 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); |
| x = new ctx.BIG(0); |
| x.rcopy(ctx.ROM_CURVE.CURVE_Bnx); |
| |
| r = new ctx.FP24(m); //r.copy(m); |
| |
| /* Easy part of final exp */ |
| lv = new ctx.FP24(r); //lv.copy(r); |
| lv.inverse(); |
| r.conj(); |
| r.mul(lv); |
| lv.copy(r); |
| r.frob(f,4); |
| r.mul(lv); |
| |
| /* Hard part of final exp */ |
| // Ghamman & Fouotsa Method |
| t7=new ctx.FP24(r); t7.usqr(); |
| t1=t7.pow(x); |
| |
| x.fshr(1); |
| t2=t1.pow(x); |
| x.fshl(1); |
| |
| if (ctx.ECP.SIGN_OF_X==ctx.ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| t3=new ctx.FP24(t1); t3.conj(); |
| t2.mul(t3); |
| t2.mul(r); |
| |
| t3=t2.pow(x); |
| t4=t3.pow(x); |
| t5=t4.pow(x); |
| |
| if (ctx.ECP.SIGN_OF_X==ctx.ECP.NEGATIVEX) { |
| t3.conj(); t5.conj(); |
| } |
| |
| t3.frob(f,6); t4.frob(f,5); |
| t3.mul(t4); |
| |
| t6=t5.pow(x); |
| if (ctx.ECP.SIGN_OF_X==ctx.ECP.NEGATIVEX) { |
| t6.conj(); |
| } |
| |
| t5.frob(f,4); |
| t3.mul(t5); |
| |
| t0=new ctx.FP24(t2); t0.conj(); |
| t6.mul(t0); |
| |
| t5.copy(t6); |
| t5.frob(f,3); |
| |
| t3.mul(t5); |
| t5=t6.pow(x); |
| t6=t5.pow(x); |
| |
| if (ctx.ECP.SIGN_OF_X==ctx.ECP.NEGATIVEX) { |
| t5.conj(); |
| } |
| |
| t0.copy(t5); |
| t0.frob(f,2); |
| t3.mul(t0); |
| t0.copy(t6); |
| t0.frob(f,1); |
| |
| t3.mul(t0); |
| t5=t6.pow(x); |
| |
| if (ctx.ECP.SIGN_OF_X==ctx.ECP.NEGATIVEX) { |
| t5.conj(); |
| } |
| t2.frob(f,7); |
| |
| t5.mul(t7); |
| t3.mul(t2); |
| t3.mul(t5); |
| |
| r.mul(t3); |
| |
| r.reduce(); |
| |
| return r; |
| } |
| }; |
| |
| /* GLV method */ |
| PAIR192.glv = function(e) { |
| var u = [], |
| q, x, x2; |
| |
| // -(x^2).P = (Beta.x,y) |
| q = new ctx.BIG(0); |
| q.rcopy(ctx.ROM_CURVE.CURVE_Order); |
| x = new ctx.BIG(0); |
| x.rcopy(ctx.ROM_CURVE.CURVE_Bnx); |
| x2 = ctx.BIG.smul(x, x); |
| x = ctx.BIG.smul(x2,x2); |
| u[0] = new ctx.BIG(e); |
| u[0].mod(x); |
| u[1] = new ctx.BIG(e); |
| u[1].div(x); |
| u[1].rsub(q); |
| |
| return u; |
| }; |
| |
| /* Galbraith & Scott Method */ |
| PAIR192.gs = function(e) { |
| var u = [], |
| i, q, x, w; |
| |
| x = new ctx.BIG(0); |
| x.rcopy(ctx.ROM_CURVE.CURVE_Bnx); |
| q = new ctx.BIG(0); |
| q.rcopy(ctx.ROM_CURVE.CURVE_Order); |
| w = new ctx.BIG(e); |
| |
| for (i = 0; i < 7; i++) { |
| u[i] = new ctx.BIG(w); |
| u[i].mod(x); |
| w.div(x); |
| } |
| |
| u[7] = new ctx.BIG(w); |
| if (ctx.ECP.SIGN_OF_X==ctx.ECP.NEGATIVEX) { |
| u[1].copy(ctx.BIG.modneg(u[1], q)); |
| u[3].copy(ctx.BIG.modneg(u[3], q)); |
| u[5].copy(ctx.BIG.modneg(u[5], q)); |
| u[7].copy(ctx.BIG.modneg(u[7], q)); |
| } |
| |
| return u; |
| }; |
| |
| /* Multiply P by e in group G1 */ |
| PAIR192.G1mul = function(P, e) { |
| var R, Q, q, bcru, cru, t, u, np, nn; |
| |
| if (ctx.ROM_CURVE.USE_GLV) { |
| //P.affine(); |
| R = new ctx.ECP(); |
| R.copy(P); |
| Q = new ctx.ECP(); |
| Q.copy(P); Q.affine(); |
| q = new ctx.BIG(0); |
| q.rcopy(ctx.ROM_CURVE.CURVE_Order); |
| bcru = new ctx.BIG(0); |
| bcru.rcopy(ctx.ROM_CURVE.CURVE_Cru); |
| cru = new ctx.FP(bcru); |
| t = new ctx.BIG(0); |
| u = PAIR192.glv(e); |
| |
| Q.getx().mul(cru); |
| |
| np = u[0].nbits(); |
| t.copy(ctx.BIG.modneg(u[0], q)); |
| nn = t.nbits(); |
| if (nn < np) { |
| u[0].copy(t); |
| R.neg(); |
| } |
| |
| np = u[1].nbits(); |
| t.copy(ctx.BIG.modneg(u[1], q)); |
| nn = t.nbits(); |
| if (nn < np) { |
| u[1].copy(t); |
| Q.neg(); |
| } |
| u[0].norm(); |
| u[1].norm(); |
| R = R.mul2(u[0], Q, u[1]); |
| } else { |
| R = P.mul(e); |
| } |
| |
| return R; |
| }; |
| |
| /* Multiply P by e in group G2 */ |
| PAIR192.G2mul = function(P, e) { |
| var R, Q, F, q, u, t, i, np, nn; |
| |
| if (ctx.ROM_CURVE.USE_GS_G2) { |
| Q = []; |
| F = ctx.ECP4.frob_constants(); |
| |
| q = new ctx.BIG(0); |
| q.rcopy(ctx.ROM_CURVE.CURVE_Order); |
| |
| u = PAIR192.gs(e); |
| t = new ctx.BIG(0); |
| //P.affine(); |
| Q[0] = new ctx.ECP4(); |
| Q[0].copy(P); |
| |
| for (i = 1; i < 8; i++) { |
| Q[i] = new ctx.ECP4(); |
| Q[i].copy(Q[i - 1]); |
| Q[i].frob(F,1); |
| } |
| |
| for (i = 0; i < 8; i++) { |
| np = u[i].nbits(); |
| t.copy(ctx.BIG.modneg(u[i], q)); |
| nn = t.nbits(); |
| |
| if (nn < np) { |
| u[i].copy(t); |
| Q[i].neg(); |
| } |
| u[i].norm(); |
| } |
| |
| R = ctx.ECP4.mul8(Q, u); |
| } else { |
| R = P.mul(e); |
| } |
| return R; |
| }; |
| |
| /* Note that this method requires a lot of RAM! Better to use compressed XTR method, see ctx.FP4.js */ |
| PAIR192.GTpow = function(d, e) { |
| var r, g, fa, fb, f, q, t, u, i, np, nn; |
| |
| if (ctx.ROM_CURVE.USE_GS_GT) { |
| g = []; |
| 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_CURVE.CURVE_Order); |
| t = new ctx.BIG(0); |
| u = PAIR192.gs(e); |
| |
| g[0] = new ctx.FP24(d); |
| |
| for (i = 1; i < 8; i++) { |
| g[i] = new ctx.FP24(0); |
| g[i].copy(g[i - 1]); |
| g[i].frob(f,1); |
| } |
| |
| for (i = 0; i < 8; i++) { |
| np = u[i].nbits(); |
| t.copy(ctx.BIG.modneg(u[i], q)); |
| nn = t.nbits(); |
| |
| if (nn < np) { |
| u[i].copy(t); |
| g[i].conj(); |
| } |
| u[i].norm(); |
| } |
| |
| r = ctx.FP24.pow8(g, u); |
| } else { |
| r = d.pow(e); |
| } |
| |
| return r; |
| }; |
| |
| return PAIR192; |
| }; |
