| /* |
| 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 BN Curve Pairing functions */ |
| |
| package org.apache.milagro.amcl.BLS48; |
| |
| public final class PAIR256 { |
| |
| public static final boolean USE_GLV =true; |
| public static final boolean USE_GS_G2 =true; |
| public static final boolean USE_GS_GT =true; |
| public static final boolean GT_STRONG=false; |
| |
| |
| /* Line function */ |
| public static FP48 line(ECP8 A,ECP8 B,FP Qx,FP Qy) |
| { |
| //System.out.println("Into line"); |
| FP16 a,b,c; // Edits here |
| // c=new FP16(0); |
| if (A==B) |
| { // Doubling |
| FP8 XX=new FP8(A.getx()); //X |
| FP8 YY=new FP8(A.gety()); //Y |
| FP8 ZZ=new FP8(A.getz()); //Z |
| FP8 YZ=new FP8(YY); //Y |
| 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.tmul(Qy); //-2YZ.Ys |
| |
| XX.imul(6); //3X^2 |
| XX.tmul(Qx); //3X^2.Xs |
| |
| int sb=3*ROM.CURVE_B_I; |
| ZZ.imul(sb); |
| |
| if (ECP.SEXTIC_TWIST==ECP.D_TYPE) |
| { |
| ZZ.div_2i(); |
| } |
| if (ECP.SEXTIC_TWIST==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 FP16(YZ,ZZ); // -2YZ.Ys | 3b.Z^2-Y^2 | 3X^2.Xs |
| if (ECP.SEXTIC_TWIST==ECP.D_TYPE) |
| { |
| b=new FP16(XX); // L(0,1) | L(0,0) | L(1,0) |
| c=new FP16(0); |
| } |
| if (ECP.SEXTIC_TWIST==ECP.M_TYPE) |
| { |
| b=new FP16(0); |
| c=new FP16(XX); c.times_i(); |
| } |
| A.dbl(); |
| } |
| else |
| { // Addition - assume B is affine |
| |
| FP8 X1=new FP8(A.getx()); // X1 |
| FP8 Y1=new FP8(A.gety()); // Y1 |
| FP8 T1=new FP8(A.getz()); // Z1 |
| FP8 T2=new FP8(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.tmul(Qy); // X1=(X1-Z1.X2).Ys |
| |
| if (ECP.SEXTIC_TWIST==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.tmul(Qx); Y1.neg(); Y1.norm(); // Y1=-(Y1-Z1.Y2).Xs |
| |
| a=new FP16(X1,T2); // (X1-Z1.X2).Ys | (Y1-Z1.Y2).X2 - (X1-Z1.X2).Y2 | - (Y1-Z1.Y2).Xs |
| if (ECP.SEXTIC_TWIST==ECP.D_TYPE) |
| { |
| b=new FP16(Y1); |
| c=new FP16(0); |
| } |
| if (ECP.SEXTIC_TWIST==ECP.M_TYPE) |
| { |
| b=new FP16(0); |
| c=new FP16(Y1); c.times_i(); |
| } |
| A.add(B); |
| } |
| //System.out.println("Out of line"); |
| return new FP48(a,b,c); |
| } |
| |
| /* Optimal R-ate pairing */ |
| public static FP48 ate(ECP8 P1,ECP Q1) |
| { |
| FP2 f; |
| BIG x=new BIG(ROM.CURVE_Bnx); |
| BIG n=new BIG(x); |
| FP48 lv; |
| int bt; |
| |
| ECP8 P=new ECP8(P1); |
| ECP Q=new ECP(Q1); |
| |
| P.affine(); |
| Q.affine(); |
| |
| |
| BIG n3=new BIG(n); |
| n3.pmul(3); |
| n3.norm(); |
| |
| FP Qx=new FP(Q.getx()); |
| FP Qy=new FP(Q.gety()); |
| |
| ECP8 A=new ECP8(); |
| FP48 r=new FP48(1); |
| A.copy(P); |
| |
| ECP8 MP=new ECP8(); |
| MP.copy(P); MP.neg(); |
| |
| int nb=n3.nbits(); |
| |
| for (int i=nb-2;i>=1;i--) |
| { |
| r.sqr(); |
| lv=line(A,A,Qx,Qy); |
| r.smul(lv,ECP.SEXTIC_TWIST); |
| |
| bt=n3.bit(i)-n.bit(i); // bt=n.bit(i); |
| if (bt==1) |
| { |
| lv=line(A,P,Qx,Qy); |
| r.smul(lv,ECP.SEXTIC_TWIST); |
| } |
| if (bt==-1) |
| { |
| //P.neg(); |
| lv=line(A,MP,Qx,Qy); |
| r.smul(lv,ECP.SEXTIC_TWIST); |
| //P.neg(); |
| } |
| } |
| |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) |
| { |
| r.conj(); |
| } |
| |
| return r; |
| } |
| |
| /* Optimal R-ate double pairing e(P,Q).e(R,S) */ |
| public static FP48 ate2(ECP8 P1,ECP Q1,ECP8 R1,ECP S1) |
| { |
| FP2 f; |
| BIG x=new BIG(ROM.CURVE_Bnx); |
| BIG n=new BIG(x); |
| FP48 lv; |
| int bt; |
| |
| ECP8 P=new ECP8(P1); |
| ECP Q=new ECP(Q1); |
| |
| P.affine(); |
| Q.affine(); |
| |
| ECP8 R=new ECP8(R1); |
| ECP S=new ECP(S1); |
| |
| R.affine(); |
| S.affine(); |
| |
| BIG n3=new BIG(n); |
| n3.pmul(3); |
| n3.norm(); |
| |
| FP Qx=new FP(Q.getx()); |
| FP Qy=new FP(Q.gety()); |
| FP Sx=new FP(S.getx()); |
| FP Sy=new FP(S.gety()); |
| |
| ECP8 A=new ECP8(); |
| ECP8 B=new ECP8(); |
| FP48 r=new FP48(1); |
| |
| A.copy(P); |
| B.copy(R); |
| |
| ECP8 MP=new ECP8(); |
| MP.copy(P); MP.neg(); |
| ECP8 MR=new ECP8(); |
| MR.copy(R); MR.neg(); |
| |
| |
| int nb=n3.nbits(); |
| |
| for (int i=nb-2;i>=1;i--) |
| { |
| r.sqr(); |
| lv=line(A,A,Qx,Qy); |
| r.smul(lv,ECP.SEXTIC_TWIST); |
| |
| lv=line(B,B,Sx,Sy); |
| r.smul(lv,ECP.SEXTIC_TWIST); |
| |
| bt=n3.bit(i)-n.bit(i); // bt=n.bit(i); |
| if (bt==1) |
| { |
| lv=line(A,P,Qx,Qy); |
| r.smul(lv,ECP.SEXTIC_TWIST); |
| lv=line(B,R,Sx,Sy); |
| r.smul(lv,ECP.SEXTIC_TWIST); |
| } |
| if (bt==-1) |
| { |
| //P.neg(); |
| lv=line(A,MP,Qx,Qy); |
| r.smul(lv,ECP.SEXTIC_TWIST); |
| //P.neg(); |
| //R.neg(); |
| lv=line(B,MR,Sx,Sy); |
| r.smul(lv,ECP.SEXTIC_TWIST); |
| //R.neg(); |
| } |
| } |
| |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) |
| { |
| r.conj(); |
| } |
| |
| return r; |
| } |
| |
| /* final exponentiation - keep separate for multi-pairings and to avoid thrashing stack */ |
| public static FP48 fexp(FP48 m) |
| { |
| FP2 f=new FP2(new BIG(ROM.Fra),new BIG(ROM.Frb)); |
| BIG x=new BIG(ROM.CURVE_Bnx); |
| FP48 r=new FP48(m); |
| |
| /* Easy part of final exp */ |
| FP48 lv=new FP48(r); |
| lv.inverse(); |
| r.conj(); |
| |
| r.mul(lv); |
| lv.copy(r); |
| r.frob(f,8); |
| r.mul(lv); |
| |
| FP48 t0,t1,t2,t3,t4,t5,t6,t7; |
| /* Hard part of final exp */ |
| // Ghamman & Fouotsa Method |
| |
| t7=new FP48(r); t7.usqr(); |
| t1=t7.pow(x); |
| |
| x.fshr(1); |
| t2=t1.pow(x); |
| x.fshl(1); |
| |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3=new FP48(t1); t3.conj(); |
| t2.mul(t3); |
| t2.mul(r); |
| |
| r.mul(t7); |
| |
| t1=t2.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| t3.copy(t1); |
| t3.frob(f,14); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,13); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,12); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,11); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,10); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,9); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,8); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t2); t3.conj(); |
| t1.mul(t3); |
| t3.copy(t1); |
| t3.frob(f,7); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,6); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,5); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,4); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,3); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,2); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| t3.copy(t1); |
| t3.frob(f,1); |
| r.mul(t3); |
| t1=t1.pow(x); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) { |
| t1.conj(); |
| } |
| |
| r.mul(t1); |
| t2.frob(f,15); |
| r.mul(t2); |
| |
| r.reduce(); |
| return r; |
| } |
| |
| /* GLV method */ |
| public static BIG[] glv(BIG e) |
| { |
| BIG[] u=new BIG[2]; |
| // -(x^8).P = (Beta.x,y) |
| BIG q=new BIG(ROM.CURVE_Order); |
| BIG x=new BIG(ROM.CURVE_Bnx); |
| BIG x2=BIG.smul(x,x); |
| x=BIG.smul(x2,x2); |
| x2=BIG.smul(x,x); |
| u[0]=new BIG(e); |
| u[0].mod(x2); |
| u[1]=new BIG(e); |
| u[1].div(x2); |
| u[1].rsub(q); |
| |
| return u; |
| } |
| |
| /* Galbraith & Scott Method */ |
| public static BIG[] gs(BIG e) |
| { |
| BIG[] u=new BIG[16]; |
| |
| BIG q=new BIG(ROM.CURVE_Order); |
| BIG x=new BIG(ROM.CURVE_Bnx); |
| BIG w=new BIG(e); |
| for (int i=0;i<15;i++) |
| { |
| u[i]=new BIG(w); |
| u[i].mod(x); |
| w.div(x); |
| } |
| u[15]=new BIG(w); |
| if (ECP.SIGN_OF_X==ECP.NEGATIVEX) |
| { |
| u[1].copy(BIG.modneg(u[1],q)); |
| u[3].copy(BIG.modneg(u[3],q)); |
| u[5].copy(BIG.modneg(u[5],q)); |
| u[7].copy(BIG.modneg(u[7],q)); |
| u[9].copy(BIG.modneg(u[9],q)); |
| u[11].copy(BIG.modneg(u[11],q)); |
| u[13].copy(BIG.modneg(u[13],q)); |
| u[15].copy(BIG.modneg(u[15],q)); |
| } |
| |
| return u; |
| } |
| |
| /* Multiply P by e in group G1 */ |
| public static ECP G1mul(ECP P,BIG e) |
| { |
| ECP R; |
| if (USE_GLV) |
| { |
| //P.affine(); |
| R=new ECP(); |
| R.copy(P); |
| int i,np,nn; |
| ECP Q=new ECP(); |
| Q.copy(P); Q.affine(); |
| BIG q=new BIG(ROM.CURVE_Order); |
| FP cru=new FP(new BIG(ROM.CURVE_Cru)); |
| BIG t=new BIG(0); |
| BIG[] u=glv(e); |
| Q.getx().mul(cru); |
| |
| np=u[0].nbits(); |
| t.copy(BIG.modneg(u[0],q)); |
| nn=t.nbits(); |
| if (nn<np) |
| { |
| u[0].copy(t); |
| R.neg(); |
| } |
| |
| np=u[1].nbits(); |
| t.copy(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 */ |
| public static ECP8 G2mul(ECP8 P,BIG e) |
| { |
| ECP8 R; |
| if (USE_GS_G2) |
| { |
| ECP8[] Q=new ECP8[16]; |
| FP2[] F=ECP8.frob_constants(); |
| |
| BIG q=new BIG(ROM.CURVE_Order); |
| BIG[] u=gs(e); |
| |
| BIG t=new BIG(0); |
| int i,np,nn; |
| //P.affine(); |
| |
| Q[0]=new ECP8(); Q[0].copy(P); |
| for (i=1;i<16;i++) |
| { |
| Q[i]=new ECP8(); Q[i].copy(Q[i-1]); |
| Q[i].frob(F,1); |
| } |
| for (i=0;i<16;i++) |
| { |
| np=u[i].nbits(); |
| t.copy(BIG.modneg(u[i],q)); |
| nn=t.nbits(); |
| if (nn<np) |
| { |
| u[i].copy(t); |
| Q[i].neg(); |
| } |
| u[i].norm(); |
| //Q[i].affine(); |
| } |
| |
| R=ECP8.mul16(Q,u); |
| } |
| else |
| { |
| R=P.mul(e); |
| } |
| return R; |
| } |
| |
| /* f=f^e */ |
| /* Note that this method requires a lot of RAM! Better to use compressed XTR method, see FP16.java */ |
| public static FP48 GTpow(FP48 d,BIG e) |
| { |
| FP48 r; |
| if (USE_GS_GT) |
| { |
| FP48[] g=new FP48[16]; |
| FP2 f=new FP2(new BIG(ROM.Fra),new BIG(ROM.Frb)); |
| BIG q=new BIG(ROM.CURVE_Order); |
| BIG t=new BIG(0); |
| int i,np,nn; |
| BIG[] u=gs(e); |
| |
| g[0]=new FP48(d); |
| for (i=1;i<16;i++) |
| { |
| g[i]=new FP48(0); g[i].copy(g[i-1]); |
| g[i].frob(f,1); |
| } |
| for (i=0;i<16;i++) |
| { |
| np=u[i].nbits(); |
| t.copy(BIG.modneg(u[i],q)); |
| nn=t.nbits(); |
| if (nn<np) |
| { |
| u[i].copy(t); |
| g[i].conj(); |
| } |
| u[i].norm(); |
| } |
| r=FP48.pow16(g,u); |
| } |
| else |
| { |
| r=d.pow(e); |
| } |
| return r; |
| } |
| |
| |
| } |
| |
