/* return -a mod m */ public static BIG ModNeg(BIG a1, BIG m) { BIG a = new BIG(a1); a.Mod(m); return(m.Minus(a)); }
/* return a^2 mod m */ public static BIG ModSqr(BIG a1, BIG m) { BIG a = new BIG(a1); a.Mod(m); DBIG d = Sqr(a); return(d.Mod(m)); }
/* Jacobi Symbol (this/p). Returns 0, 1 or -1 */ public virtual int Jacobi(BIG p) { int n8, k, m = 0; BIG t = new BIG(0); BIG x = new BIG(0); BIG n = new BIG(0); BIG zilch = new BIG(0); BIG one = new BIG(1); if (p.Parity() == 0 || Comp(this, zilch) == 0 || Comp(p, one) <= 0) { return(0); } Norm(); x.Copy(this); n.Copy(p); x.Mod(p); while (Comp(n, one) > 0) { if (Comp(x, zilch) == 0) { return(0); } n8 = n.LastBits(3); k = 0; while (x.Parity() == 0) { k++; x.Shr(1); } if (k % 2 == 1) { m += (n8 * n8 - 1) / 8; } m += (n8 - 1) * (x.LastBits(2) - 1) / 4; t.Copy(n); t.Mod(x); n.Copy(x); x.Copy(t); m %= 2; } if (m == 0) { return(1); } else { return(-1); } }
/* return a*b mod m */ public static BIG ModMul(BIG a1, BIG b1, BIG m) { BIG a = new BIG(a1); BIG b = new BIG(b1); a.Mod(m); b.Mod(m); DBIG d = Mul(a, b); return(d.Mod(m)); }
/* Map byte string to curve point */ public static ECP MapIt(sbyte[] h) { BIG q = new BIG(ROM.Modulus); BIG x = BIG.FromBytes(h); x.Mod(q); ECP P; while (true) { while (true) { if (CURVETYPE != MONTGOMERY) { P = new ECP(x, 0); } else { P = new ECP(x); } x.Inc(1); x.Norm(); if (!P.IsInfinity()) { break; } } P.Cfp(); if (!P.IsInfinity()) { break; } } return(P); }
/* P=u0.Q0+u1*Q1+u2*Q2+u3*Q3 */ /* * public static ECP2 mul4(ECP2[] Q,BIG[] u) * { * int i,j,nb; * int[] a=new int[4]; * ECP2 T=new ECP2(); * ECP2 C=new ECP2(); * ECP2 P=new ECP2(); * ECP2[] W=new ECP2[8]; * * BIG mt=new BIG(); * BIG[] t=new BIG[4]; * * byte[] w=new byte[BIG.NLEN*BIG.BASEBITS+1]; * * for (i=0;i<4;i++) * { * t[i]=new BIG(u[i]); * Q[i].affine(); * } * * // precompute table * * W[0]=new ECP2(); W[0].copy(Q[0]); W[0].sub(Q[1]); * * W[1]=new ECP2(); W[1].copy(W[0]); * W[2]=new ECP2(); W[2].copy(W[0]); * W[3]=new ECP2(); W[3].copy(W[0]); * W[4]=new ECP2(); W[4].copy(Q[0]); W[4].add(Q[1]); * W[5]=new ECP2(); W[5].copy(W[4]); * W[6]=new ECP2(); W[6].copy(W[4]); * W[7]=new ECP2(); W[7].copy(W[4]); * T.copy(Q[2]); T.sub(Q[3]); * W[1].sub(T); * W[2].add(T); * W[5].sub(T); * W[6].add(T); * T.copy(Q[2]); T.add(Q[3]); * W[0].sub(T); * W[3].add(T); * W[4].sub(T); * W[7].add(T); * * // if multiplier is even add 1 to multiplier, and add P to correction * mt.zero(); C.inf(); * for (i=0;i<4;i++) * { * if (t[i].parity()==0) * { * t[i].inc(1); t[i].norm(); * C.add(Q[i]); * } * mt.add(t[i]); mt.norm(); * } * * nb=1+mt.nbits(); * * // convert exponent to signed 1-bit window * for (j=0;j<nb;j++) * { * for (i=0;i<4;i++) * { * a[i]=(byte)(t[i].lastbits(2)-2); * t[i].dec(a[i]); t[i].norm(); * t[i].fshr(1); * } * w[j]=(byte)(8*a[0]+4*a[1]+2*a[2]+a[3]); * } * w[nb]=(byte)(8*t[0].lastbits(2)+4*t[1].lastbits(2)+2*t[2].lastbits(2)+t[3].lastbits(2)); * * P.copy(W[(w[nb]-1)/2]); * for (i=nb-1;i>=0;i--) * { * T.select(W,w[i]); * P.dbl(); * P.add(T); * } * P.sub(C); // apply correction * * P.affine(); * return P; * } */ /* needed for SOK */ public static ECP2 MapIt(sbyte[] h) { BIG q = new BIG(ROM.Modulus); BIG x = BIG.FromBytes(h); BIG one = new BIG(1); FP2 X; ECP2 Q; x.Mod(q); while (true) { X = new FP2(one, x); Q = new ECP2(X); if (!Q.IsInfinity()) { break; } x.Inc(1); x.Norm(); } BIG Fra = new BIG(ROM.Fra); BIG Frb = new BIG(ROM.Frb); X = new FP2(Fra, Frb); if (ECP.SEXTIC_TWIST == ECP.M_TYPE) { X.Inverse(); X.Norm(); } x = new BIG(ROM.CURVE_Bnx); /* Fast Hashing to G2 - Fuentes-Castaneda, Knapp and Rodriguez-Henriquez */ if (ECP.CURVE_PAIRING_TYPE == ECP.BN) { ECP2 T, K; T = new ECP2(); T.Copy(Q); T = T.Mul(x); if (ECP.SIGN_OF_X == 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); } /* Efficient hash maps to G2 on BLS curves - Budroni, Pintore */ /* Q -> x2Q -xQ -Q +F(xQ -Q) +F(F(2Q)) */ if (ECP.CURVE_PAIRING_TYPE == ECP.BLS) { // ECP2 xQ,x2Q; // xQ=new ECP2(); // x2Q=new ECP2(); ECP2 xQ = Q.Mul(x); ECP2 x2Q = xQ.Mul(x); if (ECP.SIGN_OF_X == 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); }