/* this = -this mod Modulus */ public void Neg() { int sb; BIG m = new BIG(ROM.Modulus); sb = LogB2(XES - 1); m.FShl(sb); x.RSub(m); XES = (1 << sb); if (XES > FEXCESS) { Reduce(); } }
/* return this/c */ public virtual BIG Div(BIG c) { int d, k = 0; DBIG m = new DBIG(c); DBIG dr = new DBIG(0); BIG r = new BIG(0); BIG a = new BIG(0); BIG e = new BIG(1); Norm(); while (Comp(this, m) >= 0) { e.FShl(1); m.Shl(1); k++; } while (k > 0) { m.Shr(1); e.Shr(1); dr.Copy(this); dr.Sub(m); dr.Norm(); d = (int)(1 - ((dr.w[BIG.DNLEN - 1] >> (BIG.CHUNK - 1)) & 1)); CMove(dr, d); r.Copy(a); r.Add(e); r.Norm(); a.CMove(r, d); k--; } return(a); }
/* final exponentiation - keep separate for multi-pairings and to avoid thrashing stack */ public static FP12 FExp(FP12 m) { FP2 f = new FP2(new BIG(ROM.Fra), new BIG(ROM.Frb)); BIG x = new BIG(ROM.CURVE_Bnx); FP12 r = new FP12(m); /* Easy part of final exp */ FP12 lv = new FP12(r); lv.Inverse(); r.Conj(); r.mul(lv); lv.Copy(r); r.Frob(f); r.Frob(f); r.mul(lv); /* Hard part of final exp */ if (ECP.CURVE_PAIRING_TYPE == ECP.BN) { FP12 x0, x1, x2, x3, x4, x5; lv.Copy(r); lv.Frob(f); x0 = new FP12(lv); x0.Frob(f); lv.mul(r); x0.mul(lv); x0.Frob(f); x1 = new FP12(r); x1.Conj(); x4 = r.Pow(x); if (ECP.SIGN_OF_X == ECP.POSITIVEX) { x4.Conj(); } x3 = new FP12(x4); x3.Frob(f); x2 = x4.Pow(x); if (ECP.SIGN_OF_X == ECP.POSITIVEX) { x2.Conj(); } x5 = new FP12(x2); x5.Conj(); lv = x2.Pow(x); if (ECP.SIGN_OF_X == ECP.POSITIVEX) { lv.Conj(); } x2.Frob(f); r.Copy(x2); r.Conj(); x4.mul(r); x2.Frob(f); r.Copy(lv); r.Frob(f); lv.mul(r); lv.USqr(); lv.mul(x4); lv.mul(x5); r.Copy(x3); r.mul(x5); r.mul(lv); lv.mul(x2); r.USqr(); r.mul(lv); r.USqr(); lv.Copy(r); lv.mul(x1); r.mul(x0); lv.USqr(); r.mul(lv); r.Reduce(); } else { FP12 y0, y1, y2, y3; // Ghamman & Fouotsa Method y0 = new FP12(r); y0.USqr(); y1 = y0.Pow(x); if (ECP.SIGN_OF_X == ECP.NEGATIVEX) { y1.Conj(); } x.FShr(1); y2 = y1.Pow(x); if (ECP.SIGN_OF_X == ECP.NEGATIVEX) { y2.Conj(); } x.FShl(1); y3 = new FP12(r); y3.Conj(); y1.mul(y3); y1.Conj(); y1.mul(y2); y2 = y1.Pow(x); if (ECP.SIGN_OF_X == ECP.NEGATIVEX) { y2.Conj(); } y3 = y2.Pow(x); if (ECP.SIGN_OF_X == ECP.NEGATIVEX) { y3.Conj(); } y1.Conj(); y3.mul(y1); y1.Conj(); y1.Frob(f); y1.Frob(f); y1.Frob(f); y2.Frob(f); y2.Frob(f); y1.mul(y2); y2 = y3.Pow(x); if (ECP.SIGN_OF_X == ECP.NEGATIVEX) { y2.Conj(); } y2.mul(y0); y2.mul(r); y1.mul(y2); y2.Copy(y3); y2.Frob(f); y1.mul(y2); r.Copy(y1); r.Reduce(); } return(r); }