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// qc.cc: implementation of function for mapping quartic point to curve
//////////////////////////////////////////////////////////////////////////
//
// Copyright 1990-2012 John Cremona
//
// This file is part of the eclib package.
//
// eclib is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2 of the License, or (at your
// option) any later version.
//
// eclib is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
// for more details.
//
// You should have received a copy of the GNU General Public License
// along with eclib; if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
//
//////////////////////////////////////////////////////////////////////////
#include <eclib/marith.h>
#include <eclib/points.h> // from qcurve library
#include <eclib/mquartic.h>
#include <eclib/qc.h>
//#define DEBUG
void qc(quartic& g,
const bigint& x0, const bigint& y0, const bigint& z0,
Curvedata * E,
Curvedata* IJ_curve,
const bigint& tr_u, const bigint& tr_r,
const bigint& tr_s, const bigint& tr_t,
Point& P, int verbose)
{
bigint aa,bb,cc,dd,ee,p,q,r,t,xp,yp,zp;
bigint a=g.a, b=g.b, c=g.c, d=g.d, e=g.e;
#ifdef DEBUG
cout << "In qc(...) with:\n";
cout << "IJ_curve = "<<(Curve)(*IJ_curve)<<"\n";
cout << "min curve = "<<(Curve)(*E)<<"\n";
cout << "[u,r,s,t] = ["<<tr_u<<","<<tr_r<<","<<tr_s<<","<<tr_t<<"]\n";
cout << "(x0:y0:z0) = ("<<x0<<" : "<<y0<<" : "<<z0<<")\n";
cout << "Quartic = (a,b,c,d,e) = ("<<a<<", "<<b<<", "<<c<<", "<<d<<", "<<e<<")\n";
#endif
bigint z02=sqr(z0);
if(isqrt(a,q)) {z02=1;} // else z0=0 which sets zp=0 below
else if(isqrt(e,q)){t=a; a=e; e=t; t=b; b=d; d=t; }
else
{
const bigint& z03=z0*z02; const bigint& z04=sqr(z02);
const bigint& x02=sqr(x0); const bigint& x03=x0*x02;
q=y0;
e=z04*a;
dd=z03*(4*a*x0 + b*z0);
cc=z02*(6*a*x02 + 3*b*x0*z0 + c*z02);
bb=z0*(4*a*x03 + 3*b*x02*z0 + 2*c*x0*z02 + d*z03);
a=sqr(y0);
b=bb; c=cc; d=dd;
}
#ifdef DEBUG
if(verbose) cout<<"Quartic transformed = (a,b,c,d,e) = ("<<a<<", "<<b<<", "<<c<<", "<<d<<", "<<e<<")\nq = "<<q << "\n";
#endif
p = 3*b*b-8*a*c;
r = b*b*b+8*a*a*d-4*a*b*c;
xp = 3*p, yp = 27*r, zp = 2*q*z02; // The z0^2 factor since (I,J) have
// been scaled up
Point oldP(IJ_curve,xp*zp,yp,pow(zp,3));
int valid;
#ifdef DEBUG
valid = oldP.isvalid();
if(verbose||!valid) cout << "Point "<<oldP<<" on IJ_curve "
<<(Curve)(*IJ_curve);
if(!valid) cout <<" --NOT OK\n";
if(verbose) cout<<"\n";
#endif
P = transform(oldP, E, tr_u, tr_r, tr_s, tr_t);
valid = P.isvalid();
if(verbose||!valid) cout<<"Point = "<<P;
if(!valid) {cout << " -- warning: NOT on curve " << (Curve)(*E); abort();}
if(verbose) cout << "\n\theight = " << height(P)<< "\n";
}
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