void CanZass(vec_pair_GF2X_long& factors, const GF2X& f, long verbose)
{
if (IsZero(f))
Error("CanZass: bad args");
double t;
vec_pair_GF2X_long sfd;
vec_GF2X x;
if (verbose) { cerr << "square-free decomposition..."; t = GetTime(); }
SquareFreeDecomp(sfd, f);
if (verbose) cerr << (GetTime()-t) << "\n";
factors.SetLength(0);
long i, j;
for (i = 0; i < sfd.length(); i++) {
if (verbose) {
cerr << "factoring multiplicity " << sfd[i].b
<< ", deg = " << deg(sfd[i].a) << "\n";
}
SFCanZass(x, sfd[i].a, verbose);
for (j = 0; j < x.length(); j++)
append(factors, cons(x[j], sfd[i].b));
}
}
template<> void PAlgebraModTmpl<zz_pX,vec_zz_pX,zz_pXModulus>::decodePlaintext(
vector<zz_pX>& alphas, const zz_pX& ptxt, const zz_pX &G,
const vector<zz_pX>& maps) const
{
unsigned nSlots = zmStar.NSlots();
if (nSlots==0 || maps.size()!= nSlots ||deg(G)<1|| zmStar.OrdTwo()%deg(G)!=0){
alphas.resize(0); return;
}
// First decompose p into CRT componsnt
vector<zz_pX> CRTcomps(nSlots); // allocate space for CRT component
CRT_decompoe(CRTcomps, ptxt); // CRTcomps[i] = p mod facors[i]
// Next convert each entry in CRTcomps[] back to base-G representation
// (this is roughly the inverse of the embedInSlots operation)
// maps contains all the base-G ==> base-Fi maps
// SHAI: The code below is supposed to be Nigel's code, borrowed partly
// from the constructor Algebra::Algebra(...) and partly from the
// function AElement::to_type(2). I don't really unerstand that code,
// so hopefully nothing was lost in translation
alphas.resize(nSlots);
zz_pE::init(G); // the extension field R[X]/G(X)
for (unsigned i=0; i<nSlots; i++) {
// We need to lift Fi from R[Y] to (R[X]/G(X))[Y]
zz_pEX Qi; conv(Qi,(zz_pX&)factors[i]);
vec_zz_pEX FRts=SFCanZass(Qi); // factor Fi over Z_2[X]/G(X)
// need to choose the right factor, the one that gives us back X
int j;
for (j=0; j<FRts.length(); j++) {
// lift maps[i] to (R[X]/G(X))[Y] and reduce mod j'th factor of Fi
zz_pEX GRti = to_zz_pEX((zz_pX&)maps[i]);
GRti %= FRts[j];
if (IsX(rep(coeff(GRti,0)))) { // is GRti == X?
Qi = FRts[j]; // If so, we found the right factor
break;
} // If this does not happen then move to the next factor of Fi
}
zz_pEX te; conv(te,CRTcomps[i]); // lift i'th CRT componnet to mod G(X)
te %= Qi; // reduce CRTcomps[i](Y) mod Qi(Y), over (Z_2[X]/G(X))
// the free term (no Y component) should be our answer (as a poly(X))
alphas[i] = rep(coeff(te,0));
}
}
int main(int argc, char *argv[])
{
argmap_t argmap;
argmap["p"] = "5";
argmap["m"] = "101";
argmap["r"] = "1";
if (!parseArgs(argc, argv, argmap)) usage(argv[0]);
long p = atoi(argmap["p"]);
long m = atoi(argmap["m"]);
long r = atoi(argmap["r"]);
cout << "p=" << p << ", m=" << m << ", r=" << r << "\n";
ZZX phimx = Cyclotomic(m);
zz_p::init(p);
zz_pX phimx_modp = to_zz_pX(phimx);
vec_zz_pX factors = SFCanZass(phimx_modp);
vec_ZZX FFactors;
MultiLift(FFactors, factors, phimx, r);
zz_p::init(power_long(p, r));
vec_zz_pX Factors;
Factors.SetLength(FFactors.length());
for (long i = 0; i < Factors.length(); i++)
conv(Factors[i], FFactors[i]);
zz_pX G = Factors[0];
long d = deg(G);
cout << "d=" << d << "\n";
zz_pE::init(G);
// L selects the even coefficients
vec_zz_pE L;
L.SetLength(d);
for (long j = 0; j < d; j++) {
if (j % 2 == 0)
L[j] = to_zz_pE(zz_pX(j, 1));
}
vec_zz_pE C;
buildLinPolyCoeffs(C, L, p, r);
zz_pE alpha, beta;
random(alpha);
applyLinPoly(beta, C, alpha, p);
cout << alpha << "\n";
cout << beta << "\n";
}