void berlekamp(vec_pair_ZZ_pX_long& factors, const ZZ_pX& f, long verbose)
{
double t;
vec_pair_ZZ_pX_long sfd;
vec_ZZ_pX x;
if (!IsOne(LeadCoeff(f)))
Error("berlekamp: bad args");
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";
}
SFBerlekamp(x, sfd[i].a, verbose);
for (j = 0; j < x.length(); j++)
append(factors, cons(x[j], sfd[i].b));
}
}
// return an array such that alphas[i] \in R[X]/G(X) represent the
// same element as rt = (p mod Ft) \in R[X]/Ft(X) where t=T[i].
// If the optional map pointer is non-NULL, then (*map)[i] contains
// the output of mapToFt(...G,T[i]).
template<> void PAlgebraModTmpl<GF2X,vec_GF2X,GF2XModulus>::decodePlaintext(
vector<GF2X>& alphas, const GF2X& ptxt, const GF2X &G,
const vector<GF2X>& 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<GF2X> 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);
GF2E::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]
GF2EX Qi; conv(Qi,(GF2X&)factors[i]);
vec_GF2EX FRts=SFBerlekamp(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
GF2EX GRti = to_GF2EX((GF2X&)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
}
GF2EX 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));
}
}
