void PAlgebraLift(const ZZX& phimx, const vec_zz_pX& lfactors, vec_zz_pX& factors, vec_zz_pX& crtc, long r)
{
long p = zz_p::modulus();
long nSlots = lfactors.length();
vec_ZZX vzz; // need to go via ZZX
// lift the factors of Phi_m(X) from mod-2 to mod-2^r
if (lfactors.length() > 1)
MultiLift(vzz, lfactors, phimx, r); // defined in NTL::ZZXFactoring
else {
vzz.SetLength(1);
vzz[0] = phimx;
}
// Compute the zz_pContext object for mod p^r arithmetic
zz_p::init(power_long(p, r));
zz_pX phimxmod = to_zz_pX(phimx);
factors.SetLength(nSlots);
for (long i=0; i<nSlots; i++) // Convert from ZZX to zz_pX
conv(factors[i], vzz[i]);
// Finally compute the CRT coefficients for the factors
crtc.SetLength(nSlots);
for (long i=0; i<nSlots; i++) {
zz_pX& fct = factors[i];
zz_pX te = phimxmod / fct; // \prod_{j\ne i} Fj
te %= fct; // \prod_{j\ne i} Fj mod Fi
InvModpr(crtc[i], te, fct, p, r);// \prod_{j\ne i} Fj^{-1} mod Fi
}
}
void PAlgebraMod2r::init(unsigned r, unsigned m)
{
if (m == zmStar.M()) return; // nothign to do
if (r<2 || r>=NTL_SP_NBITS) return; // sanity check
((PAlgebraModTwo&)modTwo).init(m); // initialize zmStar and modTwo, if needed
if (zmStar.M()==0 || zmStar.NSlots()==0) return; // error in zmStar init
long nSlots = zmStar.NSlots();
// Take the factors and their CRT coefficients mod 2 and lift them to mod 2^r
zz_p::init(2);
// convert the factors of Phi_m(X) from GF2X to zz_pX objects with p=2
vec_zz_pX vzzp; // no direct conversion from GF2X to zz_pX,
vec_ZZX vzz; // need to go via ZZX
vzzp.SetLength(nSlots);
vzz.SetLength(nSlots);
for (long i=0; i<nSlots; i++) {
vzz[i] = to_ZZX(modTwo.factors[i]);
conv(vzzp[i], vzz[i]);
}
// lift the factors of Phi_m(X) from mod-2 to mod-2^r
MultiLift(vzz, vzzp, zmStar.PhimX(), r); // defined in NTL::ZZXFactoring
// Compute the zz_pContext object for mod-2^r arithmetic
rr = r;
unsigned two2r = 1UL << r; // compute 2^r
zz_p::init(two2r);
mod2rContext.save();
PhimXmod = to_zz_pX(zmStar.PhimX()); // Phi_m(X) mod 2^r
factors.SetLength(nSlots);
for (long i=0; i<nSlots; i++) // Convert from ZZX to zz_pX
conv(factors[i],vzz[i]);
/* Debugging sanity-check #1: we should have Ft= GCD(F1(X^t),Phi_m(X))
zz_pXModulus F1(factors[0]); // We choose factors[0] as F1
zz_pXModulus Pm2(PhimXmod);
for (long i=1; i<nSlots; i++) {
unsigned t = zmStar.ith_rep(i);
zz_pX X2t = PowerXMod(t,PhimXmod); // X2t = X^t mod Phi_m(X)
zz_pX Ft = GCD(CompMod(F1,X2t,Pm2),Pm2);
if (Ft != factors[i]) {
cout << "Ft != F1(X^t) mod Phi_m(X), t=" << t << endl;
exit(0);
}
}*******************************************************************/
// Finally compute the CRT coefficients for the factors
crtCoeffs.SetLength(nSlots);
for (long i=0; i<nSlots; i++) {
zz_pX& fct = factors[i];
zz_pX te = PhimXmod / fct; // \prod_{j\ne i} Fj
te %= fct; // \prod_{j\ne i} Fj mod Fi
InvMod(crtCoeffs[i], te, fct);// \prod_{j\ne i} Fj^{-1} mod Fi
}
}
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";
}
