// Constructor: it is assumed that zms is already set with m>1
// If q == 0, then the current context is used
template <class type> Cmod<type>::
Cmod(const PAlgebra &zms, const zz &qq, const zz &rt)
{
assert(zms.getM()>1);
bool explicitModulus = true;
if (qq == 0) {
q = zp::modulus();
explicitModulus = false;
}
else
q = qq;
zMStar = &zms;
root = rt;
zz mm;
mm = zms.getM();
m_inv = InvMod(mm, q);
zz_pBak bak;
if (explicitModulus) {
bak.save(); // backup the current modulus
context = BuildContext(q, NextPowerOfTwo(zms.getM()) + 1);
context.restore(); // set NTL's current modulus to q
}
else
context.save();
if (IsZero(root)) { // Find a 2m-th root of unity modulo q, if not given
zp rtp;
long e = 2*zms.getM();
FindPrimitiveRoot(rtp,e); // NTL routine, relative to current modulus
if (IsZero(rtp)) // sanity check
Error("Cmod::compRoots(): no 2m'th roots of unity mod q");
root = rep(rtp);
}
rInv = InvMod(root,q); // set rInv = root^{-1} mod q
// Allocate memory (relative to current modulus that was defined above).
// These objects will be initialized when anyone calls FFT/iFFT.
zpx phimx_poly;
conv(phimx_poly, zms.getPhimX());
powers = new zpx();
Rb = new fftrep();
Ra = new fftrep();
ipowers = new zpx();
iRb = new fftrep();
phimx = new zpxModulus(phimx_poly);
scratch = new zpx();
}
// plaintextAutomorph: an auxilliary routine...maybe palce in NumbTh?
// Compute b(X) = a(X^k) mod Phi_m(X). Result is calclated in the output b
// "in place", so a should not alias b.
template <class RX, class RXModulus> static
void plaintextAutomorph(RX& b, const RX& a, long k, const PAlgebra& zMStar,
const RXModulus& PhimX)
{
long m = zMStar.getM();
assert(zMStar.inZmStar(k));
b.SetLength(m);
for (long j = 0; j < m; j++) b[j] = 0;
long d = deg(a);
// compute b(X) = a(X^k) mod (X^m-1)
mulmod_precon_t precon = PrepMulModPrecon(k, m);
for (long j = 0; j <= d; j++)
b[MulModPrecon(j, k, m, precon)] = a[j]; // b[j*k mod m] = a[j]
b.normalize();
rem(b, b, PhimX); // reduce modulo the m'th cyclotomic
}
static void
init_representatives(Vec<long>& representatives, long dim,
const Vec<long>& mvec, const PAlgebra& zMStar)
{
assert(dim >= 0 && dim < mvec.length());
// special case
if (dim >= LONG(zMStar.numOfGens())) {
representatives.SetLength(1);
representatives[0] = 1;
return;
}
long m = mvec[dim];
long D = zMStar.OrderOf(dim);
long g = InvMod(zMStar.ZmStarGen(dim) % m, m);
representatives.SetLength(D);
for (long i = 0; i < D; i++)
representatives[i] = PowerMod(g, i, m);
}
static void
init_representatives(Vec<long>& representatives, long dim,
const Vec<long>& mvec, const PAlgebra& zMStar)
{
//OLD: assert(dim >= 0 && dim < mvec.length());
helib::assertInRange(dim, 0l, mvec.length(), "Invalid argument: dim must be between 0 and mvec.length()");
// special case
if (dim >= LONG(zMStar.numOfGens())) {
representatives.SetLength(1);
representatives[0] = 1;
return;
}
long m = mvec[dim];
long D = zMStar.OrderOf(dim);
long g = InvMod(zMStar.ZmStarGen(dim) % m, m);
representatives.SetLength(D);
for (long i = 0; i < D; i++)
representatives[i] = PowerMod(g, i, m);
}
// Constructor: it is assumed that zms is already set with m>1
// If q == 0, then the current context is used
Cmodulus::Cmodulus(const PAlgebra &zms, long qq, long rt)
{
assert(zms.getM()>1);
bool explicitModulus = true;
if (qq == 0) {
q = zz_p::modulus();
explicitModulus = false;
}
else
q = qq;
zMStar = &zms;
root = rt;
long mm;
mm = zms.getM();
m_inv = InvMod(mm, q);
zz_pBak bak;
if (zms.getPow2()) {
// special case when m is a power of 2
assert( explicitModulus );
bak.save();
RandomState state; SetSeed(conv<ZZ>("84547180875373941534287406458029"));
// DIRT: this ensures the roots are deterministically generated
// inside the zz_pContext constructor
context = zz_pContext(INIT_USER_FFT, q);
state.restore();
context.restore();
powers.set_ptr(new zz_pX);
ipowers.set_ptr(new zz_pX);
long k = zms.getPow2();
long phim = 1L << (k-1);
assert(k <= zz_pInfo->MaxRoot);
// rootTables get initialized 0..zz_pInfo->Maxroot
#ifdef FHE_OPENCL
altFFTInfo = MakeSmart<AltFFTPrimeInfo>();
InitAltFFTPrimeInfo(*altFFTInfo, *zz_pInfo->p_info, k-1);
#endif
long w0 = zz_pInfo->p_info->RootTable[0][k];
long w1 = zz_pInfo->p_info->RootTable[1][k];
powers->rep.SetLength(phim);
powers_aux.SetLength(phim);
for (long i = 0, w = 1; i < phim; i++) {
powers->rep[i] = w;
powers_aux[i] = PrepMulModPrecon(w, q);
w = MulMod(w, w0, q);
}
ipowers->rep.SetLength(phim);
ipowers_aux.SetLength(phim);
for (long i = 0, w = 1; i < phim; i++) {
ipowers->rep[i] = w;
ipowers_aux[i] = PrepMulModPrecon(w, q);
w = MulMod(w, w1, q);
}
return;
}
if (explicitModulus) {
bak.save(); // backup the current modulus
context = BuildContext(q, NextPowerOfTwo(zms.getM()) + 1);
context.restore(); // set NTL's current modulus to q
}
else
context.save();
if (root==0) { // Find a 2m-th root of unity modulo q, if not given
zz_p rtp;
long e = 2*zms.getM();
FindPrimitiveRoot(rtp,e); // NTL routine, relative to current modulus
if (rtp==0) // sanity check
Error("Cmod::compRoots(): no 2m'th roots of unity mod q");
root = rep(rtp);
}
rInv = InvMod(root,q); // set rInv = root^{-1} mod q
// Allocate memory (relative to current modulus that was defined above).
// These objects will be initialized when anyone calls FFT/iFFT.
zz_pX phimx_poly;
conv(phimx_poly, zms.getPhimX());
powers.set_ptr(new zz_pX);
Rb.set_ptr(new fftRep);
ipowers.set_ptr(new zz_pX);
iRb.set_ptr(new fftRep);
phimx.set_ptr(new zz_pXModulus1(zms.getM(), phimx_poly));
BluesteinInit(mm, conv<zz_p>(root), *powers, powers_aux, *Rb);
BluesteinInit(mm, conv<zz_p>(rInv), *ipowers, ipowers_aux, *iRb);
}
// Helper function
CubeSignature::CubeSignature(const PAlgebra& alg): ndims(0)
{
Vec<long> _dims(INIT_SIZE, alg.numOfGens());
for (long i=0; i<(long)alg.numOfGens(); i++) _dims[i] = alg.OrderOf(i);
initSignature(_dims);
}
long coordinate(const PAlgebra& al, long i, long k)
// returns ith coord of index k
{
return al.dLog(al.ith_rep(k))[i];
}
