long PAlgebra::addCoord(long i, long k, long offset) const
{
if (isDryRun()) return 0;
assert(k >= 0 && k < (long) nSlots);
assert(i >= 0 && i < (long) gens.size());
offset = offset % ((long) OrderOf(i));
if (offset < 0) offset += OrderOf(i);
long k_i = coordinate(i, k);
long k_i1 = (k_i + offset) % OrderOf(i);
long k1 = k + (k_i1 - k_i) * prods[i+1];
return k1;
}
void
Reorder(void)
{
intish i;
intish j;
int min;
struct entry* e;
int o1, o2;
for (i = 0; i < nidents-1; i++) {
min = i;
for (j = i+1; j < nidents; j++) {
o1 = OrderOf(identtable[ j ]->name);
o2 = OrderOf(identtable[ min ]->name);
if (o1 < o2 ) min = j;
}
e = identtable[ min ];
identtable[ min ] = identtable[ i ];
identtable[ i ] = e;
}
}
bool PAlgebra::nextExpVector(vector<unsigned long>& buffer) const
{
// increment the vector in lexicographic order
if (!isDryRun()) for (long i=gens.size()-1; i>=0; i--) {
if (i>=(long)buffer.size()) continue; // sanity check
// increment current index, set all the ones after it to zero
if (buffer[i] < OrderOf(i)-1) {
buffer[i]++;
for (unsigned long j=i+1; j<buffer.size(); j++) buffer[j] = 0;
return true; // succeeded in incrementing the vector
}
// if buffer[i] >= OrderOf(i)-1, mover to previous index i
}
return false; // cannot increment the vector anymore
}
void PAlgebra::printout() const
{
unsigned long i;
cout << "m = " << m << ", p = " << p << ", phi(m) = " << phiM << endl;
cout << " ord(p)=" << ordP << endl;
for (i=0; i<gens.size(); i++) if (gens[i]) {
cout << " generator " << gens[i] << " has order ("
<< (SameOrd(i)? "=":"!") << "= Z_m^*) of "
<< OrderOf(i) << endl;
}
if (qGrpOrd()<100) {
cout << " T = [";
for (i=0; i<T.size(); i++) cout << T[i] << " ";
cout << "]\n";
}
}
PAlgebra::PAlgebra(unsigned long mm, unsigned long pp,
const vector<long>& _gens, const vector<long>& _ords )
{
assert( ProbPrime(pp) );
assert( (mm % pp) != 0 );
assert( mm < NTL_SP_BOUND );
assert( mm > 1 );
cM = 1.0; // default value for the ring constant
m = mm;
p = pp;
long k = NextPowerOfTwo(m);
if (mm == (1UL << k))
pow2 = k;
else
pow2 = 0;
// For dry-run, use a tiny m value for the PAlgebra tables
if (isDryRun()) mm = (p==3)? 4 : 3;
// Compute the generators for (Z/mZ)^* (defined in NumbTh.cpp)
if (_gens.size() == 0 || isDryRun())
ordP = findGenerators(this->gens, this->ords, mm, pp);
else {
assert(_gens.size() == _ords.size());
gens = _gens;
ords = _ords;
ordP = multOrd(pp, mm);
}
nSlots = qGrpOrd();
phiM = ordP * nSlots;
// Allocate space for the various arrays
T.resize(nSlots);
dLogT.resize(nSlots*gens.size());
Tidx.assign(mm,-1); // allocate m slots, initialize them to -1
zmsIdx.assign(mm,-1); // allocate m slots, initialize them to -1
long i, idx;
for (i=idx=0; i<(long)mm; i++) if (GCD(i,mm)==1) zmsIdx[i] = idx++;
// Now fill the Tidx and dLogT translation tables. We identify an element
// t\in T with its representation t = \prod_{i=0}^n gi^{ei} mod m (where
// the gi's are the generators in gens[]) , represent t by the vector of
// exponents *in reverse order* (en,...,e1,e0), and order these vectors
// in lexicographic order.
// FIXME: is the comment above about reverse order true? It doesn't
// seem like it to me. VJS.
// buffer is initialized to all-zero, which represents 1=\prod_i gi^0
vector<unsigned long> buffer(gens.size()); // temporaty holds exponents
i = idx = 0;
long ctr = 0;
do {
ctr++;
unsigned long t = exponentiate(buffer);
for (unsigned long j=0; j<buffer.size(); j++) dLogT[idx++] = buffer[j];
assert(GCD(t,mm) == 1); // sanity check for user-supplied gens
assert(Tidx[t] == -1);
T[i] = t; // The i'th element in T it t
Tidx[t] = i++; // the index of t in T is i
// increment buffer by one (in lexigoraphic order)
} while (nextExpVector(buffer)); // until we cover all the group
assert(ctr == long(nSlots)); // sanity check for user-supplied gens
PhimX = Cyclotomic(mm); // compute and store Phi_m(X)
// initialize prods array
long ndims = gens.size();
prods.resize(ndims+1);
prods[ndims] = 1;
for (long j = ndims-1; j >= 0; j--) {
prods[j] = OrderOf(j) * prods[j+1];
}
// pp_factorize(mFactors,mm); // prime-power factorization from NumbTh.cpp
}
// Generate the representation of Z_m^* for a given odd integer m
// and plaintext base p
PAlgebra::PAlgebra(unsigned long mm, unsigned long pp)
{
m = mm;
p = pp;
assert( (m&1) == 1 );
assert( ProbPrime(p) );
// replaced by Mahdi after a conversation with Shai
// assert( m > p && (m % p) != 0 ); // original line
assert( (m % p) != 0 );
// end of replace by Mahdi
assert( m < NTL_SP_BOUND );
// Compute the generators for (Z/mZ)^*
vector<unsigned long> classes(m);
vector<long> orders(m);
unsigned long i;
for (i=0; i<m; i++) { // initially each element in its own class
if (GCD(i,m)!=1)
classes[i] = 0; // i is not in (Z/mZ)^*
else
classes[i] = i;
}
// Start building a representation of (Z/mZ)^*, first use the generator p
conjClasses(classes,p,m); // merge classes that have a factor of 2
// The order of p is the size of the equivalence class of 1
ordP = (unsigned long) count (classes.begin(), classes.end(), 1);
// Compute orders in (Z/mZ)^*/<p> while comparing to (Z/mZ)^*
long idx, largest;
while (true) {
compOrder(orders,classes,true,m);
idx = argmax(orders); // find the element with largest order
largest = orders[idx];
if (largest <= 0) break; // stop comparing to order in (Z/mZ)^*
// store generator with same order as in (Z/mZ)^*
gens.push_back(idx);
ords.push_back(largest);
conjClasses(classes,idx,m); // merge classes that have a factor of idx
}
// Compute orders in (Z/mZ)^*/<p> without comparing to (Z/mZ)^*
while (true) {
compOrder(orders,classes,false,m);
idx = argmax(orders); // find the element with largest order
largest = orders[idx];
if (largest <= 0) break; // we have the trivial group, we are done
// store generator with different order than (Z/mZ)^*
gens.push_back(idx);
ords.push_back(-largest); // store with negative sign
conjClasses(classes,idx,m); // merge classes that have a factor of idx
}
nSlots = qGrpOrd();
phiM = ordP * nSlots;
// Allocate space for the various arrays
T.resize(nSlots);
dLogT.resize(nSlots*gens.size());
Tidx.assign(m,-1); // allocate m slots, initialize them to -1
zmsIdx.assign(m,-1); // allocate m slots, initialize them to -1
for (i=idx=0; i<m; i++) if (GCD(i,m)==1) zmsIdx[i] = idx++;
// Now fill the Tidx and dLogT translation tables. We identify an element
// t\in T with its representation t = \prod_{i=0}^n gi^{ei} mod m (where
// the gi's are the generators in gens[]) , represent t by the vector of
// exponents *in reverse order* (en,...,e1,e0), and order these vectors
// in lexicographic order.
// buffer is initialized to all-zero, which represents 1=\prod_i gi^0
vector<unsigned long> buffer(gens.size()); // temporaty holds exponents
i = idx = 0;
do {
unsigned long t = exponentiate(buffer);
for (unsigned long j=0; j<buffer.size(); j++) dLogT[idx++] = buffer[j];
T[i] = t; // The i'th element in T it t
Tidx[t] = i++; // the index of t in T is i
// increment buffer by one (in lexigoraphic order)
} while (nextExpVector(buffer)); // until we cover all the group
PhimX = Cyclotomic(m); // compute and store Phi_m(X)
// initialize prods array
long ndims = gens.size();
prods.resize(ndims+1);
prods[ndims] = 1;
for (long j = ndims-1; j >= 0; j--) {
prods[j] = OrderOf(j) * prods[j+1];
}
}
