// Takes as arguments a ciphertext-part p relative to s' and a key-switching
// matrix W = W[s'->s], uses W to switch p relative to (1,s), and adds the
// result to *this.
// It is assumed that the part p does not include any of the special primes,
// and that if *this is not an empty ciphertext then its primeSet is
// p.getIndexSet() \union context.specialPrimes
void Ctxt::keySwitchPart(const CtxtPart& p, const KeySwitch& W)
{
FHE_TIMER_START;
// no special primes in the input part
assert(context.specialPrimes.disjointFrom(p.getIndexSet()));
// For parts p that point to 1 or s, only scale and add
if (p.skHandle.isOne() || p.skHandle.isBase(W.toKeyID)) {
CtxtPart pp = p;
pp.addPrimesAndScale(context.specialPrimes);
addPart(pp, /*matchPrimeSet=*/true);
return;
}
// some sanity checks
assert(W.fromKey == p.skHandle); // the handles must match
// Compute the number of digits that we need and the esitmated
// added noise from switching this ciphertext part.
long nDigits;
NTL::xdouble addedNoise;
std::tie(nDigits,addedNoise)= keySwitchNoise(p, pubKey, W.ptxtSpace);
// Break the ciphertext part into digits, if needed, and scale up these
// digits using the special primes. This is the most expensive operation
// during homormophic evaluation, so it should be thoroughly optimized.
vector<DoubleCRT> polyDigits;
p.breakIntoDigits(polyDigits, nDigits);
// Finally we multiply the vector of digits by the key-switching matrix
keySwitchDigits(W, polyDigits);
noiseVar += addedNoise; // update the noise estimate
} // restore random state upon destruction of the RandomState, see NumbTh.h
// Compute the number of digits that we need and the esitmated
// added noise from switching this ciphertext part.
static std::pair<long, NTL::xdouble>
keySwitchNoise(const CtxtPart& p, const FHEPubKey& pubKey, long pSpace)
{
const FHEcontext& context = p.getContext();
long nDigits = 0;
xdouble addedNoise = to_xdouble(0.0);
double sizeLeft = context.logOfProduct(p.getIndexSet());
for (size_t i=0; i<context.digits.size() && sizeLeft>0.0; i++) {
nDigits++;
double digitSize = context.logOfProduct(context.digits[i]);
if (sizeLeft<digitSize) digitSize=sizeLeft;// need only part of this digit
// Added noise due to this digit is phi(m) *sigma^2 *pSpace^2 *|Di|^2/4,
// where |Di| is the magnitude of the digit
// WARNING: the following line is written just so to prevent overflow
addedNoise += to_xdouble(context.zMStar.getPhiM()) * pSpace*pSpace
* xexp(2*digitSize) * context.stdev*context.stdev / 4.0;
sizeLeft -= digitSize;
}
// Sanity-check: make sure that the added noise is not more than the special
// primes can handle: After dividing the added noise by the product of all
// the special primes, it should be smaller than the added noise term due
// to modulus switching, i.e., keyWeight * phi(m) * pSpace^2 / 12
long keyWeight = pubKey.getSKeyWeight(p.skHandle.getSecretKeyID());
double phim = context.zMStar.getPhiM();
double logModSwitchNoise = log((double)keyWeight)
+2*log((double)pSpace) +log(phim) -log(12.0);
double logKeySwitchNoise = log(addedNoise)
-2*context.logOfProduct(context.specialPrimes);
assert(logKeySwitchNoise < logModSwitchNoise);
return std::pair<long, NTL::xdouble>(nDigits,addedNoise);
}
// Takes as arguments a ciphertext-part p relative to s' and a key-switching
// matrix W = W[s'->s], uses W to switch p relative to (1,s), and adds the
// result to *this.
// It is assumed that the part p does not include any of the special primes,
// and that if *this is not an empty ciphertext then its primeSet is
// p.getIndexSet() \union context.specialPrimes
void Ctxt::keySwitchPart(const CtxtPart& p, const KeySwitch& W)
{
FHE_TIMER_START;
// no special primes in the input part
assert(context.specialPrimes.disjointFrom(p.getIndexSet()));
// For parts p that point to 1 or s, only scale and add
if (p.skHandle.isOne() || p.skHandle.isBase(W.toKeyID)) {
CtxtPart pp = p;
pp.addPrimesAndScale(context.specialPrimes);
addPart(pp, /*matchPrimeSet=*/true);
return;
}
// some sanity checks
assert(W.fromKey == p.skHandle); // the handles must match
// Compute the number of digits that we need and the esitmated added noise
// from switching this ciphertext part.
long pSpace = W.ptxtSpace;
long nDigits = 0;
xdouble addedNoise = to_xdouble(0.0);
double sizeLeft = context.logOfProduct(p.getIndexSet());
for (size_t i=0; i<context.digits.size() && sizeLeft>0.0; i++) {
nDigits++;
double digitSize = context.logOfProduct(context.digits[i]);
if (sizeLeft<digitSize) digitSize=sizeLeft; // need only part of this digit
// Added noise due to this digit is phi(m) * sigma^2 * pSpace^2 * |Di|^2/4,
// where |Di| is the magnitude of the digit
// WARNING: the following line is written just so to prevent overflow
addedNoise += to_xdouble(context.zMStar.getPhiM()) * pSpace*pSpace
* xexp(2*digitSize) * context.stdev*context.stdev / 4.0;
sizeLeft -= digitSize;
}
// Sanity-check: make sure that the added noise is not more than the special
// primes can handle: After dividing the added noise by the product of all
// the special primes, it should be smaller than the added noise term due
// to modulus switching, i.e., keyWeight * phi(m) * pSpace^2 / 12
long keyWeight = pubKey.getSKeyWeight(p.skHandle.getSecretKeyID());
double phim = context.zMStar.getPhiM();
double logModSwitchNoise = log((double)keyWeight)
+2*log((double)pSpace) +log(phim) -log(12.0);
double logKeySwitchNoise = log(addedNoise)
-2*context.logOfProduct(context.specialPrimes);
assert(logKeySwitchNoise < logModSwitchNoise);
// Break the ciphertext part into digits, if needed, and scale up these
// digits using the special primes. This is the most expensive operation
// during homormophic evaluation, so it should be thoroughly optimized.
vector<DoubleCRT> polyDigits;
p.breakIntoDigits(polyDigits, nDigits);
// Finally we multiply the vector of digits by the key-switching matrix
// An object to hold the pseudorandom ai's, note that it must be defined
// with the maximum number of levels, else the PRG will go out of synch.
// FIXME: This is a bug waiting to happen.
DoubleCRT ai(context);
// Set the first ai using the seed, subsequent ai's (if any) will
// use the evolving RNG state (NOTE: this is not thread-safe)
RandomState state;
SetSeed(W.prgSeed);
// Add the columns in, one by one
DoubleCRT tmp(context, IndexSet::emptySet());
for (unsigned long i=0; i<polyDigits.size(); i++) {
ai.randomize();
tmp = polyDigits[i];
// The operations below all use the IndexSet of tmp
// add part*a[i] with a handle pointing to base of W.toKeyID
tmp.Mul(ai, /*matchIndexSet=*/false);
addPart(tmp, SKHandle(1,1,W.toKeyID), /*matchPrimeSet=*/true);
// add part*b[i] with a handle pointing to one
polyDigits[i].Mul(W.b[i], /*matchIndexSet=*/false);
addPart(polyDigits[i], SKHandle(), /*matchPrimeSet=*/true);
}
noiseVar += addedNoise;
} // restore random state upon destruction of the RandomState, see NumbTh.h