NTL::ZZX Vector<long>::encode(const EncryptedArray &ea) const { assert(this->size() <= ea.size()); NTL::ZZX encoded; if (this->size() < ea.size()) { auto tmp(*this); tmp.resize(ea.size()); ea.encode(encoded, tmp); } else { ea.encode(encoded, *this); } return encoded; }
// incrementalZeroTest sets each res[i], for i=0..n-1, to // a ciphertext in which each slot is 0 or 1 according // to whether or not bits 0..i of corresponding slot in ctxt // is zero (1 if not zero, 0 if zero). // It is assumed that res and each res[i] is already initialized // by the caller. // Complexity: O(d + n log d) smart automorphisms // O(n d) void incrementalZeroTest(Ctxt* res[], const EncryptedArray& ea, const Ctxt& ctxt, long n) { FHE_TIMER_START; long nslots = ea.size(); long d = ea.getDegree(); // compute linearized polynomial coefficients vector< vector<ZZX> > Coeff; Coeff.resize(n); for (long i = 0; i < n; i++) { // coeffients for mask on bits 0..i // L[j] = X^j for j = 0..i, L[j] = 0 for j = i+1..d-1 vector<ZZX> L; L.resize(d); for (long j = 0; j <= i; j++) SetCoeff(L[j], j); vector<ZZX> C; ea.buildLinPolyCoeffs(C, L); Coeff[i].resize(d); for (long j = 0; j < d; j++) { // Coeff[i][j] = to the encoding that has C[j] in all slots // FIXME: maybe encrtpted array should have this functionality // built in vector<ZZX> T; T.resize(nslots); for (long s = 0; s < nslots; s++) T[s] = C[j]; ea.encode(Coeff[i][j], T); } } vector<Ctxt> Conj(d, ctxt); // initialize Cong[j] to ctxt^{2^j} for (long j = 0; j < d; j++) { Conj[j].smartAutomorph(1L << j); } for (long i = 0; i < n; i++) { res[i]->clear(); for (long j = 0; j < d; j++) { Ctxt tmp = Conj[j]; tmp.multByConstant(Coeff[i][j]); *res[i] += tmp; } // *res[i] now has 0..i in each slot // next, we raise to the power 2^d-1 fastPower(*res[i], d); } FHE_TIMER_STOP; }
// Return in poly a polynomial with X^i encoded in all the slots static void x2iInSlots(ZZX& poly, long i, vector<ZZX>& xVec, const EncryptedArray& ea) { xVec.resize(ea.size()); ZZX x2i = ZZX(i,1); for (long j=0; j<(long)xVec.size(); j++) xVec[j] = x2i; ea.encode(poly, xVec); }
// selects range of slots [lo..hi) static void SelectRange(const EncryptedArray& ea, ZZX& mask, long lo, long hi) { long nSlots = ea.size(); assert(lo >= 0 && lo <= hi && hi <= nSlots); vector<long> maskArray; maskArray.resize(nSlots); for (long i = 0; i < nSlots; i++) maskArray[i] = 0; for (long i = lo; i < hi; i++) maskArray[i] = 1; ea.encode(mask, maskArray); }
// Apply the same linear transformation to all the slots. // C is the output of ea.buildLinPolyCoeffs void applyLinPoly1(const EncryptedArray& ea, Ctxt& ctxt, const vector<ZZX>& C) { assert(&ea.getContext() == &ctxt.getContext()); long d = ea.getDegree(); assert(d == lsize(C)); long nslots = ea.size(); vector<ZZX> encodedC(d); for (long j = 0; j < d; j++) { vector<ZZX> v(nslots); for (long i = 0; i < nslots; i++) v[i] = C[j]; ea.encode(encodedC[j], v); } applyLinPolyLL(ctxt, encodedC, ea.getDegree()); }
void benchmark(const EncryptedArray & ea, const FHEPubKey & pk, const FHESecKey & sk, const MDL::Matrix<long>& data) { const long BATCH_SIZE = 5000; MDL::Timer encTimer, evalTimer; MDL::EncVector mu(pk), sigma(pk); for (long part = 0; part *BATCH_SIZE < data.rows(); part++) { long from = std::min<long>(part * BATCH_SIZE, data.rows()); long to = std::min<long>(from + BATCH_SIZE, data.rows()); encTimer.start(); auto ctxts = encrypt(data, pk, ea, from, to); encTimer.end(); evalTimer.start(); auto sum = summation(ctxts); mu += sum.first; sigma += sum.second; evalTimer.end(); } evalTimer.start(); auto mu_mu = mu.covariance(ea, data.cols()); NTL::ZZX N; std::vector<long> n(ea.size(), data.rows()); ea.encode(N, n); sigma.multByConstant(N); for (size_t col = 0; col < data.cols(); col++) { ea.rotate(mu_mu[col], col * data.cols()); sigma -= mu_mu[col]; } evalTimer.end(); MDL::Vector<long> mat; sigma.unpack(mat, sk, ea, true); for (int i = 0; i < data.cols(); i++) { for (int j = 0; j < data.cols(); j++) { std::cout << mat[i * data.cols() + j] << " "; } std::cout << std::endl; } printf("Covariance of %zd data, enc %f, eval %f\n", data.rows(), encTimer.second(), evalTimer.second()); }
// Apply a permutation network to a ciphertext void PermNetwork::applyToCtxt(Ctxt& c, const EncryptedArray& ea) const { const PAlgebra& al = ea.getPAlgebra(); // Apply the layers, one at a time for (long i=0; i<layers.length(); i++) { const PermNetLayer& lyr = layers[i]; if (lyr.isID) continue; // this layer is the identity permutation // This layer is shifted via powers of g^e mod m long g2e = PowerMod(al.ZmStarGen(lyr.genIdx), lyr.e, al.getM()); Vec<long> unused = lyr.shifts; // copy to a new vector vector<long> mask(lyr.shifts.length()); // buffer to hold masks Ctxt sum(c.getPubKey(), c.getPtxtSpace()); // an empty ciphertext long shamt = 0; bool frst = true; while (true) { pair<long,bool> ret=makeMask(mask, unused, shamt); // compute mask if (ret.second) { // non-empty mask Ctxt tmp = c; ZZX maskPoly; ea.encode(maskPoly, mask); // encode mask as polynomial tmp.multByConstant(maskPoly); // multiply by mask if (shamt!=0) // rotate if the shift amount is nonzero tmp.smartAutomorph(PowerMod(g2e, shamt, al.getM())); if (frst) { sum = tmp; frst = false; } else sum += tmp; } if (ret.first >= 0) shamt = unused[ret.first]; // next shift amount to use else break; // unused is all-zero, done with this layer } c = sum; // update the cipehrtext c before the next layer } }
// selects range of slots [lo..hi) in dimension d static void SelectRangeDim(const EncryptedArray& ea, ZZX& mask, long lo, long hi, long d) { long nSlots = ea.size(); assert(d >= 0 && d < ea.dimension()); assert(lo >= 0 && lo <= hi && hi <= ea.sizeOfDimension(d)); vector<long> maskArray; maskArray.resize(nSlots); for (long i = 0; i < nSlots; i++) { long c = ea.coordinate(d, i); if (c >= lo && c < hi) maskArray[i] = 1; else maskArray[i] = 0; } ea.encode(mask, maskArray); }
// recursiveReplicateDim: // d = dimension // ea.sizeOfDimension(d)/2 <= extent <= ea.sizeOfDimension(d), // only positions [0..extent) are non-zero // 1 <= 2^k <= extent: size of current interval // 0 <= pos < ea.sizeOfDimension(d): relative position of first vector // 0 <= limit < ea.sizeOfDimension(): max # of positions to process // dimProd: product of dimensions 0..d // recBound: recursion bound (controls noise) // // SHAI: limit and extent are always the same, it seems static void recursiveReplicateDim(const EncryptedArray& ea, const Ctxt& ctxt, long d, long extent, long k, long pos, long limit, long dimProd, long recBound, RepAuxDim& repAux, ReplicateHandler *handler) { if (pos >= limit) return; if (replicateVerboseFlag) { // DEBUG code cerr << "check: " << k; CheckCtxt(ctxt, ""); } long dSize = ea.sizeOfDimension(d); long nSlots = ea.size(); if (k == 0) { // last level in this dimension: blocks of size 2^k=1 if ( extent >= dSize) { // nothing to do in this dimension replicateAllNextDim(ea, ctxt, d+1, dimProd, recBound, repAux, handler); return; } // SHAI: Will we ever have extent > dSize?? // need to replicate to fill positions [ (1L << n) .. dSize-1 ] if (repAux.tab(d,0).null()) { // generate mask if not there already ZZX mask; SelectRangeDim(ea, mask, 0, dSize - extent, d); repAux.tab(d, 0).set_ptr(new DoubleCRT(mask, ea.getContext())); } Ctxt ctxt_tmp = ctxt; ctxt_tmp.multByConstant(*repAux.tab(d, 0)); ea.rotate1D(ctxt_tmp, d, extent, /*don't-care-flag=*/true); ctxt_tmp += ctxt; replicateAllNextDim(ea, ctxt_tmp, d+1, dimProd, recBound, repAux, handler); return; } // If we need to stop early, call the handler if (handler->earlyStop(d, k, dimProd)) { handler->handle(ctxt); return; } k--; Ctxt ctxt_masked = ctxt; { // artificial scope to miminize storage in the recursion { // another artificial scope (SHAI: this seems redundant) // generate mask at index k+1, if not there yet if (repAux.tab(d, k+1).null()) { // need to generate vector< long > maskArray(nSlots,0); for (long i = 0; i < nSlots; i++) { long c = ea.coordinate(d, i); if (c < extent && bit(c, k) == 0) maskArray[i] = 1; } // store this mask in the repAux table ZZX mask; ea.encode(mask, maskArray); repAux.tab(d, k+1).set_ptr(new DoubleCRT(mask, ea.getContext())); } // Apply mask to zero out slots in ctxt ctxt_masked.multByConstant(*repAux.tab(d, k+1)); } Ctxt ctxt_left = ctxt_masked; ea.rotate1D(ctxt_left, d, 1L << k, /*don't-care-flag=*/true); ctxt_left += ctxt_masked; recursiveReplicateDim(ea, ctxt_left, d, extent, k, pos, limit, dimProd, recBound, repAux, handler); } pos += (1L << k); if (pos >= limit) return; Ctxt ctxt_right = ctxt; ctxt_right -= ctxt_masked; ctxt_masked = ctxt_right; // reuse ctxt_masked as a temp ea.rotate1D(ctxt_masked, d, -(1L << k), /*don't-care-flag=*/true); ctxt_right += ctxt_masked; recursiveReplicateDim(ea, ctxt_right, d, extent, k, pos, limit, dimProd, recBound, repAux, handler); }
static void recursiveReplicate(const EncryptedArray& ea, const Ctxt& ctxt, long n, long k, long pos, long limit, RepAux& repAux, ReplicateHandler *handler) { if (pos >= limit) return; if (replicateVerboseFlag) { // DEBUG code cerr << "check: " << k; CheckCtxt(ctxt, ""); } long nSlots = ea.size(); if (k == 0) { if ( (1L << n) >= nSlots) { handler->handle(ctxt); return; } // need to replicate to fill positions [ (1L << n) .. nSlots ) if (repAux.tab(0).null()) { // need to generate mask ZZX mask; SelectRange(ea, mask, 0, nSlots - (1L << n)); repAux.tab(0).set_ptr(new DoubleCRT(mask, ea.getContext())); } Ctxt ctxt_tmp = ctxt; ctxt_tmp.multByConstant(*repAux.tab(0)); ea.rotate(ctxt_tmp, 1L << n); ctxt_tmp += ctxt; handler->handle(ctxt_tmp); return; } k--; Ctxt ctxt_masked = ctxt; { // artificial scope to miminize storage in // the recursion { // another artificial scope // mask should be at index k+1 if (repAux.tab(k+1).null()) { // need to generate mask vector< long > maskArray; maskArray.resize(nSlots); for (long i = 0; i < (1L << n); i++) maskArray[i] = 1- bit(i, k); // the reverse of bit k of i for (long i = (1L << n); i < nSlots; i++) maskArray[i] = 0; ZZX mask; ea.encode(mask, maskArray); repAux.tab(k+1).set_ptr(new DoubleCRT(mask, ea.getContext())); } ctxt_masked.multByConstant(*repAux.tab(k+1)); } Ctxt ctxt_left = ctxt_masked; ea.rotate(ctxt_left, 1L << k); ctxt_left += ctxt_masked; recursiveReplicate(ea, ctxt_left, n, k, pos, limit, repAux, handler); } pos += (1L << k); if (pos >= limit) return; Ctxt ctxt_right = ctxt; ctxt_right -= ctxt_masked; ctxt_masked = ctxt_right; // reuse ctxt_masked as a temp ea.rotate(ctxt_masked, -(1L << k)); ctxt_right += ctxt_masked; recursiveReplicate(ea, ctxt_right, n, k, pos, limit, repAux, handler); }