reduce the number of DoubleCRT constants in unpack function

[fionser]

PR for this issue.

[fionser]

Unfortunately, the current code increases the number of frobeniusAutomorph (i.e., O(d^2)) times. (Perhaps with the Baby-step/Giant-step tech, we can reduce it to O(d \sqrt(d))) Even with hoisting, I found it slower than previous version.

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Following is slow due to O(d^2) frobeniusAutomorph;

    DoubleCRT coeff(unpackSlotEncoding.front(), ctxt.getContext(), ctxt.getPrimeSet());
    Ctxt tmp1(ZeroCtxtLike, ctxt);
    for (long i = 0; i < unpacked.size(); i++) {
        /// accumulative frobenius: frobenius(v, 2) = frobenius(frobenius(v, 1), 1)
        if (i > 0)
            coeff.automorph(t % m); 
        *(unpacked[i]) = ctxt;
        unpacked[i]->multByConstant(coeff);
        Ctxt origin(*unpacked[i]);
        /// TODO use hoisting here
        for (long j = 1; j < d; j++) {
            tmp1 = origin;
            tmp1.frobeniusAutomorph(j);
            tmp1.cleanUp();
            *(unpacked[i]) += tmp1;
        }
    }

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A quick fix is to exchange the outer-side and inner-side loop. This keeps the number of frobeniusAutomorph to O(d); at the cost of increasing the number of multByConstant from O(d) to O(d^2) (also, with BSGS, it should be O(d sqrt(d))

// make sure the unpacked ciphertext is empty
    for (long i = 0; i < unpacked.size(); i++)
        unpacked[i]->clear();

    DoubleCRT coeff(unpackSlotEncoding.front(), ctxt.getContext(), ctxt.getPrimeSet());
    Ctxt tmp1(ZeroCtxtLike, ctxt);
    Ctxt tmp2(ZeroCtxtLike, ctxt);
    /// TODO Use hoisting for the outer-loop
    for (long j = 0; j < d; j++) {
        tmp1 = ctxt;
        tmp1.frobeniusAutomorph(j);
        tmp1.cleanUp();
        for (long i = 0; i < unpacked.size(); i++) {
            tmp2 = tmp1;
            auto coeff_cpy{coeff};
            coeff_cpy.automorph(NTL::PowerMod(t, mcMod(i + j, d), m));
            tmp2.multByConstant(coeff_cpy);
            *unpacked[i] += tmp2;
        }
    }

[faberga]

Hi @fionser, would you have time to rebase your fork and check the conflicts or whether your suggestions still apply to the newer version of HElib, please?

Thank you