It looks like the runtimes are close for everything except for decryption and MultCC. Several remarks and suggestions/questions:
Decryption in OpenFHE also does flooding to provide some protection for scenarios where decryption results are (accidentally) shared (see Section 5.1 of Securing Approximate Homomorphic Encryption Using Differential Privacy for more details). This flooding involves somewhat expensive generating discrete Gaussians using a relatively large standard deviation. SEAL does not do any flooding. This is why the decryption is SEAL is faster. In other words, OpenFHE provides more security for CKKS by design.
For MultCC, it is not clear whether relinearization (more expensive than multiplication itself) is called. OpenFHE provides different options for relinearization/ley switching, such as BV and hybrid key switching + digit size/number of large digits. If relinearization is used, then the same mode in OpenFHE should be used for fairness of comparison. It is also not clear whether rescaling is called.
Typically the main bottleneck operations in homomorphic computations are key switching, e.g., rotation, and rescaling. They should be the primary benchmarks.
Was the timing done in the single-threaded mode for both libraries?
Settings for MultCC, both libraries are set with relinearization keys, and key switching was set as BV for OpenFHE CKKS in order to set the same polynomial degree and mod sizes in both libraries.
When performing multiplying two ciphertexts, no relinearization was called:
– OpenFHE: EvalMult(ctxt1, ctxt2)
– TenSeal: ctxt1 * ctxt2
The time was measured in a single-threaded model for both libraries.
In OpenFHE, EvalMult(ctxt1, ctxt2) calls relinearization (a.k.a. Key Switching) internally. To evaluate multiplication without relinearization, you can use EvalMultNoRelin(ctxt1, ctxt2).
As @Caesar pointed out, EvalMult calls both EvalMultNoRelin and KeySwitch. The first one is many times faster for CKKS than the second one. So it is incorrect to compare multiplication w/o relinearization with just multiplication. In other words, the current MultCC benchmarking results are not correct, at least relinearization in the case of OpenFHE EvalMult is definitely called.
After using EvalMultNoRelin(ctxt1, ctxt2) to measure multiplication time, the average time is 1122 micro seconds, which is much quicker than using EvalMult(ctxt1, ctxt2).
It is hard to say whether you are doing an-apple-to-apple comparison. For example, are all moduli the same? Is \log Q the same for both cases? Are you using the binary serialization for OpenFHE (not JSON)? OpenFHE ciphertexts include some metadata (which should be relatively small) and then use binary encoding to encode vectors of random-like integers. In other words, the size should be close to the optimal size (for efficiently packing vectors of random-like numbers). I am also not familiar with the internal implementation of serialization in SEAL. So I cannot really comment for this part.
