On-the-fly Homomorphic Batching/Unbatching

We introduce a homomorphic batching technique that can be used to pack multiple ciphertext messages into one ciphertext for parallel processing. One is able to use the method to batch or unbatch messages homomorphically to further improve the flexibility of encrypted domain evaluations. In particular, we show various approaches to implement Number Theoretic Transform (NTT) homomorphically in Fast Fourier Transform (FFT) speed. Also, we present the limitations that we encounter in application of these methods. We implement homomorphic batching in various settings and present concrete performance figures. Finally, we present an implementation of a homomorphic NTT method in which we process each element in an independent ciphertext. The advantage of this method is we are able to batch independent homomorphic NTT evaluations and achieve better amortized time.