[osaariki]

CPU is currently a rather natural baseline as the various GPU implementations are still somewhat preliminary. I'm not quite an expert on the implementation challenges around FHE (I work on compilers targeting FHE), but my understanding is that the access patterns of the core operation, the number theoretic transform (NTT, a DFT in a finite field), are not particularly GPU friendly. Dedicated hardware is expected to comparatively very well here.

[xsamgreen]

Definitely agreed that CPU is a natural baseline. But there are promising results for implementing NTT on GPUs. Here is something recent https://eprint.iacr.org/2021/124

Nothing will beat an ASIC for NTT though.