When I read about BFV or BGV, they all look similar: they use polynomials from $\mathbb{Z}[X]/X^n+1$ as secret keys/pubic keys, etc.

What is the main difference?


1 Answer 1


The encryption/decryption functions are different, the message is encoded in the lower order bits for BGV and the higher order bits for BFV. This causes other aspects of the scheme to be a bit different like noise management and bootstrapping, but the idea remains the same.

Nevertheless, these two schemes are very similar and the ciphertext can be converted from one to the other (see Appendix A of https://eprint.iacr.org/2021/204.pdf).


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