Faster homomorphic comparison operations for BGV and BFV

Abstract

Fully homomorphic encryption (FHE) allows to compute any function on encrypted values. However, in practice, there is no universal FHE scheme that is effi-cient in all possible use cases. In this work, we show that FHE schemes suitable for arithmetic circuits (e.g. BGV or BFV) have a similar performance as FHE schemes for non-arithmetic circuits (TFHE) in basic comparison tasks such as less-than, maximum and minimum operations. Our implementation of the less-than function in the HElib library is up to 3 times faster than the prior work based on BGV/BFV. It allows to compare a pair of 64-bit integers in 11 milliseconds, sort 64 32-bit integers in 19 seconds and find the minimum of 64 32-bit integers in 9.5 seconds on an average laptop without multi-threading.