Faster homomorphic comparison operations for BGV and BFV

Ilia Iliashenko (1) , Vincent Zucca (2)

1 KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven
2 DALI - Digits, Architectures et Logiciels Informatiques

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.

Domaines: Cryptographie et sécurité [cs.CR]

Ilia Iliashenko, Vincent Zucca. Faster homomorphic comparison operations for BGV and BFV. Proceedings on Privacy Enhancing Technologies, 2021, 2021 (3), pp.246-264. ⟨10.2478/popets-2021-0046⟩. ⟨hal-03506798⟩