Bootstrapping for BGV and BFV Revisited

Robin Geelen; Frederik Vercauteren

Paper 2022/1363

Bootstrapping for BGV and BFV Revisited

Robin Geelen

, KU Leuven

Frederik Vercauteren

, KU Leuven

Abstract

We unify the state-of-the-art bootstrapping algorithms for BGV and BFV in a single framework, and show that both schemes can be bootstrapped with identical complexity. This result corrects a claim by Chen and Han (Eurocrypt 2018) that BFV is more efficient to bootstrap than BGV. We also fix an error in their optimized procedure for power-of-two cyclotomics, which occurs for some parameter sets. Our analysis is simpler, yet more general than earlier work, in that it simultaneously covers both BGV and BFV. Furthermore, we also design and implement a high-level open source software library for bootstrapping in the Magma Computer Algebra System. It is the first library to support both BGV and BFV bootstrapping in full generality, with all recent techniques (including the above fixes) and trade-offs.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: A minor revision of an IACR publication in JOC 2023
DOI: 10.1007/s00145-023-09454-6
Keywords: Fully homomorphic encryption Bootstrapping Brakerski-Gentry-Vaikuntanathan Brakerski-Fan-Vercauteren Recryption
Contact author(s): robin geelen @ esat kuleuven be
frederik vercauteren @ esat kuleuven be
History: 2023-11-18: last of 5 revisions; 2022-10-11: received; See all versions
Short URL: https://ia.cr/2022/1363
License: CC BY

BibTeX

@misc{cryptoeprint:2022/1363,
      author = {Robin Geelen and Frederik Vercauteren},
      title = {Bootstrapping for {BGV} and {BFV} Revisited},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/1363},
      year = {2022},
      doi = {10.1007/s00145-023-09454-6},
      url = {https://eprint.iacr.org/2022/1363}
}