Bootstrapping for BGV and BFV Revisited

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...

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Vydané v:Journal of cryptology Ročník 36; číslo 2; s. 12
Hlavní autori: Geelen, Robin, Vercauteren, Frederik
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.04.2023
Springer Nature B.V
Predmet:
Circuits
Coding and Information Theory
Combinatorics
Communications Engineering
Computational Mathematics and Numerical Analysis
Computer algebra
Computer Science
Computing on Encrypted Data
Data encryption
Magma
Networks
Open source software
Polynomials
Probability Theory and Stochastic Processes
Research Article
Bootstrapping
Fully homomorphic encryption
Brakerski–Fan–Vercauteren
Recryption
Brakerski–Gentry–Vaikuntanathan
ISSN:0933-2790, 1432-1378
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Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0933-2790
1432-1378
DOI:10.1007/s00145-023-09454-6