AuthorsM. N. Hovd, H. Raddum and P. Fauzi
TitleOn the IND-CCA1 Security of FHE Schemes
AfilliationCryptography
Project(s)Cryptography Section
StatusPublished
Publication TypeJournal Article
Year of Publication2022
JournalMDPI Cryptography
Volume6
Issue1
Number13
Date Published03/2022
PublisherMDPI
Place PublishedOnline
ISSN2410-387X
KeywordsCryptanalysis, FHE schemes, IND-CCA1
Abstract

Fully homomorphic encryption (FHE) is a powerful tool in cryptography that allows one to perform arbitrary computations on encrypted material without having to decrypt it first. There are numerous FHE schemes, all of which are expanded from somewhat homomorphic encryption (SHE) schemes, and some of which are considered viable in practice. However, while these FHE schemes are semantically (IND-CPA) secure, the question of their IND-CCA1 security is much less studied, and we therefore provide an overview of the IND-CCA1 security of all acknowledged FHE schemes in this paper. To give this overview, we group SHE schemes into broad categories based on their similarities and underlying hardness problems. For each category, we show that the SHE schemes are susceptible to either known adaptive key recovery attacks, a natural extension of known attacks, or our proposed attacks. Finally, we discuss the known techniques to achieve IND-CCA1 secure FHE and SHE schemes. We conclude that none of the proposed schemes are IND-CCA1 secure, and that the known general constructions all have their shortcomings.

URLhttps://www.mdpi.com/2410-387X/6/1/13
DOI10.3390/cryptography6010013
Citation Key43114

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