Paper 2022/1386
A multivariate noise-free HE proposal
Abstract
Recently, new ideas to build homomorphic noise-free encryption schemes have been proposed. The starting point of these schemes deals with private-key encryption schemes whose secret key is a rational function. By construction, these schemes are not homomorphic. To get homomorphic properties, nonlinear homomorphic operators are derived from the secret key. In this paper, we adopt the same approach to build a HE. We obtain a multivariate encryption scheme in the sense that the knowledge of the CPA attacker can be turned into an over-defined system of nonlinear equations. The factoring assumption is introduced in order to make a large class of attacks based on Groebner basis irrelevant. While we did not propose a formal security proof relying on a classical cryptographic assumption, we hopefully provide convincing evidence for security.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- homomorphic encryption multivariate cryptography factoring assumption
- Contact author(s)
-
gerald gavin @ univ-lyon1 fr
sandrine-tainturier @ orange fr - History
- 2022-10-14: approved
- 2022-10-13: received
- See all versions
- Short URL
- https://ia.cr/2022/1386
- License
-
CC0
BibTeX
@misc{cryptoeprint:2022/1386,
author = {Gerald Gavin and Sandrine Tainturier},
title = {A multivariate noise-free {HE} proposal},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1386},
year = {2022},
url = {https://eprint.iacr.org/2022/1386}
}
