Paper 2015/821
A general framework for building noise-free homomorphic cryptosystems
Gérald Gavin
Abstract
We present a general framework for developing and analyzing homomorphic cryptosystems whose security relies on the difficulty of solving systems of nonlinear equations over Z/nZ, n being an RSA modulus. In this framework, many homomorphic cryptosystems can be conceptualized. Based on symmetry considerations, we propose a general assumption that ensures the security of these schemes. To highlight this, we present an additive homomorphic private-key cryptosystem and we prove its security. Finally, we propose two motivating perspectives of this work. We first propose an FHE based on the previous scheme by defining a simple multiplicative operator. Secondly, we propose ways to remove the factoring assumption in order to get pure multivariate schemes.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Homomorphic cryptosystemFHEMultivariate encryption schemeFactoring assumption
- Contact author(s)
- gavin @ univ-lyon1 fr
- History
- 2015-08-21: received
- Short URL
- https://ia.cr/2015/821
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2015/821,
author = {Gérald Gavin},
title = {A general framework for building noise-free homomorphic cryptosystems},
howpublished = {Cryptology {ePrint} Archive, Paper 2015/821},
year = {2015},
url = {https://eprint.iacr.org/2015/821}
}
