Partially homomorphic encryption schemes over finite fields

Jian Liu; Lusheng Chen; Sihem Mesnager

Paper 2016/430

Partially homomorphic encryption schemes over finite fields

Jian Liu, Lusheng Chen, and Sihem Mesnager

Abstract

Homomorphic encryption scheme enables computation in the encrypted domain, which is of great importance because of its wide and growing range of applications. The main issue with the known fully (or partially) homomorphic encryption schemes is the high computational complexity and large communication cost required for their execution. In this work, we study symmetric partially homomorphic encryption schemes over finite fields, establishing relationships between homomorphisms over finite fields with $q$ -ary functions. Our proposed partially homomorphic encryption schemes have perfect secrecy and resist cipher-only attacks to some extent.

Note: Some details and improvements were added.

Metadata

Available format(s): PDF
Publication info: Preprint. MINOR revision.
Keywords: Homomorphic encryption -ary functions perfect secrecy finite fields symmetric cryptography.
Contact author(s): smesnager @ univ-paris8 fr
History: 2016-05-08: revised; 2016-05-02: received; See all versions
Short URL: https://ia.cr/2016/430
License: CC BY

BibTeX

@misc{cryptoeprint:2016/430,
      author = {Jian Liu and Lusheng Chen and Sihem Mesnager},
      title = {Partially homomorphic encryption schemes over finite fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2016/430},
      year = {2016},
      url = {https://eprint.iacr.org/2016/430}
}