Noise-Free Symmetric Fully Homomorphic Encryption Based on Non-Commutative Rings

Jing Li; Licheng Wang

Paper 2015/641

Noise-Free Symmetric Fully Homomorphic Encryption Based on Non-Commutative Rings

Jing Li and Licheng Wang

Abstract

A framework of noise-free symmetric fully homomorphic encryption (FHE) is proposed in this work. Dierent from the frameworks that are dened over non-commutative groups, our framework is constructed from matrices over noncommutative rings. The scheme is one-way secure against chosen plaintext attacks (OW-CPA) based on the factorization problem of matrices over noncommutative rings as well as the hardness of an overdened system of multivariate polynomial equations over the given non-commutative algebraic structure. On the basis of this framework, a verifiable FHE is proposed, where the receiver can check the validity of ciphertexts.

Metadata

Available format(s): PDF
Publication info: Preprint. MINOR revision.
Keywords: Non-commutative rings Noise-free Symmetric-FHE Verifiable FHE
Contact author(s): wanglc2012 @ 126 com
L19861986 @ 126 com
History: 2015-10-13: revised; 2015-06-30: received; See all versions
Short URL: https://ia.cr/2015/641
License: CC BY

BibTeX

@misc{cryptoeprint:2015/641,
      author = {Jing Li and Licheng Wang},
      title = {Noise-Free Symmetric Fully Homomorphic Encryption Based on Non-Commutative Rings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/641},
      year = {2015},
      url = {https://eprint.iacr.org/2015/641}
}