Cryptology ePrint Archive: Report 2015/641

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

Jing Li, Licheng Wang

Abstract: A framework of noise-free symmetric fully homomorphic encryption (FHE) is proposed in this work. Di erent from the frameworks that are de ned 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 overde ned system of multivariate polynomial equations over the given non-commutative algebraic structure. On the basis of this framework, a verifi able FHE is proposed, where the receiver can check the validity of ciphertexts.

Category / Keywords: Non-commutative rings, Noise-free, Symmetric-FHE, Veri fiable FHE

Date: received 28 Jun 2015, last revised 12 Oct 2015

Contact author: wanglc2012 at 126 com; L19861986@126 com

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Version: 20151013:031710 (All versions of this report)

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