Cryptology ePrint Archive: Report 2016/430

Partially homomorphic encryption schemes over finite fields

Jian Liu and 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.

Category / Keywords: Homomorphic encryption; $q$-ary functions; perfect secrecy; finite fields, symmetric cryptography.

Date: received 1 May 2016, last revised 7 May 2016

Contact author: smesnager at univ-paris8 fr

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Note: Some details and improvements were added.

Version: 20160508:051644 (All versions of this report)

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