Cryptology ePrint Archive: Report 2012/144

Somewhat Practical Fully Homomorphic Encryption

Junfeng Fan and Frederik Vercauteren

Abstract: In this paper we port Brakerski's fully homomorphic scheme based on the Learning With Errors (LWE) problem to the ring-LWE setting. We introduce two optimised versions of relinearisation that not only result in a smaller relinearisation key, but also faster computations. We provide a detailed, but simple analysis of the various homomorphic operations, such as multiplication, relinearisation and bootstrapping, and derive tight worst case bounds on the noise caused by these operations. The analysis of the bootstrapping step is greatly simplified by using a modulus switching trick. Finally, we derive concrete parameters for which the scheme provides a given level of security and becomes fully homomorphic.

Category / Keywords: public-key cryptography / Fully homomorphic encryption

Date: received 17 Mar 2012

Contact author: frederik vercauteren at gmail com

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Version: 20120322:031216 (All versions of this report)

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