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Designs, Codes and Cryptography

, Volume 71, Issue 1, pp 57–81 | Cite as

Fully homomorphic SIMD operations

  • N. P. Smart
  • F. Vercauteren
Article

Abstract

At PKC 2010 Smart and Vercauteren presented a variant of Gentry’s fully homomorphic public key encryption scheme and mentioned that the scheme could support SIMD style operations. The slow key generation process of the Smart–Vercauteren system was then addressed in a paper by Gentry and Halevi, but their key generation method appears to exclude the SIMD style operation alluded to by Smart and Vercauteren. In this paper, we show how to select parameters to enable such SIMD operations. As such, we obtain a somewhat homomorphic scheme supporting both SIMD operations and operations on large finite fields of characteristic two. This somewhat homomorphic scheme can be made fully homomorphic in a naive way by recrypting all data elements separately. However, we show that the SIMD operations can be used to perform the recrypt procedure in parallel, resulting in a substantial speed-up. Finally, we demonstrate how such SIMD operations can be used to perform various tasks by studying two use cases: implementing AES homomorphically and encrypted database lookup.

Keywords

Fully homomorphic encryption Implementation SIMD operations 

Mathematics Subject Classification (2010)

94A60 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BristolBristolUK
  2. 2.COSIC, Department of Electrical EngineeringKatholieke Universiteit LeuvenHeverleeBelgium

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