Cryptology ePrint Archive: Report 2011/328

Cryptanalysis of the Smart-Vercauteren and Gentry-Haleviís Fully Homomorphic Encryption

Gu Chunsheng

Abstract: For the fully homomorphic encryption schemes in [SV10, GH11], this paper presents attacks to solve equivalent secret key and directly recover plaintext from ciphertext for lattice dimensions n=2048 by using lattice reduction algorithm. According to the average-case behavior of LLL in [NS06], their schemes are also not secure for n=8192.

Category / Keywords: Fully Homomorphic Encryption, Cryptanalysis, Principal Ideal Lattice, Lattice Reduction

Date: received 14 Jun 2011, last revised 8 Jan 2012

Contact author: guchunsheng at gmail com

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Version: 20120108:211650 (All versions of this report)

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