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Title: Analysis of Gong et al.'s CCA2-secure homomorphic encryption
Authors: Lee, Hyung Tae
Ling, San
Wang, Huaxiong
Keywords: Additively Homomorphic Encryption
Adaptive Chosen Ciphertext Attack
Issue Date: 2016
Source: Lee, H. T., Ling, S., & Wang, H. (2016). Analysis of Gong et al.'s CCA2-secure homomorphic encryption. Theoretical Computer Science, 640, 104-114.
Series/Report no.: Theoretical Computer Science
Abstract: It is a well-known result that homomorphic encryption is not secure against adaptive chosen ciphertext attacks (CCA2) because of its malleable property. Very recently, however, Gong et al. proposed a construction asserted to be a CCA2-secure additively homomorphic encryption (AHE) scheme; in their construction, the adversary is not able to obtain a correct answer when querying the decryption oracle on a ciphertext obtained by modifying the challenge ciphertext (Theoretical Computer Science, 2016). Because their construction is very similar to Paillier's AHE, it appeared to support an additively homomorphic property, though they did not specify an evaluation algorithm for the scheme in their paper. In this paper, we present a simple CCA2 attack on their construction by re-randomizing the challenge ciphertext. Furthermore, we look into an additively homomorphic property of their construction. To do this, we first consider a typical candidate for an addition algorithm on ciphertexts, as provided for previous AHE constructions, and establish that it does not function correctly. Subsequently, we provide plausible evidence for the hardness of achieving an additively homomorphic property with their construction. According to our analysis, it seems hard to preserve an additively homomorphic property of their construction without any modification. In addition, as a minor contribution, we point out a flaw in the decryption algorithm of their construction and present a rectified algorithm for correct decryption.
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2016.06.014
Schools: School of Physical and Mathematical Sciences 
Rights: © 2016 Elsevier B.V. This is the author created version of a work that has been peer reviewed and accepted for publication by Theoretical Computer Science, Elsevier B.V. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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