Correction of a Secure Comparison Protocol for Encrypted Integers in IEEE WIFS 2012 (Short Paper)
In secure multi-party computation, one of the most useful and basic functionalities that have been realized over additive homomorphic encryption is secure comparison of two integers, where one party has encrypted integers to be compared while only the other party has the decryption key. In IEEE WIFS 2012, Veugen proposed an efficient protocol for this problem in the semi-honest model, which provides perfect security against the latter party. In this paper, we point out that the protocol by Veugen outputs an incorrect value in some cases, and then propose a way to fix the flaws with only slight overhead in efficiency. Our proposed correction is not straightforward, in the sense that it required an “outsourced” homomorphic multiplication protocol for two encrypted values, which was not needed in the original protocol.
The authors thank Goichiro Hanaoka, Kana Shimizu and more generally all the members of Advanced Cryptography Research Group, Information Technology Research Institute from AIST for their supervision, help and collaboration. They also thank Jean-Pierre Hubaux from the EPFL Laboratory for Communications and Applications for assuming the role of supervising teacher of the first author’s Master Thesis during which this paper was mainly produced. They also thank the anonymous reviewers for their comments. This work was supported by JST PRESTO Grant Number JPMJPR14E8, Japan.