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On Extension of Evaluation Algorithms in Keyed-Homomorphic Encryption

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Advances in Information and Computer Security (IWSEC 2022)

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Abstract

Homomorphic encryption (HE) is public key encryption that enables computation over ciphertexts without decrypting them, while it is known that HE cannot achieve IND-CCA2 security. To overcome this issue, the notion of keyed-homomorphic encryption (KH-PKE) was introduced, which has a separate homomorphic evaluation key and can achieve stronger security (Emura et al., PKC 2013).

The contributions of this paper are twofold. First, the syntax of KH-PKE assumes that homomorphic evaluation is performed for single operations, and its security notion called KH-CCA security was formulated based on this syntax. Consequently, if the homomorphic evaluation algorithm is enhanced in a way of gathering up sequential operations as a single evaluation, then it is not obvious whether or not KH-CCA security is preserved. In this paper, we show that KH-CCA security is in general not preserved under such modification, while KH-CCA security is preserved when the original scheme additionally satisfies circuit privacy.

Secondly, Catalano and Fiore (ACM CCS 2015) proposed a conversion method from linearly HE schemes into two-level HE schemes, the latter admitting addition and a single multiplication for ciphertexts. In this paper, we extend the conversion to the case of linearly KH-PKE schemes to obtain two-level KH-PKE schemes.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 19H01109, Japan, by JST CREST Grant Number JPMJCR2113, Japan, and by JST AIP Acceleration Research JPMJCR22U5, Japan.

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Authors and Affiliations

  1. Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan

    Hirotomo Shinoki

  2. Institute of Mathematics for Industry (IMI), Kyushu University, Fukuoka, Japan

    Koji Nuida

  3. National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Koji Nuida

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  1. Hirotomo Shinoki
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Correspondence to Koji Nuida .

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  1. BTQ AG, Vaduz, Liechtenstein

    Chen-Mou Cheng

  2. NTT, Tokyo, Japan

    Mitsuaki Akiyama

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Shinoki, H., Nuida, K. (2022). On Extension of Evaluation Algorithms in Keyed-Homomorphic Encryption. In: Cheng, CM., Akiyama, M. (eds) Advances in Information and Computer Security. IWSEC 2022. Lecture Notes in Computer Science, vol 13504. Springer, Cham. https://doi.org/10.1007/978-3-031-15255-9_10

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  • DOI: https://doi.org/10.1007/978-3-031-15255-9_10

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