On Extension of Evaluation Algorithms in Keyed-Homomorphic Encryption

Hirotomo SHINOKI; Koji NUIDA

doi:10.1587/transfun.2023CIP0007

On Extension of Evaluation Algorithms in Keyed-Homomorphic Encryption

Hirotomo SHINOKI, Koji NUIDA

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Homomorphic encryption (HE) is public key encryption that enables computation over ciphertexts without decrypting them. To overcome an issue that HE cannot achieve IND-CCA2 security, the notion of keyed-homomorphic encryption (KH-PKE) was introduced (Emura et al., PKC 2013), which has a separate homomorphic evaluation key and can achieve stronger security named KH-CCA security. The contributions of this paper are twofold. First, recall that the syntax of KH-PKE assumes that homomorphic evaluation is performed for single operations, and 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. Moreover, based on the generalized version of Catalano-Fiore conversion, we also construct a similar conversion from d-level KH-PKE schemes into 2d-level KH-PKE schemes.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E107-A No.3 pp.218-233

Publication Date: 2024/03/01

Publicized: 2023/06/27

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2023CIP0007

Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)

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Authors

Hirotomo SHINOKI
Hitachi, Ltd.
Koji NUIDA
Kyushu University,National Institute of Advanced Industrial Science and Technology (AIST)

Keyword

keyed-homomorphic encryption, KH-CCA security, Catalano-Fiore conversion

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Hirotomo SHINOKI, Koji NUIDA, "On Extension of Evaluation Algorithms in Keyed-Homomorphic Encryption" in IEICE TRANSACTIONS on Fundamentals, vol. E107-A, no. 3, pp. 218-233, March 2024, doi: 10.1587/transfun.2023CIP0007.
Abstract: Homomorphic encryption (HE) is public key encryption that enables computation over ciphertexts without decrypting them. To overcome an issue that HE cannot achieve IND-CCA2 security, the notion of keyed-homomorphic encryption (KH-PKE) was introduced (Emura et al., PKC 2013), which has a separate homomorphic evaluation key and can achieve stronger security named KH-CCA security. The contributions of this paper are twofold. First, recall that the syntax of KH-PKE assumes that homomorphic evaluation is performed for single operations, and 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. Moreover, based on the generalized version of Catalano-Fiore conversion, we also construct a similar conversion from d-level KH-PKE schemes into 2d-level KH-PKE schemes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023CIP0007/_p

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@ARTICLE{e107-a_3_218,
author={Hirotomo SHINOKI, Koji NUIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On Extension of Evaluation Algorithms in Keyed-Homomorphic Encryption},
year={2024},
volume={E107-A},
number={3},
pages={218-233},
abstract={Homomorphic encryption (HE) is public key encryption that enables computation over ciphertexts without decrypting them. To overcome an issue that HE cannot achieve IND-CCA2 security, the notion of keyed-homomorphic encryption (KH-PKE) was introduced (Emura et al., PKC 2013), which has a separate homomorphic evaluation key and can achieve stronger security named KH-CCA security. The contributions of this paper are twofold. First, recall that the syntax of KH-PKE assumes that homomorphic evaluation is performed for single operations, and 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. Moreover, based on the generalized version of Catalano-Fiore conversion, we also construct a similar conversion from d-level KH-PKE schemes into 2d-level KH-PKE schemes.},
keywords={},
doi={10.1587/transfun.2023CIP0007},
ISSN={1745-1337},
month={March},}

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TY - JOUR
TI - On Extension of Evaluation Algorithms in Keyed-Homomorphic Encryption
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 218
EP - 233
AU - Hirotomo SHINOKI
AU - Koji NUIDA
PY - 2024
DO - 10.1587/transfun.2023CIP0007
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E107-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2024
AB - Homomorphic encryption (HE) is public key encryption that enables computation over ciphertexts without decrypting them. To overcome an issue that HE cannot achieve IND-CCA2 security, the notion of keyed-homomorphic encryption (KH-PKE) was introduced (Emura et al., PKC 2013), which has a separate homomorphic evaluation key and can achieve stronger security named KH-CCA security. The contributions of this paper are twofold. First, recall that the syntax of KH-PKE assumes that homomorphic evaluation is performed for single operations, and 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. Moreover, based on the generalized version of Catalano-Fiore conversion, we also construct a similar conversion from d-level KH-PKE schemes into 2d-level KH-PKE schemes.
ER -