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Keyed-Fully Homomorphic Encryption Without Indistinguishability Obfuscation

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Applied Cryptography and Network Security (ACNS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13269))

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Abstract

(Fully) homomorphic encryption ((F)HE) allows users to publicly evaluate circuits on encrypted data. Although public homomorphic evaluation property has various applications, (F)HE cannot achieve security against chosen ciphertext attacks (CCA2) due to its nature. To achieve both the CCA2 security and homomorphic evaluation property, Emura et al. (PKC 2013) introduced keyed-homomorphic public key encryption (KH-PKE) and formalized its security denoted by \(\mathsf {KH}\text {-}\mathsf {CCA}\) security. KH-PKE has a homomorphic evaluation key that enables users to perform homomorphic operations. Intuitively, KH-PKE achieves the CCA2 security unless adversaries have a homomorphic evaluation key. Although Lai et al. (PKC 2016) proposed the first keyed-fully homomorphic encryption (keyed-FHE) scheme, its security relies on the indistinguishability obfuscation (\(\mathsf {iO}\)), and this scheme satisfies a weak variant of \(\mathsf {KH}\text {-}\mathsf {CCA}\) security. Here, we propose a generic construction of a \(\mathsf {KH}\text {-}\mathsf {CCA}\) secure keyed-FHE scheme from an FHE scheme secure against non-adaptive chosen ciphertext attack (CCA1) and a strong dual-system simulation-sound non-interactive zero-knowledge (strong DSS-NIZK) argument system by using the Naor-Yung paradigm. We show that there are a strong DSS-NIZK and an IND-CCA1 secure FHE scheme that are suitable for our generic construction. This shows that there exists a keyed-FHE scheme from simpler primitives than iO.

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Notes

  1. 1.

    Although Desmedt et al. [18] proposed a HE scheme with a designated evaluation called controlled HE, no CCA security was considered unlike the KH-PKE.

  2. 2.

    In this paper, keyed-FHE is a public key setting.

  3. 3.

    \((x,\beta )\) is correct for a language \(\mathcal {L}(R)\) (or \(\beta \) is correct for x) if \(x \in \mathcal {L}(R) \wedge \beta = 1\), or \(x \notin \mathcal {L}(R) \wedge \beta = 0\). \((x,\beta )\) is not correct for \(\mathcal {L}(R)\) (or \(\beta \) is not correct for x) otherwise.

  4. 4.

    Concretely, two FHE ciphertexts \(\mathsf {Enc}(\mathsf {pk}_1,\mathsf {m}_1)\) and \(\mathsf {Enc}(\mathsf {pk}_2,\mathsf {m}_2)\) can be transformed into a ciphertext \(\mathsf {Enc}(\mathsf {pk}_1,\mathsf {Enc}(\mathsf {pk}_2,\mathsf {m}_1 - \mathsf {m}_2))\). If for two FHE ciphertexts \(\mathsf {Enc}(\mathsf {pk}_1,\mathsf {m}_1;r_1)\) and \(\mathsf {Enc}(\mathsf {pk}_2,\mathsf {m}_2;r_2)\), \((\mathsf {m},r_1,r_2)\) where \(\mathsf {m}= \mathsf {m}_1 = \mathsf {m}_2\) is a witness of the Naor-Yung language, then \(\mathsf {Enc}(\mathsf {pk}_1,\mathsf {Enc}(\mathsf {pk}_2,\mathsf {m}_1 - \mathsf {m}_2))\) is a statement in \(L_H\).

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Acknowledgments

This work was supported by JST CREST Grant Numbers JPMJCR19F6 and JPMJCR2113, Japan, and JSPS KAKENHI Grant Number 19K20267. We would like to thank Prof. Thomas Peters since he gave us insightful suggestion to instantiate our keyed-FHE scheme in the standard model.

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Authors and Affiliations

  1. Yokohama National University, Yokohama, Japan

    Shingo Sato

  2. National Institute of Information and Communications Technology (NICT), Koganei, Japan

    Keita Emura

  3. The University of Tokyo, Bunkyo-ku, Japan

    Atsushi Takayasu

Authors
  1. Shingo Sato
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  2. Keita Emura
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  3. Atsushi Takayasu
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Correspondence to Shingo Sato .

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Editors and Affiliations

  1. Stevens Institute of Technology, Hoboken, NJ, USA

    Giuseppe Ateniese

  2. Sapienza University of Rome, Rome, Italy

    Daniele Venturi

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Sato, S., Emura, K., Takayasu, A. (2022). Keyed-Fully Homomorphic Encryption Without Indistinguishability Obfuscation. In: Ateniese, G., Venturi, D. (eds) Applied Cryptography and Network Security. ACNS 2022. Lecture Notes in Computer Science, vol 13269. Springer, Cham. https://doi.org/10.1007/978-3-031-09234-3_1

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  • DOI: https://doi.org/10.1007/978-3-031-09234-3_1

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