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IND-CCA Security of Kyber in the Quantum Random Oracle Model, Revisited

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Information Security and Cryptology (Inscrypt 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13837))

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Abstract

In this paper, we answer the open question pointed out by Grubbs et al. (EUROCRYPT 2022) and Xagawa (EUROCRYPT 2022), i.e., the \(\textit{concrete}\) \(\textsf{IND}\)-\(\textsf{CCA}\) security proof of \(\textsf{Kyber}\). In order to add robustness, \(\textsf{Kyber}\) uses a slightly tweaked Fujisaki-Okamoto (FO) transformation. Specifically, it uses a “double-nested-hash” to generate the final key. This makes the proof techniques (Jiang et al., CRYPTO 2018) of proving standard FO transformation invalid. Hence, we develop a novel approach to overcome the difficulties, and prove that \(\textsf{Kyber}\) is \(\textsf{IND}\)-\(\textsf{CCA}\) secure in the quantum random oracle model (QROM) if the underlying encryption scheme is \(\textsf{IND}\)-\(\textsf{CPA}\) secure. Our result provides a solid quantum security guarantee for the post-quantum cryptography standard of NIST competition, \(\textsf{Kyber}\) algorithm.

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Notes

  1. 1.

    The standard FO-KEMs including \(\textsf{FO}^{\not \bot }\), \(\textsf{FO}_{m}^{\not \bot }\), \(\textsf{FO}^{\bot }\) and \(\textsf{FO}_{m}^{\bot }\) [11], where m (without m) means \(K:=\textsf{H}(m)\) (\(K:=\textsf{H}(m,c)\)).

  2. 2.

    \(\mathsf {H'} \circ g \circ \textsf{G}^{-1}_{1}(\cdot )\) is not even a function.

  3. 3.

    The set \(\mathcal {S}\) must satisfy public verifiability, i.e., given any input A, there is a polynomial time algorithm that can effectively check whether A belongs to \(\mathcal {S}\).

  4. 4.

    For any fixed \(\left( pk,sk \right) \), we say that a ciphertext c is valid if \(c=\textsf{Enc}\left( pk,m;\textsf{G}(m) \right) \), where \(m:=\textsf{Dec}\left( sk,c \right) \), and invalid otherwise.

  5. 5.

    In \(\textsf{FO}^{\not \bot }\), \(\mathcal {E}(m,c)\) directly outputs c.

  6. 6.

    We say that \(\mathcal {A}\) is a q-query oracle algorithm [2] if it performs at most q oracle queries.

  7. 7.

    In [10, 14, 15], the correctness bound is \({q}_{\textsf{G}}\sqrt{\delta }\), and ours is \({{q}_\textsf{G}}^2{\delta }\).

  8. 8.

    \(\textsf{Kyber}\) requires the underlying PKE scheme to be \(\textsf{IND}\)-\(\textsf{CPA}\) secure.

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Acknowledgments

We thank the anonymous Inscrypt 2022 reviewers for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61972391, 62272455).

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Zhao Chen, Xianhui Lu, Dingding Jia & Bao Li

  2. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

    Zhao Chen & Xianhui Lu

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  1. Zhao Chen
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Correspondence to Xianhui Lu .

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  1. Institute of Information Engineering, CAS, Beijing, China

    Yi Deng

  2. Columbia University, New York, NY, USA

    Moti Yung

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Chen, Z., Lu, X., Jia, D., Li, B. (2023). IND-CCA Security of Kyber in the Quantum Random Oracle Model, Revisited. In: Deng, Y., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2022. Lecture Notes in Computer Science, vol 13837. Springer, Cham. https://doi.org/10.1007/978-3-031-26553-2_8

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  • DOI: https://doi.org/10.1007/978-3-031-26553-2_8

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