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Implicit Rejection in Fujisaki-Okamoto: Framework and a Novel Realization

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Information Security (ISC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13640))

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Abstract

The generic \(\textsf{IND}\)-\(\textsf{CCA}\) secure key encapsulation mechanism (KEM) constructions in the quantum random oracle model (QROM) attract much attention due to the NIST post-quantum competition. Most of the NIST KEM submissions follow the generic Fujisaki-Okamoto transformation with implicit rejection (FO-IR). We propose a framework for the construction of quantum random oracles that supports implicit rejection, and prove that the KEMs satisfying our framework are \(\textsf{IND}\)-\(\textsf{CCA}\) secure in the QROM. Specifically, we use the idea of hash combination to eliminate the requirement for checking the validity of ciphertexts, which is the key point to achieve \(\textsf{IND}\)-\(\textsf{CCA}\) security. We show that the existing FO-IR widely used in the NIST KEM submissions can be explained by our framework. Additionally, we also propose a novel realization which exploits the verifiability of the private key.

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Notes

  1. 1.

    There are some variants of \(\textsf{U}^{\not \bot }\) including \(\textsf{U}_{m}^{\not \bot }\), \(\textsf{U}^{\bot }\) and \(\textsf{U}_{m}^{\bot }\) [12], where \({\bot }\) means explicit rejection, and m (without m) means \(K:=\textsf{H}(m)\) (\(K:=\textsf{H}(m,c)\)).

  2. 2.

    Here, “\(\text {DS}\)” is a domain separator, and it should be a bit string of sufficient length, otherwise it is easy to be guessed by the adversary.

  3. 3.

    For any fixed key pair \(\left( pk,sk \right) \), we say that a ciphertext c is invalid if \(\mathsf {Dec'}\left( sk,c \right) = \bot \), and valid otherwise.

  4. 4.

    Since quantum adversaries may evaluate random oracles on quantum superposition states, the simulator can only \({\textbf {test}}\) whether \(A_{1}=sk\) and cannot extract sk, which means the simulator need to measure the quantum queries.

  5. 5.

    We will explain in Sect. 3.2 why we require the intermediate scheme to be \(\textsf{OW}\)-\(\textsf{qPCA}\) secure.

  6. 6.

    By the definitions of \(\mathsf {Dec'}\) and condition on \(c\leftarrow \mathsf {Enc'}\left( pk,m \right) \), if \(\mathsf {Dec'}\left( sk,c \right) \ne m\), then we must have \(\textsf{Dec}\left( sk,c \right) =m'\ne m\) or \(\textsf{Dec}\left( sk,c \right) =\bot \), i.e., \(\textsf{Dec}\left( sk,c \right) \ne m\).

  7. 7.

    In Lemma 1, since there is no assumption on the size of z, the additional oracles can simply be encoded as part of z [1, 3].

  8. 8.

    In addition, the simulator can also test whether \(A_{1}=sk\) by repeated random encryption and trial decryption.

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Acknowledgments

We thank the anonymous ISC2022 reviewers for their helpful comments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61972391).

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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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Editors and Affiliations

  1. University of Wollongong, Wollongong, NSW, Australia

    Willy Susilo

  2. Xidian University, Xian, China

    Xiaofeng Chen

  3. University of Wollongong, Wollongong, NSW, Australia

    Fuchun Guo

  4. University of Wollongong, Wollongong, NSW, Australia

    Yudi Zhang

  5. Petra Christian University, Surabaya, Indonesia

    Rolly Intan

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Chen, Z., Lu, X., Jia, D., Li, B. (2022). Implicit Rejection in Fujisaki-Okamoto: Framework and a Novel Realization. In: Susilo, W., Chen, X., Guo, F., Zhang, Y., Intan, R. (eds) Information Security. ISC 2022. Lecture Notes in Computer Science, vol 13640. Springer, Cham. https://doi.org/10.1007/978-3-031-22390-7_8

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