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A Lattice-Based Provably Secure Multisignature Scheme in Quantum Random Oracle Model

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Provable and Practical Security (ProvSec 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12505))

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Abstract

The multisignature schemes are attracted to utilize in some cryptographic applications such as the blockchain. Though the lattice-based constructions of multisignature schemes exist as quantum-secure multisignature, a multisignature scheme whose security is proven in the quantum random oracle model (QROM), rather than the classical random oracle model (CROM), is not known.

In this paper, we propose a first lattice-based multisignature scheme whose security is proven in QROM. The difficultly of proving the security in QROM than CROM is how to program the random oracle in the security proof. Although our proposed scheme is based on the Dilithium-QROM signature whose security is proven in QROM, their proof technique cannot be directly applied to the multisignature setting. To solve the problems in the security proof, we develop several proof techniques in QROM. First, we employ the searching query technique by Targi and Unruh to convert the Dilithium-QROM into the multisignature setting. For the second, we develop a new programming technique in QROM, since the conventional programming techniques seem not to work in the multisignature setting of QROM. We combine the programming technique by Unruh with the one by Liu and Zhandry. The new technique enables us to program the random oracle in QROM and to construct the signing oracle in the security proof.

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Notes

  1. 1.

    [7] pointed out that \(\textit{\textbf{w}}^{(i)}_1\) in the case where \({\mathcal {C}}\) restarts should be simulated strictly.We employ a method by  [2, 3] to deal with the case.

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Acknowledgements

We would like to thank anonymous reviewers for their valuable comments and suggestions. We are also grateful to Akira Takahashi for his fruitful comments on the security proof. This work was supported in part by JSPS KAKENHI Grant Numbers JP18K11288 and JP19K20272.

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Authors and Affiliations

  1. Faculty of Information Media, Hokkaido Information University, Nishi-Nopporo 59-2, Ebetsu, Hokkaido, 069-8585, Japan

    Masayuki Fukumitsu

  2. Graduate School of Information Sciences, Tohoku University, 41 Kawauchi, Aoba-ku, Sendai, Miyagi, 980-8576, Japan

    Shingo Hasegawa

Authors
  1. Masayuki Fukumitsu
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  2. Shingo Hasegawa
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Correspondence to Masayuki Fukumitsu .

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Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Khoa Nguyen

  2. Chinese Academy of Sciences, Beijing, China

    Wenling Wu

  3. Nanyang Technological University, Singapore, Singapore

    Kwok Yan Lam

  4. Nanyang Technological University, Singapore, Singapore

    Huaxiong Wang

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Fukumitsu, M., Hasegawa, S. (2020). A Lattice-Based Provably Secure Multisignature Scheme in Quantum Random Oracle Model. In: Nguyen, K., Wu, W., Lam, K.Y., Wang, H. (eds) Provable and Practical Security. ProvSec 2020. Lecture Notes in Computer Science(), vol 12505. Springer, Cham. https://doi.org/10.1007/978-3-030-62576-4_3

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  • DOI: https://doi.org/10.1007/978-3-030-62576-4_3

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