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Practical Post-Quantum Signature Schemes from Isomorphism Problems of Trilinear Forms

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Advances in Cryptology – EUROCRYPT 2022 (EUROCRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13277))

Abstract

In this paper, we propose a practical signature scheme based on the alternating trilinear form equivalence problem. Our scheme is inspired by the Goldreich-Micali-Wigderson’s zero-knowledge protocol for graph isomorphism, and can be served as an alternative candidate for the NIST’s post-quantum digital signatures.

First, we present theoretical evidences to support its security, especially in the post-quantum cryptography context. The evidences are drawn from several research lines, including hidden subgroup problems, multivariate cryptography, cryptography based on group actions, the quantum random oracle model, and recent advances on isomorphism problems for algebraic structures in algorithms and complexity.

Second, we demonstrate its potential for practical uses. Based on algorithm studies, we propose concrete parameter choices, and then implement a prototype. One concrete scheme achieves 128 bit security with public key size \(\approx 4100\) bytes, signature size \(\approx 6800\) bytes, and running times (key generation, sign, verify) \(\approx 0.8\) ms on a common laptop computer.

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Notes

  1. 1.

    In [4] this is called weak pseudorandom group actions.

  2. 2.

    In [46] an algorithm in such time was presented for CFI, but its algorithmic idea can be readily applied to ATFE.

  3. 3.

    Processor: 2.6 GHz 18-core Intel(R) Xeon(R) Gold 6132; Memory 87 GB.

  4. 4.

    We would like to thank Charles Bouillaguet for his help with understanding these methods here.

  5. 5.

    There is another algorithm in [16] with time complexity \(q^{n/2}\cdot {{\,\mathrm{\mathrm {poly}}\,}}(n, \log q)\), but it was designed for characteristic 2 fields, which we do not use for concrete instantiations in Sect. 6.1.

  6. 6.

    By Table 3, for \(n=10\) which will be used to instantiate our scheme in Sect. 6.1, we see that \(|R_{\phi , 6}|\approx q^7\), where \(7\approx 20/3\). On the other hand for odd n there is no such r.

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Acknowledgement

We thank the reviewers for their careful reading and several questions and suggestions. Y.Q. was partly supported by the Australian Research Council Discovery Projects DP200100950. D.H.D. and W.S. were partly supported by the Australian Research Council Linkage Projects LP190100984. A.J. was supported by the European Union’s H2020 Programme under grant agreement number ERC-669891.

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Authors and Affiliations

  1. Centre for Quantum Software and Information, School of Computer Science, Faculty of Engineering and Information Technology, University of Technology Sydney, Ultimo, NSW, Australia

    Gang Tang & Youming Qiao

  2. Institute of Cybersecurity and Cryptology, School of Computing and Information Technology, University of Wollongong, Northfields Avenue, Wollongong, NSW, 2522, Australia

    Dung Hoang Duong & Willy Susilo

  3. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Antoine Joux

  4. Emerging Technology Research Group, PayPal, San Jose, USA

    Thomas Plantard

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  1. Gang Tang
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  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

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Tang, G., Duong, D.H., Joux, A., Plantard, T., Qiao, Y., Susilo, W. (2022). Practical Post-Quantum Signature Schemes from Isomorphism Problems of Trilinear Forms. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13277. Springer, Cham. https://doi.org/10.1007/978-3-031-07082-2_21

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