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A Tightly Secure ID-Based Signature Scheme Under DL Assumption in AGM

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Information Security and Privacy (ACISP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13915))

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Abstract

Identity-based signatures (IBS) can be verified using the signer identity information as the public key, and hence, there is no need for certificate management that proves the corresponding public key ownership. Unfortunately, none of the existing IBS schemes has security proven as tight as the discrete logarithm (DL) problem, the hardest problem in the cyclic group setting, under the standard EUF-CMA security model. Recently, the introduction of proving security in the algebraic group model (AGM), where the adversary’s computation is algebraic, enables some ordinary signature schemes to be proven tightly reducible under DL assumption and EUF-CMA. To date, however, it remains unknown whether IBS schemes can also be proven as secure as the DL problem in the AGM. Achieving tight security in IBS schemes under standard EUF-CMA is challenging, due to the need to take extra precautions against adaptive queries on user private keys by the adversary. In this work, we show, for the first time, an IBS scheme with tight security under DL assumption and EUF-CMA in the AGM. The scheme features a minimal signature size of two group elements, with a reduction loss factor of two.

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Acknowledgement

We would like to thank the anonymous reviewers for their constructive comments. Fuchun Guo was supported by ARC Future Fellowship (FT220100046).

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Authors and Affiliations

  1. Institute of Cybersecurity and Cryptology, School of Computing and Information Technology, University of Wollongong, Wollongong, Australia

    Jia-Chng Loh, Fuchun Guo & Willy Susilo

  2. Singapore Management University, Singapore, Singapore

    Guomin Yang

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  1. Jia-Chng Loh
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Correspondence to Jia-Chng Loh .

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Editors and Affiliations

  1. Queensland University of Technology, Brisbane, QLD, Australia

    Leonie Simpson

  2. Queensland University of Technology, Brisbane, QLD, Australia

    Mir Ali Rezazadeh Baee

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Loh, JC., Guo, F., Susilo, W., Yang, G. (2023). A Tightly Secure ID-Based Signature Scheme Under DL Assumption in AGM. In: Simpson, L., Rezazadeh Baee, M.A. (eds) Information Security and Privacy. ACISP 2023. Lecture Notes in Computer Science, vol 13915. Springer, Cham. https://doi.org/10.1007/978-3-031-35486-1_10

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  • DOI: https://doi.org/10.1007/978-3-031-35486-1_10

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