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Threshold Structure-Preserving Signatures: Strong and Adaptive Security Under Standard Assumptions

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Public-Key Cryptography – PKC 2024 (PKC 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14601))

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Abstract

Structure-preserving signatures (SPS) have emerged as an important cryptographic building block, as their compatibility with the Groth-Sahai (GS) NIZK framework allows to construct protocols under standard assumptions with reasonable efficiency.

Over the last years there has been a significant interest in the design of threshold signature schemes. However, only very recently Crites et al. (ASIACRYPT 2023) have introduced threshold SPS (TSPS) along with a fully non-interactive construction. While this is an important step, their work comes with several limitations. With respect to the construction, they require the use of random oracles, interactive complexity assumptions and are restricted to so called indexed Diffie-Hellman message spaces. Latter limits the use of their construction as a drop-in replacement for SPS. When it comes to security, they only support static corruptions and do not allow partial signature queries for the forgery.

In this paper, we ask whether it is possible to construct TSPS without such restrictions. We start from an SPS from Kiltz, Pan and Wee (CRYPTO 2015) which has an interesting structure, but thresholdizing it requires some modifications. Interestingly, we can prove it secure in the strongest model (TS-UF-1) for fully non-interactive threshold signatures (Bellare et al., CRYPTO 2022) and even under fully adaptive corruptions. Surprisingly, we can show the latter under a standard assumption without requiring any idealized model. All known constructions of efficient threshold signatures in the discrete logarithm setting require interactive assumptions and idealized models.

Concretely, our scheme in type III bilinear groups under the SXDH assumption has signatures consisting of 7 group elements. Compared to the TSPS from Crites et al. (2 group elements), this comes at the cost of efficiency. However, our scheme is secure under standard assumptions, achieves strong and adaptive security guarantees and supports general message spaces, i.e., represents a drop-in replacement for many SPS applications. Given these features, the increase in the size of the signature seems acceptable even for practical applications.

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Notes

  1. 1.

    Here we follow the group notation by Escala et al. [38]. See Definition 2 for more details.

  2. 2.

    A signature is called strongly unforgeable when the adversary is not only incapable of producing a valid signature for a fresh message but also, it cannot generate a new signature for a challenge message \(M^*\), by observing a valid signature for the same message \(M^*\).

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Acknowledgements

Mahdi Sedaghat was supported in part by the Research Council KU Leuven C1 on Security and Privacy for Cyber-Physical Systems and the Internet of Things with contract number C16/15/058 and by CyberSecurity Research Flanders with reference number VR20192203. Daniel Slamanig was supported by the Austrian Science Fund (FWF) and netidee SCIENCE Profet (GA No. P31621-N38). His work was done while being affiliated with AIT Austrian Institute of Technology.

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  1. University of St. Gallen, St. Gallen, Switzerland

    Aikaterini Mitrokotsa & Jenit Tomy

  2. Indian Institute of Technology, Jammu, India

    Sayantan Mukherjee

  3. COSIC, KU Leuven, Leuven, Belgium

    Mahdi Sedaghat

  4. Research Institute CODE, Universität der Bundeswehr München, München, Germany

    Daniel Slamanig

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  1. Aikaterini Mitrokotsa
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  1. The University of Sydney, Sydney, NSW, Australia

    Qiang Tang

  2. The Australian National University, Acton, ACT, Australia

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Mitrokotsa, A., Mukherjee, S., Sedaghat, M., Slamanig, D., Tomy, J. (2024). Threshold Structure-Preserving Signatures: Strong and Adaptive Security Under Standard Assumptions. In: Tang, Q., Teague, V. (eds) Public-Key Cryptography – PKC 2024. PKC 2024. Lecture Notes in Computer Science, vol 14601. Springer, Cham. https://doi.org/10.1007/978-3-031-57718-5_6

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