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A key leakage resistant linearly homomorphic signature scheme and its application

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Abstract

A linearly homomorphic signature (LHS) enables linear computation on signed data and has been investigated in many contexts, such as network coding to resist pollution attacks and computation on outsourced data. Traditional LHS security relies entirely on the secrecy of the signing keys. The exposure of signing keys necessitates updating all generated signatures. However, with the increasing use of relatively insecure mobile devices in network coding and data outsourcing systems, key exposure has become more prevalent. To mitigate the hazard of key exposure in the LHS setting, we integrate key update mechanisms into the LHS by presenting a forward-secure linearly homomorphic signature (FSLHS). Specifically, we formalize the definition and security notions for the FSLHS scheme and present a concrete implementation. We prove our scheme to be forward secure against adaptively chosen message attacks, assuming the hardness of the CDH problem. Compared to previous works, our performance analysis shows that all parameters of our scheme exhibit logarithmic complexity with respect to the total number of time periods.

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All data generated or analysed during this study are included in this article.

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Acknowledgements

The authors express their gratitude to the reviewers and editors for their invaluable assistance. This preprint has been submitted and is currently undergoing the prescreening process.

Funding

This research was supported by the Gansu Provincial Department of Education through the Innovation Fund Project for University Teachers (2023A-041) and by the Young Scholars Science Foundation of Lanzhou Jiaotong University (2022011), and by the Natural Science Foundation of Gansu Province(25JRRA156).

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Authors and Affiliations

  1. College of Electronics and Information Engineering, Lanzhou Jiaotong University, 730070, Lanzhou, PR China

    Bin Wu, Ning Shi, Yahong Li & Kaijun Wu

  2. College of Big Data and Internet, Shenzhen Technology University, 518118, Shenzhen, PR China

    Caifen Wang

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  1. Bin Wu
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Contributions

Conceptualization: Bin Wu, Ning Shi. Formal analysis: Bin Wu, Yahong Li. Methodology: Bin Wu, Yahong Li. Resources: Bin Wu, Caifen Wang, Kaijun Wu. Software: Bin Wu, Kaijun Wu. Writing-original draft: Bin Wu, Caifen Wang. Writing-review & editing: Bin Wu, Ning Shi, Yahong Li.

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Correspondence to Bin Wu.

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Wu, B., Shi, N., Li, Y. et al. A key leakage resistant linearly homomorphic signature scheme and its application. Peer-to-Peer Netw. Appl. 18, 101 (2025). https://doi.org/10.1007/s12083-025-01917-w

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