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A digital signature scheme based on general Chebyshev polynomial

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Abstract

Despite the operational efficiency and lower computational costs of public key cryptography based on the Chebyshev polynomial compared to elliptic curve cryptography (ECC), the digital signature schemes based on the Chebyshev polynomial have not been widely applied. The primary obstacle includes its short period characteristic and coefficient fixation issue, which makes cryptosystems vulnerable to exhaustive attacks. To enhance the resistance of cryptosystems to the exhaustive attack, the general Chebyshev polynomial (GCP) is developed in this paper. It still possesses the semigroup property that public key cryptosystems rely on and provides an optional parameter that improves its complexity and pluralism. A novel digital signature scheme with reduced design complexity and enhanced security based on GCP is proposed. Theoretical analyses and experimental results show that this digital signature scheme offers more advantages in terms of both security and efficiency than existing schemes.

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Acknowledgements

The authors gratefully acknowledge the anonymous reviewers for their constructive comments. This work is supported in part by Gansu Provincial Science and Technology Plan Project Foundation (No.22YF7GA006), the Fundamental Research Funds for the Central Universities of China (No. lzujbky-2022-pd12), Talent Project of Gansu Province, China, and the National Key Research and Development Program of China (No.2021ZD0111405). All authors have read and agreed to the published version of the manuscript.

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Authors and Affiliations

  1. School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Shouliang Li, Rudong Min, Jilong Zhang, Jiale Han, Zhen Yang & Yi Yang

  2. Gansu Computing Center, Lanzhou, 730000, People’s Republic of China

    Yulin Shen

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  1. Shouliang Li
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  2. Rudong Min
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Contributions

S.L. and R.M. wrote the main manuscript text. J.Z. prepared the software validation, and J.H. and Y.S. contributed to the formal analysis and investigation. Z.Y. supervised the methodology and project administration, while Y.Y. reviewed and edited the manuscript. All authors reviewed the manuscript.

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Correspondence to Rudong Min or Zhen Yang.

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Li, S., Min, R., Zhang, J. et al. A digital signature scheme based on general Chebyshev polynomial. J Supercomput 81, 595 (2025). https://doi.org/10.1007/s11227-025-07074-4

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