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<p>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.</p>

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A digital signature scheme based on general Chebyshev polynomial

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • Shouliang Li,
  • Rudong Min,
  • Jilong Zhang,
  • Jiale Han,
  • Yulin Shen,
  • Zhen Yang,
  • Yi Yang

摘要

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.