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AIMS Mathematics

2024, Volume 9, Issue 8: 20677-20691. doi: 10.3934/math.20241005
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A new semiring and its cryptographic applications

  • 1.
    School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
  • 2.
    School of Mathematics and Information Science, Guiyang University, Guiyang 550005, China
  • Received: 07 March 2024 Revised: 28 May 2024 Accepted: 13 June 2024 Published: 26 June 2024

  • MSC : 15A80, 94A60

  • This paper introduced a novel semiring structure involving nonnegative integers, where operations depended on the comparison of the magnitudes of decimal digit sums. Consequently, a corresponding matrix semiring can be established on this commutative semiring. We showed that the 3-satisfiability problem can be polynomial-time reduced to solving systems of quadratic polynomial equations over this semiring. We proposed a key exchange protocol based on this matrix semiring, with its security relying on the two-sided digital circulant matrix action problem over this semiring. This scheme provides a novel cryptographic primitive for post-quantum cryptography.

    Citation: Huawei Huang, Xin Jiang, Changwen Peng, Geyang Pan. A new semiring and its cryptographic applications[J]. AIMS Mathematics, 2024, 9(8): 20677-20691. doi: 10.3934/math.20241005

    Related Papers:

  • This paper introduced a novel semiring structure involving nonnegative integers, where operations depended on the comparison of the magnitudes of decimal digit sums. Consequently, a corresponding matrix semiring can be established on this commutative semiring. We showed that the 3-satisfiability problem can be polynomial-time reduced to solving systems of quadratic polynomial equations over this semiring. We proposed a key exchange protocol based on this matrix semiring, with its security relying on the two-sided digital circulant matrix action problem over this semiring. This scheme provides a novel cryptographic primitive for post-quantum cryptography.


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