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May 9, 2026MathematicsOpen Access

New Constructions of Complete Permutation Polynomials over Finite Fields of Even Characteristic

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Authors

JLJian LiZZZhengbang ZhaZTZiran Tu

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Overview

Randomized trial explores new constructions of complete permutation polynomials, highlighting cryptographic applications.

Key Points

  • This research aims to explore new constructions of complete permutation polynomials over finite fields of even characteristic.
  • Examined the polynomial xh(xq−1)q+1 over Fq2, with h(x) defined as h1(x+xq)+h2(x+xq)xk.
  • Utilized trace functions and Dickson polynomials for constructing complete permutations.
  • Proposed suitable forms of h1(x), h2(x), and k to achieve the complete permutation property.
  • Introduced new configurations of h1(x) and h2(x) that enhance the permutation property.
  • Demonstrated that specific choices of h1, h2, and k yield complete permutation polynomials.
  • Showed potential applications in cryptography, broadening the utility of these polynomials.

Cite This Study

Li et al. (2026) studied this question.

synapsesocial.com/papers/69fed17eb9154b0b82878ce8https://doi.org/10.3390/math14091571
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