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

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.