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Explores new constructions of complete permutation polynomials, highlighting cryptographic applications.
Complete permutation polynomials have many applications in mathematics and cryptography. In this paper, we study the complete permutation property of polynomial xh(xq−1)q+1 over Fq2, where h(x)=h1(x+xq)+h2(x+xq)xk. Based on the trace functions and Dickson polynomials, we present several new constructions of such complete permutations by choosing suitable h1(x), h2(x), and k.
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Li et al. (2026) studied this question.
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