Some more constructions of n-cycle permutation polynomials

2025/06/27 by Varsha Jarali, Jarali, Varsha, Prasanna Poojary +3
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Advanced Wireless Communication Techniques

paper · pdf · doi:10.48550/arxiv.2506.21936

Abstract

n-cycle permutation polynomials with small n have the advantage that their compositional inverses are efficient in terms of implementation. These permutation polynomials have significant applications in cryptography and coding theory. In this article, we propose criteria for the construction of n-cycle permutation using linearized polynomial L(x) for larger n . Furthermore, we investigate and generalize certain novel forms of n-cycle permutation polynomials. Finally, we demonstrate our approach by constructing explicit n-cycle permutation of the form L(x)+γh(Tr_q^m/q(x)) , and G(x)+γf(x) with a Boolean function f(x) . The polynomial x^d+γf(x) with f(x) being a Boolean function is shown to be quadruple and quintuple permutation polynomials. Moreover, linear binomial triple-cycle permutation polynomials are constructed.

Citations

• Constructions of involutions over finite fields
• Binary Cyclic Codes from Explicit Polynomials over \gf(2^m)
• Further Results on Permutation Polynomials over Finite Fields
• Linearized polynomials over finite fields revisited
• Specific permutation polynomials over finite fields
• A method for obtaining digital signatures and public-key cryptosystems

Related

• On the constructions of n-cycle permutations
• Linear Permutations and their Compositional Inverses over \mathbbF_qⁿ
• Construction of Permutation Polynomials of Certain Specific Cycle Structure over Finite Fields
• Some permutation polynomials via linear translators
• Constructions and necessities of some permutation polynomials