Further Investigation on Cyclotomic Mapping Permutation Polynomials over Finite Fields

2025/10/09 by Mondal, Suman
Computer Science · #11T06 #12E20 #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2510.08760

openalex publication_date 2025/10/09 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

We explore the connection between cyclotomic mapping permutation polynomials and permutation polynomials of the form x^rf(x^(q-1)/(l)) over finite fields. We present a new necessary and a new sufficient condition to verify permutation behavior of such polynomials over finite field. As its application, for particular values of r, we point out some permutation trinomials of the form P(x)=2x^r+8+x^r+4+2x^r ∈ \mathbbF₁₃[x], and work on few classes of permutation binomials.

Related

• A note on permutation polynomials over finite fields
• Some results about permutation properties of a kind of binomials over finite fields
• Further results on some classes of permutation polynomials over finite fields
• New results on permutation polynomials over finite fields
• Further Results on Permutation Polynomials over Finite Fields