Constructions of complete permutation polynomials

DOI10.1007/s10623-018-0480-7zbMath1398.05012OpenAlexW2796162630WikidataQ130026444 ScholiaQ130026444MaRDI QIDQ1801102

Xiaofang Xu, Tor Helleseth, Chunlei Li, Xiangyong Zeng

Publication date: 26 October 2018

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-018-0480-7

zbMATH Keywords

permutation polynomialalgebraic degreecomplete permutation polynomial

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Polynomials over finite fields (11T06) Arithmetic theory of polynomial rings over finite fields (11T55)

Related Items

New classes of complete permutation polynomials ⋮ Further results on permutation polynomials and complete permutation polynomials over finite fields ⋮ Survey on recent trends towards generalized differential and boomerang uniformities ⋮ Full classification of permutation rational functions and complete rational functions of degree three over finite fields ⋮ Complete permutation polynomials with the form \((x^{p^m} - x + \delta)^s + a x^{p^m} + b x\) over \(\mathbb{F}_{p^n}\) ⋮ Exceptionality of \((X+1)^n + (X -1)^n\) ⋮ On a generalization of planar functions ⋮ On the \(c\)-differential uniformity of certain maps over finite fields ⋮ Several classes of complete permutation polynomials over finite fields of even characteristic

Uses Software

• MISTY

Cites Work

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• Some classes of monomial complete permutation polynomials over finite fields of characteristic two
• Constructing permutations and complete permutations over finite fields via subfield-valued polynomials
• Complete permutation polynomials over finite fields of odd characteristic
• On monomial complete permutation polynomials
• Permutation polynomials over finite fields from a powerful lemma
• Some classes of complete permutation polynomials over \(\mathbb F_q\)
• Block substitutions using orthomorphic mappings
• Permutation and complete permutation polynomials
• On constructing complete permutation polynomials over finite fields of even characteristic
• Several classes of complete permutation polynomials
• A note on complete polynomials over finite fields and their applications in cryptography
• Permutation polynomials over finite fields -- a survey of recent advances
• Handbook of Finite Fields
• Loiss: A Byte-Oriented Stream Cipher
• On Some Permutation Binomials of the Form $x^{\frac{2^n-1}{k}+1} +ax$ over $\mathbb{F}_{2^n}$ : Existence and Count
• On the need for multipermutations: Cryptanalysis of MD4 and SAFER
• New block encryption algorithm MISTY
• Shapeless quasigroups derived by Feistel orthomorphisms
• Investigations on Bent and Negabent Functions via the Nega-Hadamard Transform
• Complete Mapping Polynomials over Finite Field F 16
• The Construction of Orthogonal Latin Squares