APN permutations on \(\mathbb Z_n\) and Costas arrays

DOI10.1016/j.dam.2009.06.029zbMath1227.05014OpenAlexW1566384674MaRDI QIDQ967388

Gary McGuire, Konstantinos Drakakis, Roderick Gow

Publication date: 28 April 2010

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2009.06.029

zbMATH Keywords

almost perfect nonlinear permutationsAPN permutationsperfect nonlinear permutationsPN permutationsWelch-Costas permutations

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Shift register sequences and sequences over finite alphabets in information and communication theory (94A55) Combinatorial probability (60C05) Other designs, configurations (05B30)

Related Items (13)

Construction of highly nonlinear permutations on \(\mathbb{Z}_{2p}\) with differential uniformity at most 8 ⋮ A new class of differential 4-uniform permutations from exponential permutation ⋮ Circular Costas maps: a multidimensional analog of circular Costas sequences ⋮ Comparing balanced sequences obtained from ElGamal function to random balanced sequences ⋮ On full differential uniformity of permutations on the ring of integers modulo \(n\) ⋮ Finite field constructions of combinatorial arrays ⋮ An upper bound for the linearity of exponential Welch-Costas functions ⋮ Permutation polynomials and their differential properties over residue class rings ⋮ ON THE DISJOINTNESS OF ALGEBRAICALLY CONSTRUCTED COSTAS ARRAYS ⋮ On the measurement of the (non)linearity of Costas permutations ⋮ Perfect nonlinear functions and cryptography ⋮ Differential \(\delta \)-uniformity and non-linearity of permutations over \(\mathbb{Z}_n\) ⋮ Permutations of finite fields with prescribed properties

Uses Software

• SAFER

Cites Work

• Polynomial functions (mod m)
• Nonlinear functions in abelian groups and relative difference sets.
• A review of Costas arrays
• SAFER K-64: A byte-oriented block-ciphering algorithm
• On Almost Perfect Nonlinear Permutations
• Permutation polynomials modulo \(2^w\)

This page was built for publication: APN permutations on \(\mathbb Z_n\) and Costas arrays