On differential uniformity and nonlinearity of functions

DOI10.1016/j.disc.2007.12.025zbMath1159.94005OpenAlexW2013405595MaRDI QIDQ998534

Alexander Pott, Lilya Budaghyan

Publication date: 28 January 2009

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

Full work available at URL: https://doi.org/10.1016/j.disc.2007.12.025

zbMATH Keywords

NonlinearityAlmost bentAlmost perfect nonlinearDifferential uniformityVectorial Boolean function

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (7)

Construction of highly nonlinear permutations on \(\mathbb{Z}_{2p}\) with differential uniformity at most 8 ⋮ On full differential uniformity of permutations on the ring of integers modulo \(n\) ⋮ Association schemes arising from bent functions ⋮ Characterization of \(p\)-ary functions in terms of association schemes and its applications ⋮ On differential uniformity and nonlinearity of permutations on \(\mathbb{Z}_n\) ⋮ Unnamed Item ⋮ Linear codes and incidence structures of bent functions and their generalizations

Cites Work

• Two results on maximum nonlinear functions
• On binary cyclic codes with minimum distance \(d=3\).
• Codes, bent functions and permutations suitable for DES-like cryptosystems
• A survey of partial difference sets
• On \((p^ a,p^ b,p^ a,p^{a-b})\)-relative difference sets
• On three weights in cyclic codes with two zeros.
• Nonlinear functions in abelian groups and relative difference sets.
• Finite geometry and character theory
• Almost perfect nonlinear power functions on \(\mathrm{GF}(2^n)\): the Niho case.
• Affinity of permutations of \(\mathbb F_{2}^{n}\)
• Weight congruence for p-ary cyclic codes
• New classes of almost bent and almost perfect nonlinear polynomials
• The Geometry of Two-Weight Codes
• Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
• Almost perfect nonlinear power functions on GF(2/sup n/): the Welch case
• Some new three-valued crosscorrelation functions for binary m-sequences
• On Almost Perfect Nonlinear Permutations
• Weight Divisibility of Cyclic Codes, Highly Nonlinear Functions on F2m, and Crosscorrelation of Maximum-Length Sequences
• Covering radius of RM(1,9) in RM(3,9)
• The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes
• Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.)
• A proof of the Welch and Niho conjectures on cross-correlations of binary \(m\)-sequences
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