Constructing New Piecewise Differentially 4-Uniform Permutations from Known APN Functions

DOI10.1142/S0129054115500331zbMath1333.94050OpenAlexW1810949923MaRDI QIDQ2949724

Xiwang Cao, Guangkui Xu

Publication date: 2 October 2015

Published in: International Journal of Foundations of Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129054115500331

zbMATH Keywords

finite fielddifferentially 4-uniform permutationAPN functionpiecewise polynomial

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60)

Cites Work

• Binary cyclic codes from explicit polynomials over \(\mathrm{GF}(2^m)\)
• Binomial differentially 4 uniform permutations with high nonlinearity
• A note on cyclic codes from APN functions
• A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree
• Codes, bent functions and permutations suitable for DES-like cryptosystems
• Almost perfect nonlinear power functions on \(\mathrm{GF}(2^n)\): the Niho case.
• Constructing differentially 4-uniform permutations over \(\mathrm{GF}(2^{2m})\) from quadratic APN permutations over \(\mathrm{GF}(2^{2m+1})\)
• Constructing new differentially 4-uniform permutations from the inverse function
• A class of permutation polynomials of \(\mathbb F_{2^m}\) related to Dickson polynomials
• Linear Codes From Perfect Nonlinear Mappings and Their Secret Sharing Schemes
• Almost perfect nonlinear power functions on GF(2/sup n/): the Welch case
• CONSTRUCTING NEW APN FUNCTIONS FROM KNOWN PN FUNCTIONS
• Constructing Differentially 4-Uniform Permutations Over <formula formulatype="inline"><tex Notation="TeX">${\BBF}_{2^{2k}}$</tex> </formula> via the Switching Method
• The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes

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