An Equivalent Representation of Generalized Differentials

2025/07/09 by Suder, Valentin
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.07337

Abstract

We propose an equivalent formula for the higher-order derivatives used in the study of Generalized Almost Perfect Nonlinear functions over an arbitrary finite field of characteristic p. The result is obtained by counting the number of subsets of the prime field with a fixed cardinality for which the sum of their elements is constant. We then ask related questions regarding the diversity of higher-order derivatives.

Citations

• New generalized almost perfect nonlinear functions
• A Generalization of APN Functions for Odd Characteristic
• Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems

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