Problem
Research questions and friction points this paper is trying to address.
Second-order zero differential uniformity
Almost perfect nonlinear functions
Mathematical properties
The second-order zero differential spectra of some functions over finite fields
🤖 AI Summary
This work investigates higher-order differential security of cryptographic functions over finite fields, focusing on the second-order zero-differential spectrum—the quantitative measure of second-order zero-difference uniformity. Methodologically, it integrates finite-field algebra, Walsh transform theory, exponential sum estimation, and combinatorial counting techniques. Theoretical contributions include: (i) a rigorous characterization of fundamental differences in higher-order differential behavior between power functions (e.g., Gold and Kasami functions) and non-power functions; and (ii) complete determination of the second-order zero-differential spectra for several important S-box families, revealing significantly narrower value ranges compared to their first-order counterparts. These results provide a more precise analytical tool for evaluating resistance against higher-order differential cryptanalysis and extend the mathematical framework for nonlinear function security analysis.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Weakly Perfect Nonlinearity
Almost Perfect Nonlinearity
Second-Order Zero-Differential Uniformity
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