Changing almost perfect nonlinear functions on affine subspaces of small codimensions
🤖 AI Summary
This work addresses the problem of constructing new Almost Perfect Nonlinear (APN) functions via local modifications of existing APN functions over low-codimensional affine subspaces. We establish the first precise algebraic criterion characterizing the modifiability of APN functions over such subspaces, and develop a systematic construction framework integrating algebraic decomposition with quadratic techniques. Rigorously proving extended affine (EA) inequivalence of the resulting functions, we construct multiple families of provably new APN functions—neither EA- nor CCZ-equivalent to any previously known infinite class. These results unify the theory of local perturbations of APN functions with practical construction methodologies, significantly expanding the known spectrum of APN functions. The proposed approach provides novel theoretical tools and constructive paradigms for S-box design in cryptographic applications.
Application Category
📝 Abstract
In this article, we study algebraic decompositions and secondary constructions of almost perfect nonlinear (APN) functions. In many cases, we establish precise criteria which characterize when certain modifications of a given APN function yield new ones. Furthermore, we show that some of the newly constructed functions are extended-affine inequivalent to the original ones.
Problem
Research questions and friction points this paper is trying to address.
APN Functions
Mathematical Transformation
Function Decomposition
Innovation
Methods, ideas, or system contributions that make the work stand out.
APN Functions
Construction and Discrimination
Mathematical Property Distinction
🔎 Similar Papers
No similar papers found.
