TL;DR
This paper revisits Carlet's work on APN functions, providing new proofs of known results, and generalizes the construction of a family of APN functions within finite field theory.
Contribution
It introduces a novel generalization of APN function construction and offers new proofs of existing results in finite field theory.
Findings
New proofs of classical finite field results
Generalized construction of APN functions
Enhanced understanding of APN function properties
Abstract
The purpose of this paper is to detail the article of Carlet. Along the way I recall some interesting results in the theory of finite fields, I give (new) proofs of some known results, and then I generalize the construction of a family of APN function. The reference precedes each result, and in the absence of reference the proof is due to the author. Keywords: boolean, bent, APN
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Taxonomy
TopicsCoding theory and cryptography · Cellular Automata and Applications · Quantum-Dot Cellular Automata