On Known APNs
Val\'erie Gillot ad Philippe Langevin
TL;DR
This paper introduces new invariants and a backtracking method to analyze APN functions, providing evidence that the set of 6-bit APN functions is limited to 14 CCZ-classes, supporting a longstanding conjecture.
Contribution
It presents novel invariants and a systematic approach to classify 6-bit APN functions, advancing understanding of their structure and limitations.
Findings
Supports the conjecture that only 14 CCZ-classes exist for 6-bit APN functions
Introduces an APN-extendibility criterion for classification
Develops a backtracking approach to identify numerical facts about APN functions
Abstract
We present new invariants, APN-extendibility criterion and a backtracking approach to identify several numerical facts supporting the conjecture that the set of 6-bit \APN functions is limited to 14 CCZ-classes.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · Rings, Modules, and Algebras · Cryptographic Implementations and Security