Work

Classification of quadratic APN functions with coefficients in $$\mathbb {F}_2$$ in dimension 10

Year: 2025

Type: article

Abstract: Yu et al. described an algorithm for conducting computational searches for quadratic APN functions over the finite field $$\mathbb {F}_{2^n}$$ , and used this algorithm to give a classification of all quadratic APN functions with coefficients in $$\mathbb {F}_{2}$$ for dimensions n up to 9. In this paper, we speed up the running time of that algorithm by a factor of approximately $$\frac{2^n}{n^2}$$ . Based on this result, we give a complete classification of all quadratic APN functions over $$\mathbb {F}_{2^{10}}$$ with coefficients in $$\mathbb {F}_{2}$$ . We also perform some partial computations for quadratic APN functions with coefficients in $$\mathbb {F}_{2}$$ over $$\mathbb {F}_{2^{11}}$$ , and conjecture that they form 6 CCZ-inequivalent classes which also correspond to known APN functions.

Source: Applicable Algebra in Engineering Communication and Computing

DOI: 10.1007/s00200-025-00711-8

Authors: Yuyin Yu, Jingchen Li, Nadiia Ichanska, Nikolay Kaleyski

Institutions: Guangzhou University, University of Bergen

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Universitetet i Bergen, Haukeland Universitetssjukehus, Basic and Applied Basic Research Foundation of Guangdong Province