Year: 2025
Type: article
Abstract: APN functions offer optimal resistance to differential attacks and are instrumental in the design of block ciphers in cryptography. While finding APN functions is very difficult in general, a promising way to construct APN functions is through symmetric matrices called Quadratic APN matrices (QAM). It is known that the search space for the QAM method can be reduced by means of orbit partitions induced by linear equivalences. This paper builds upon and improves these approaches in the case of homogeneous quadratic functions over $$\mathbb {F}_{2^n}$$ with coefficients in the subfield $$\mathbb {F}_{2^m}$$ . We propose an innovative approach for computing orbit partitions for cases where it is infeasible due to the large search space, resulting in the applications for the dimensions $$(n,m)=(8,4)$$ , and $$(n,m)=(9,3)$$ . We find and classify, up to CCZ-equivalence, all quadratic APN functions for the cases of $$(n,m)=(8,2)$$ , and $$(n,m)=(10,1)$$ . Also, we show that exhaustive searches for $$(n,m) = (10,2)$$ , and $$(n,m)=(8,4)$$ are infeasible for the QAM method using currently available means, following partial searches for these cases.
Source: Cryptography and Communications
Institutions: University of Bergen, Guangzhou University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4416725786