New Perfect Nonlinear Functions and Their Semifields
This work addresses the problem of constructing new perfect nonlinear functions for applications in cryptography and coding theory, representing an incremental advancement in the field.
The authors introduced two new classes of perfect nonlinear functions over finite fields with odd prime characteristics and demonstrated that the corresponding semifields are not isotopic to known ones, with the functions being CCZ-inequivalent to other classes in general.
In this paper, two new classes of perfect nonlinear functions over $\mathbb{F}_{p^{2m}}$ are proposed, where $p$ is an odd prime. Furthermore, we investigate the nucleus of the corresponding semifields of these functions and show that the semifields are not isotopic to all the known semifields. Particularly, the new perfect nonlinear functions are CCZ-inequivalent to other classes in general.