The second-order zero differential spectra of some APN and other maps over finite fields
Abstract
The Feistel Boomerang Connectivity Table and the related notion of -Boomerang uniformity (also known as the second-order zero differential uniformity) has been recently introduced by Boukerrou et al.~\cite{Bouk}. These tools shall provide a major impetus in the analysis of the security of the Feistel network-based ciphers. In the same paper, a characterization of almost perfect nonlinear functions (APN) over fields of even characteristic in terms of second-order zero differential uniformity was also given. Here, we find a sufficient condition for an odd or even function over fields of odd characteristic to be an APN function, in terms of second-order zero differential uniformity. Moreover, we compute the second-order zero differential spectra of several APN or other low differential uniform functions, and show that our considered functions also have low second-order zero differential uniformity, though it may vary widely, unlike the case for even characteristic when it is always zero.
Keywords
Cite
@article{arxiv.2310.13775,
title = {The second-order zero differential spectra of some APN and other maps over finite fields},
author = {Kirpa Garg and Sartaj Ul Hasan and Constanza Riera and Pantelimon Stanica},
journal= {arXiv preprint arXiv:2310.13775},
year = {2023}
}