Investigations on <i>c</i>-(Almost) Perfect Nonlinear Functions
Sihem Mesnager, Constanza Riera, Pantelimon Stănică, Haode Yan, Zhengchun Zhou
Abstract
In a prior paper (Ellingsen <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2020), two of us, along with P. Ellingsen, P. Felke, and A. Tkachenko, defined a new (output) multiplicative differential and the corresponding <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c$ </tex-math></inline-formula> -differential uniformity, which has the potential of extending differential cryptanalysis. Here, we continue the work by looking at some APN functions through the mentioned concept and showing that their <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c$ </tex-math></inline-formula> -differential uniformity increases significantly in some cases.