CRMar 27, 2017
On Some Properties of Quadratic APN Functions of a Special Form
arXiv:1703.09080v2
AI Analysis
This work addresses a theoretical problem in cryptography for researchers studying APN functions, but it appears incremental as it extends prior findings on specific function forms.
The paper tackles the problem of determining necessary and sufficient conditions for quadratic APN functions of the form L1(x^3) + L2(x^9) to be APN, building on prior work that identified such functions as a source for new infinite families.
In a recent paper, it is shown that functions of the form $L_1(x^3)+L_2(x^9)$, where $L_1$ and $L_2$ are linear, are a good source for construction of new infinite families of APN functions. In the present work we study necessary and sufficient conditions for such functions to be APN.