Asset Details
Do you wish to reserve the book?
On Second-Order Derivatives of Boolean Functions and Cubic APN Permutations in Even Dimension
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
On Second-Order Derivatives of Boolean Functions and Cubic APN Permutations in Even Dimension
Do you wish to request the book?
On Second-Order Derivatives of Boolean Functions and Cubic APN Permutations in Even Dimension
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
On Second-Order Derivatives of Boolean Functions and Cubic APN Permutations in Even Dimension
2024
Overview
The big APN problem is one of the most important challenges in the theory of Boolean functions, i.e. finding a new APN permutation in even dimension. Among this class of functions, those with the lowest possible degree are cubic. Yet, none has been found so far. In this paper, we introduce new parameters for Boolean functions and for vectorial Boolean functions, mostly derived from the behavior of their second-order derivatives. These parameters are invariant under extended affine equivalence, and they are particularly relevant for small-degree functions. They allow studying bent, semi-bent and APN functions of degrees two and three. In particular, they allow tackling the big APN problem for cubic permutations. Notably, we focus on the case of dimension 8, providing some computational results.
Publisher
Springer International Publishing,Springer Nature B.V
Subject
