Antiderivative functions over F-2n

作者：Suder Valentin^*

来源：Designs, Codes and Cryptography, 2017, 82(1-2): 435-447.

DOI：10.1007/s10623-016-0186-7

• Derivative functions
• Higher order derivative functions
• Antidifferentiation over F-2n
• Antiderivative functions
• Linear structure
• Quadratic APN functions

In this paper, we use a linear algebra point of view to describe the derivatives and higher order derivatives over . On one hand, this new approach enables us to prove several properties of these functions, as well as the functions that have these derivatives. On the other hand, we provide a method to construct all of the higher order derivatives in given directions. We also demonstrate some properties of the higher order derivatives and their decomposition as a sum of functions with 0-linear structure. Moreover, we introduce a criterion and an algorithm to realize discrete antidifferentiation of vectorial Boolean functions. This leads us to define a new equivalence of functions, that we call differential equivalence, which links functions that share the same derivatives in directions given by some subspace. Finally, we discuss the importance of finding 2-to-1 functions.

• 出版日期2017-1