Generalized isotopic shift construction for APN functions
نویسندگان
چکیده
منابع مشابه
Construction methods for generalized bent functions
Generalized bent (gbent) functions is a class of functions f : Z 2 → Zq, where q ≥ 2 is a positive integer, that generalizes a concept of classical bent functions through their codomain extension. A lot of research has recently been devoted towards derivation of the necessary and sufficient conditions when f is represented as a collection of Boolean functions. Nevertheless, apart from the neces...
متن کاملNew construction of APN quaratic
The purpose of this paper is to detail the article of Carlet. Along the way I recall some interesting results in the theory of finite fields, I give (new) proofs of some known results, and then I generalize the construction of a family of APN function. The reference precedes each result, and in the absence of reference the proof is due to the author. Keywords: boolean, bent, APN
متن کاملA divisibility criterion for exceptional APN functions
We are interested in the functions from F2m to itself which are Almost Perfectly Nonlinear over infinitely many extensions of F2, namely, the exceptional APN functions. In particular, we study the case of the polynomial functions of degree 4e with e odd and we give a necessary condition on an associated multivariate polynomial for the function to be exceptional APN. We use this condition to con...
متن کاملEquivalences of quadratic APN functions
The following conjecture due to Y. Edel is affirmatively solved: two quadratic APN (almost perfect nonlinear) functions are CCZ-equivalent if and only if they are extended affine equivalent.
متن کاملCyclic Codes from APN and Planar Functions
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear functions and planar functions over finite fields are employed to construct a number of classes of cyclic codes. Lower bounds on the minimum weight of some class...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2020
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-020-00803-1