Construction of bent functions of 2k variables from a basis of
نویسندگان
چکیده
Construction of bent functions of 2k variables from a basis of Joan-Josep Climent a , Francisco J. García b & Verónica Requena a a Departament d'Estadística i Investigació Operativa , Universitat d'Alacant , Campus de Sant Vicent del Raspeig, Apartat de correus 99, Alacant , E-03080 , Spain b Departament de Fonaments de l'Anàlisi Econòmica , Universitat d'Alacant , Spain Published online: 22 Mar 2012.
منابع مشابه
Construction of bent functions via Niho power functions
A Boolean function with an even number n = 2k of variables is called bent if it is maximally nonlinear. We present here a new construction of bent functions. Boolean functions of the form f(x) = tr(α1x1 + α2x2), α1, α2, x ∈ F2n , are considered, where the exponents di (i = 1, 2) are of Niho type, i.e. the restriction of xi on F2k is linear. We prove for d1 = 2 + 1 and d2 = 3 · 2k−1 − 1, d2 = 2 ...
متن کاملConstructions of Bent Functions from Two Known Bent Functions
A (1,-1)-matrix will be called a bent type matrix if each row and each column are bent sequences. A similar description can be found in Carlisle M. in which the authors use the properties of bent type matrices to construct a class of bent functions. In this paper we give a general method to construct bent type matrices and show that the bent sequence obtained from a bent type matrix is a genera...
متن کاملOn the Primary Constructions of Vectorial Boolean Bent Functions∗
Vectorial Boolean bent functions, which possess the maximal nonlinearity and the minimum differential uniformity, contribute to optimum resistance against linear cryptanalysis and differential cryptanalysis for the cryptographic algorithms that adopt them as nonlinear components. This paper is devoted to the new primary constructions of vectorial Boolean bent functions, including four types: ve...
متن کاملA new construction of bent functions based on Z-bent functions
Dobbertin has embedded the problem of construction of bent functions in a recursive framework by using a generalization of bent functions called Z-bent functions. Following his ideas, we generalize the construction of partial spreads bent functions to partial spreads Z-bent functions of arbitrary level. Furthermore, we show how these partial spreads Z-bent functions give rise to a new construct...
متن کاملThe graph of minimal distances of bent functions and its properties
A notion of the graph of minimal distances of bent functions is introduced. It is an undirected graph (V , E) where V is the set of all bent functions in 2k variables and (f, g) ∈ E if the Hamming distance between f and g is equal to 2 (it is the minimal possible distance between two different bent functions). The maximum degree of the graph is obtained and it is shown that all its vertices of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Int. J. Comput. Math.
دوره 89 شماره
صفحات -
تاریخ انتشار 2012