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Count of rotational symmetric bent Boolean functions
Rotational Symmetric Boolean Function Algebraic Normal Form Bent Boolean Function
2019/8/2
Counting the Boolean functions having specific cryptographic features is an interesting problem in combinatorics and cryptography. Count of bent functions for more than eight variables is unexplored. ...
Relation between o-equivalence and EA-equivalence for Niho bent functions
Bent function Boolean function EA-equivalence
2019/7/15
Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for ...
Composition of Boolean Functions: An Application to the Secondary Constructions of Bent Functions
Secondary constructions Composition of Boolean functions Bent
2019/4/28
Bent functions are optimal combinatorial objects and have been attracted their research for four decades. Secondary constructions play a central role in constructing bent functions since a complete cl...
Algebraic normal form of a bent function: properties and restrictions
Boolean function bent function linear function
2018/12/3
Maximally nonlinear Boolean functions in nn variables, where n is even, are called bent functions. There are several ways to represent Boolean functions. One of the most useful is via algebraic normal...
A Construction of Bent Functions with Optimal Algebraic Degree and Large Symmetric Group
secret-key cryptography Large Symmetric Group
2017/3/6
We present a construction of bent function fa,Sfa,S with n=2mn=2m variables for any nonzero vector a∈Fm2a∈F2m and subset SS of Fm2F2m satisfying a+S=Sa+S=S. We give the simple expression of the dual b...
Complete characterization of generalized bent and 2^k-bent Boolean functions
Boolean functions 2k-bent Boolean functions
2016/4/7
In this paper we investigate properties of generalized bent Boolean functions and 2k-bent (i.e., negabent, octabent, hex- adecabent, et al.) Boolean functions in a uniform framework. We generalize the...
The graph of minimal distances of bent functions and its properties
Boolean functions bent functions the minimal distance
2016/1/27
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 d...
When a Boolean Function can be Expressed as the Sum of two Bent Functions
Bent functions Sum of bent functions Maiorana-MacFarland bent function
2016/1/26
In this paper we study the problem that when a Boolean function can
be represented as the sum of two bent functions. This problem was recently
presented by N. Tokareva in studying the number of bent...
Constructing hyper-bent functions from Boolean functions with the Walsh spectrum taking the same value twice
Bent function hyper-bent function Dillon exponents
2016/1/8
Hyper-bent functions as a subclass of bent functions attract much
interest and it is elusive to completely characterize hyper-bent functions. Most
of known hyper-bent functions are Boolean functions...
On the Primary Constructions of Vectorial Boolean Bent Functions
Bent functions vetorial Boolean functions perfect nonlinear functions
2016/1/4
Vectorial Boolean bent functions, which possess the maximal nonlinearity and the minimum differential uniformity, contribute to optimum resistance against linear cryptanalysis and differential cryptan...
Two general classes (constructions) of bent functions are derived from the notion of spread. The first class, PS, gives a useful framework for designing bent functions which are constant (except maybe...
On the Systematic Constructions of Rotation Symmetric Bent Functions with Any Possible Algebraic Degrees
Orbit rotation symmetric function Walsh transform
2015/12/30
In the literature, few constructions of n-variable rotation symmetric bent functions have been presented,
which either have restriction on n or have algebraic degree no more than 4. In this paper, fo...
An analysis of the $C$ class of bent functions
Boolean functions bent functions permutation polynomials
2015/12/29
Two (so-called C, D) classes of permutation-based bent Boolean functions were introduced
by Carlet two decades ago, but without specifying some explicit construction methods
for their construction (...
On weak and strong 2^k-bent Boolean functions
Boolean functions Walsh-Hadamard transforms bent
2015/12/24
In this paper we introduce a sequence of discrete Fourier transforms and define new versions of bent functions, which we shall call (weak, strong) octa/hexa/2^k-bent functions. We investigate relation...
Bent and Semi-bent Functions via Linear Translators
Boolean functions Bent functions Semi-bent functions
2015/12/23
The paper is dealing with two important subclasses of plateaued functions: bent
and semi-bent functions. In the first part of the paper, we construct mainly bent and semi-bent
functions in the Maior...