61 research outputs found
Decomposing generalized bent and hyperbent functions
In this paper we introduce generalized hyperbent functions from to
, and investigate decompositions of generalized (hyper)bent functions.
We show that generalized (hyper)bent functions from to
consist of components which are generalized (hyper)bent functions from
to for some . For odd , we show
that the Boolean functions associated to a generalized bent function form an
affine space of semibent functions. This complements a recent result for even
, where the associated Boolean functions are bent.Comment: 24 page
On bent and hyper-bent functions
Bent functions are Boolean functions which have maximum possible nonlinearity i.e. maximal distance to the set of affine functions. They were introduced by Rothaus in 1976. In the last two decades, they have been studied widely due to their interesting combinatorial properties and their applications in cryptography. However the complete classification of bent functions has not been achieved yet. In 2001 Youssef and Gong introduced a subclass of bent functions which they called hyper-bent functions. The construction of hyper-bent functions is generally more difficult than the construction of bent functions. In this thesis we give a survey of recent constructions of infinite classes of bent and hyper-bent functions where the classification is obtained through the use of Kloosterman and cubic sums and Dickson polynomials
A new class of hyper-bent functions and Kloosterman sums
This paper is devoted to the characterization of hyper-bent functions.
Several classes of hyper-bent functions have been studied, such as
Charpin and Gong\u27s and Mesnager\u27s , where is a set of representations of the cyclotomic
cosets modulo of full size and .
In this paper, we generalize their results and consider a class of Boolean functions of the form , where , is odd, , and .
With the restriction of , we present the characterization of hyper-bentness of these functions with character sums. Further, we reformulate this characterization in terms of the number of points on
hyper-elliptic curves. For some special cases, with the help of Kloosterman sums and cubic sums, we determine the characterization for some hyper-bent functions including functions with four, six and ten traces terms. Evaluations of Kloosterman sums at three general points are used in the characterization. Actually, our results can generalized to the general
case: . And we explain this for characterizing binomial, trinomial and quadrinomial hyper-bent functions
Unique Aspects of Usage of the Quadratic Cryptanalysis Method to the GOST 28147-89 Encryption Algorithm
In this article, issues related to the application of the quadratic cryptanalysis method to the five rounds of GOST 28147-89 encryption algorithm are given. For example, the role of the bit gains in the application of the quadratic cryptanalysis method, which is formed in the operation of addition according to mod232 used in this algorithm is described. In this case, it is shown that the selection of the relevant bits of the incoming plaintext and cipher text to be equal to zero plays an important role in order to obtain an effective result in cryptanalysi
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