The Experts below are selected from a list of 6036 Experts worldwide ranked by ideXlab platform

Xiangyong Zeng - One of the best experts on this subject based on the ideXlab platform.

Nikolay Kolomeec - One of the best experts on this subject based on the ideXlab platform.

  • constructions of Bent Functions on the minimal distance from the quadratic Bent Function
    International Symposium on Information Theory, 2011
    Co-Authors: Nikolay Kolomeec
    Abstract:

    In this paper we study how to construct new Bent Functions by slight modifications of the initial one. The answer to this question is directly connected to the studying of Bent Functions on the minimal Hamming distance from the given Bent Function. Here we constructively describe all Bent Functions on the minimal distance from the quadratic Bent Function and calculate their exact number. We get a lower bound for the number of Bent Functions on the minimal distance from a Bent Function of Maiorana-McFarland type. We present several facts and hypotheses on the maximal number of Bent Functions that can be obtained in this way.

  • ISIT - Constructions of Bent Functions on the minimal distance from the quadratic Bent Function
    2011 IEEE International Symposium on Information Theory Proceedings, 2011
    Co-Authors: Nikolay Kolomeec
    Abstract:

    In this paper we study how to construct new Bent Functions by slight modifications of the initial one. The answer to this question is directly connected to the studying of Bent Functions on the minimal Hamming distance from the given Bent Function. Here we constructively describe all Bent Functions on the minimal distance from the quadratic Bent Function and calculate their exact number. We get a lower bound for the number of Bent Functions on the minimal distance from a Bent Function of Maiorana-McFarland type. We present several facts and hypotheses on the maximal number of Bent Functions that can be obtained in this way.

Alexander Pott - One of the best experts on this subject based on the ideXlab platform.

  • on design theoretic aspects of boolean and vectorial Bent Function
    IEEE Transactions on Information Theory, 2021
    Co-Authors: Alexandr Polujan, Alexander Pott
    Abstract:

    There are two construction methods of designs from $(n,m)$ -Bent Functions, known as translation and addition designs. In this article we analyze, which equivalence relation for Boolean Bent Functions, i.e. $(n,1)$ -Bent Functions, and vectorial Bent Functions, i.e. $(n,m)$ -Bent Functions with $2\le m\le n/2$ , is coarser: extended-affine equivalence or isomorphism of associated translation and addition designs. First, we observe that similar to the Boolean Bent Functions, extended-affine equivalence of vectorial $(n,m)$ -Bent Functions and isomorphism of addition designs are the same concepts for all even $n$ and $m\le n/2$ . Further, we show that extended-affine inequivalent Boolean Bent Functions in $n$ variables, whose translation designs are isomorphic, exist for all $n\ge 6$ . This implies, that isomorphism of translation designs for Boolean Bent Functions is a coarser equivalence relation than extended-affine equivalence. However, we do not observe the same phenomenon for vectorial Bent Functions in a small number of variables. We classify and enumerate all vectorial Bent Functions in six variables and show, that in contrast to the Boolean case, one cannot exhibit isomorphic translation designs from extended-affine inequivalent vectorial $(6,m)$ -Bent Functions with $m\in \{ 2,3 \}$ .

  • Vectorial Bent Functions in odd characteristic and their components
    Cryptography and Communications, 2020
    Co-Authors: Ayça Çeşmelioğlu, Wilfried Meidl, Alexander Pott
    Abstract:

    Bent Functions in odd characteristic can be either (weakly) regular or non-weakly regular. Furthermore one can distinguish between dual-Bent Functions, which are Bent Functions for which the dual is Bent as well, and non-dual Bent Functions. Whereas a weakly regular Bent Function always has a Bent dual, a non-weakly regular Bent Function can be either dual-Bent or non-dual-Bent. The classical constructions (like quadratic Bent Functions, Maiorana-McFarland or partial spread) yield weakly regular Bent Functions, but meanwhile one knows constructions of infinite classes of non-weakly regular Bent Functions of both types, dual-Bent and non-dual-Bent. In this article we focus on vectorial Bent Functions in odd characteristic. We first show that most p -ary Bent monomials and binomials are actually vectorial constructions. In the second part we give a positive answer to the question if non-weakly regular Bent Functions can be components of a vectorial Bent Function. We present the first construction of vectorial Bent Functions of which the components are non-weakly regular but dual-Bent, and the first construction of vectorial Bent Functions with non-dual-Bent components.

  • On the dual of (non)-weakly regular Bent Functions and self-dual Bent Functions
    Advances in Mathematics of Communications, 2013
    Co-Authors: Ayça Çeşmelioğlu, Wilfried Meidl, Alexander Pott
    Abstract:

    For weakly regular Bent Functions in odd characteristic the dual Function is also Bent. We analyse a recently introduced construction of non-weakly regular Bent Functions and show conditions under which their dual is Bent as well. This leads to the definition of the class of dual-Bent Functions containing the class of weakly regular Bent Functions as a proper subclass. We analyse self-duality for Bent Functions in odd characteristic, and characterize quadratic self-dual Bent Functions. We construct non-weakly regular Bent Functions with and without a Bent dual, and Bent Functions with a dual Bent Function of a different algebraic degree.

Liu Zhigao - One of the best experts on this subject based on the ideXlab platform.

  • The Construction of a Class of Multi-output Semi-Bent Functions and Their Cryptographic Properties
    Journal of Nanjing Normal University, 2006
    Co-Authors: Liu Zhigao, Zhang Futai
    Abstract:

    A method to construct multi-output semi-Bent Functions is presented.In the method,a higher order multi-output semi-Bent Function is constructed by concatenating two lower order multi-output Bent Functions.Since many good results on the construction of multi-output Bent Functions have been given,the new method is very effective and many multi-output semi-Bent Functions can be constructed by it.Furthermore,some cryptographic properties of this kind of Functions such as balance,nonlinearity,stability and propagation characters etc,are discussed.The discussion shows that the multi-output semi-Bent Function is a class of multi-output Functions with odd variables that hold good cryptographic properties.Besides applications in multi-output feedforward networks,multi-output semi-Bent Functions can also be used as nonlinear combiner in block ciphers.

  • Construction of a Class of Multi-output Bent Functions
    Journal of Nanjing Normal University, 2005
    Co-Authors: Liu Zhigao
    Abstract:

    The concept of semi-Bent Functions is generalized. Meanwhile, the concept of multi-output semi-Bent Functions is introduced. Based on the new concept, a method of construct ing multi-output Bent Functions is presented. In the method, a multi-output Bent Function is constructed by concatenating two multi-output semi-Bent Functions. Compared with the existing methods, our newly proposed method has a simple structure and is convenient to use. With this new method, multi-output Bent Functions with arbitrary even variables can be constructed. Moreover, a method of constructing multi-output semi-Bent Functions is proposed. Besides, applications in the construction of multi-output Bent Functions, multi-output semi-Bent Functions can also be applied in multi-output feedforward networks.

Patrick Sole - One of the best experts on this subject based on the ideXlab platform.

  • the rayleigh quotient of Bent Functions
    Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding, 2009
    Co-Authors: Lars Eirik Danielsen, Matthew G Parker, Patrick Sole
    Abstract:

    The Rayleigh quotient of a Bent Function is an invariant under the action of the orthogonal group, and it measures the distance of the Function to its dual. An efficient algorithm is derived that generates all Bent Functions of given Rayleigh quotient. The Rayleigh quotient of some Bent Functions obtained by primary (Maiorana McFarland, Dillon) or secondary (direct and indirect sum) constructions is computed.

  • IMA Int. Conf. - The Rayleigh Quotient of Bent Functions
    Cryptography and Coding, 2009
    Co-Authors: Lars Eirik Danielsen, Matthew G Parker, Patrick Sole
    Abstract:

    The Rayleigh quotient of a Bent Function is an invariant under the action of the orthogonal group, and it measures the distance of the Function to its dual. An efficient algorithm is derived that generates all Bent Functions of given Rayleigh quotient. The Rayleigh quotient of some Bent Functions obtained by primary (Maiorana McFarland, Dillon) or secondary (direct and indirect sum) constructions is computed.