The Experts below are selected from a list of 33 Experts worldwide ranked by ideXlab platform

Sihem Mesnager - One of the best experts on this subject based on the ideXlab platform.

  • New characterizations and construction methods of Bent and hyper-Bent Boolean Functions
    Discrete Mathematics, 2020
    Co-Authors: Sihem Mesnager, Bimal Mandal, Chunming Tang
    Abstract:

    Abstract In this paper, we first derive a necessary and sufficient condition for a Bent Boolean Function by analyzing their support set. Next, using this condition and the Pless power moment identities, we propose a construction method of Bent Functions of 2 k variables by a suitable choice of 2 k -dimension subspace of F 2 2 2 k − 1 − 2 k − 1 . Further, we extend our results to the so-called hyper-Bent Functions.

  • Further Results on Generalized Bent Functions and Their Complete Characterization
    IEEE Transactions on Information Theory, 2018
    Co-Authors: Sihem Mesnager, Chunming Tang, Libo Wang, Keqin Feng
    Abstract:

    This paper contributes to increase our knowledge on generalized Bent Functions (including generalized Bent Boolean Functions and generalized $p$ -ary Bent Functions with odd prime $p$ ) by bringing new results on their characterization and construction in arbitrary characteristic. More specifically, we first investigate relations between generalized Bent Functions and Bent Functions by the decomposition of generalized Bent Functions. This enables us to completely characterize generalized Bent Functions and $\mathbb Z_{p^{k}}$ -Bent Functions by some affine space associated with the generalized Bent Functions. We also present the relationship between generalized Bent Boolean Functions with an odd number of variables and generalized Bent Boolean Functions with an even number of variables. Based on the well-known Maiorana-McFarland class of Boolean Functions, we present some infinite classes of generalized Bent Boolean Functions. In addition, we introduce a class of generalized hyperBent Functions that can be seen as generalized Dillon’s $PS$ Functions. Finally, we solve an open problem related to the description of the dual Function of a weakly regular generalized Bent Boolean Function with an odd number of variables via the Walsh–Hadamard transform of their component Functions, and we generalize these results to the case of odd prime.

Chunming Tang - One of the best experts on this subject based on the ideXlab platform.

  • New characterizations and construction methods of Bent and hyper-Bent Boolean Functions
    Discrete Mathematics, 2020
    Co-Authors: Sihem Mesnager, Bimal Mandal, Chunming Tang
    Abstract:

    Abstract In this paper, we first derive a necessary and sufficient condition for a Bent Boolean Function by analyzing their support set. Next, using this condition and the Pless power moment identities, we propose a construction method of Bent Functions of 2 k variables by a suitable choice of 2 k -dimension subspace of F 2 2 2 k − 1 − 2 k − 1 . Further, we extend our results to the so-called hyper-Bent Functions.

  • Further Results on Generalized Bent Functions and Their Complete Characterization
    IEEE Transactions on Information Theory, 2018
    Co-Authors: Sihem Mesnager, Chunming Tang, Libo Wang, Keqin Feng
    Abstract:

    This paper contributes to increase our knowledge on generalized Bent Functions (including generalized Bent Boolean Functions and generalized $p$ -ary Bent Functions with odd prime $p$ ) by bringing new results on their characterization and construction in arbitrary characteristic. More specifically, we first investigate relations between generalized Bent Functions and Bent Functions by the decomposition of generalized Bent Functions. This enables us to completely characterize generalized Bent Functions and $\mathbb Z_{p^{k}}$ -Bent Functions by some affine space associated with the generalized Bent Functions. We also present the relationship between generalized Bent Boolean Functions with an odd number of variables and generalized Bent Boolean Functions with an even number of variables. Based on the well-known Maiorana-McFarland class of Boolean Functions, we present some infinite classes of generalized Bent Boolean Functions. In addition, we introduce a class of generalized hyperBent Functions that can be seen as generalized Dillon’s $PS$ Functions. Finally, we solve an open problem related to the description of the dual Function of a weakly regular generalized Bent Boolean Function with an odd number of variables via the Walsh–Hadamard transform of their component Functions, and we generalize these results to the case of odd prime.

Krasimir Kordov - One of the best experts on this subject based on the ideXlab platform.

Borislav Stoyanov - One of the best experts on this subject based on the ideXlab platform.

  • Yet Another Pseudorandom Number Generator
    International Journal of Electronics and Telecommunications, 2017
    Co-Authors: Borislav Stoyanov, Krzysztof Szczypiorski, Krasimir Kordov
    Abstract:

    We propose a novel pseudorandom number generator based on Roessler attractor and Bent Boolean Function. We estimated the output bits properties by number of statistical tests. The results of the cryptanalysis show that the new pseudorandom number generation scheme provides a high level of data security.

  • cryptanalysis of a modified encryption scheme based on Bent Boolean Function and feedback with carry shift register
    APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 5th International Conference for Promoting the Application of Mathematics in Technical a, 2013
    Co-Authors: Borislav Stoyanov, Krasimir Kordov
    Abstract:

    We propose a modified encryption scheme based on 256 bit Bent Boolean Function and Feedback with Carry Shift Register. We estimated the output bits properties by the NIST, DIEHARD and ENT test packages. The results of the cryptanalysis show that the new cryptographic scheme provides an exclusive level of data security.

  • Chaotic cryptographic scheme and its randomness evaluation
    2012
    Co-Authors: Borislav Stoyanov
    Abstract:

    We propose a new cryptographic scheme based on the Lorenz chaos attractor and 32 bit Bent Boolean Function. We evaluated the keystream generated by the scheme with batteries of the NIST statistical tests. We also applied a number of statistical analysis techniques, such as calculating histograms, correlations between two adjacent pixels, information entropy, and differential resistance, all refer to images encrypted by the proposed system. The results of the analysis show that the new cryptographic scheme ensures a secure way for sending digital data with potential applications in real-time image encryption.

Keqin Feng - One of the best experts on this subject based on the ideXlab platform.

  • Further Results on Generalized Bent Functions and Their Complete Characterization
    IEEE Transactions on Information Theory, 2018
    Co-Authors: Sihem Mesnager, Chunming Tang, Libo Wang, Keqin Feng
    Abstract:

    This paper contributes to increase our knowledge on generalized Bent Functions (including generalized Bent Boolean Functions and generalized $p$ -ary Bent Functions with odd prime $p$ ) by bringing new results on their characterization and construction in arbitrary characteristic. More specifically, we first investigate relations between generalized Bent Functions and Bent Functions by the decomposition of generalized Bent Functions. This enables us to completely characterize generalized Bent Functions and $\mathbb Z_{p^{k}}$ -Bent Functions by some affine space associated with the generalized Bent Functions. We also present the relationship between generalized Bent Boolean Functions with an odd number of variables and generalized Bent Boolean Functions with an even number of variables. Based on the well-known Maiorana-McFarland class of Boolean Functions, we present some infinite classes of generalized Bent Boolean Functions. In addition, we introduce a class of generalized hyperBent Functions that can be seen as generalized Dillon’s $PS$ Functions. Finally, we solve an open problem related to the description of the dual Function of a weakly regular generalized Bent Boolean Function with an odd number of variables via the Walsh–Hadamard transform of their component Functions, and we generalize these results to the case of odd prime.