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Boolean functions are widely used because they can be used to precisely describe logical circuits. Properties of Boolean functions with respect to their applications to cryptography have been studied, but relationship between Boolean functions are rarely studied. This paper studies the independence of Boolean functions, gives necessary and sufficient conditions for judging whether two given Boolean functions are independent. Some enumeration formulae are given. [ABSTRACT FROM AUTHOR]

Correlation immunity of symmetric Boolean functions is studied in this paper. Lower bounds on the number of constructible correlation immune symmetric functions are given. Constructions for such new balanced functions are presented. These functions are also known as 1-resilient functions. In 1985, Chor et al. conjectured that the only 1-resilient symmetric functions are the exclusive-or of all n variables and its negation. This conjecture, however, was disproved by Gopalakrishnan, Hoffman and Stinson in 1993 by giving a class of infinite counterexamples, and they noted that it does not seem to extend any further in an obvious way. In this paper two more infinite classes of such examples are presented for n being even and being odd, respectively, and consequently one of the two open problems proposed by Gopalakrishnan et al., is addressed by constructing new symmetric resilient functions. [Copyright &y& Elsevier]

Recently, the polynomial-based radial basis function neural networks (P-RBFNNs) have been successfully applied to regression tasks. However, the redundant and non-linear partitioned data easily interfere with accurate partitioning of clusters completed in P-RBFNNs, affecting the regression performance of this existing model. Because the squared error is used as the cost function of the learning method, P-RBFNNs are sensitive to noise interference. In order to cope with these problems, this study introduces a double iterative learning-based polynomial based-RBFNNs (DP-RBFNNs) modeling that focuses on the formation of architectures to improve the accuracy of regression performance as well as enhance the robustness through double iterative learning as follows: a) support vector-based Gaussian kernel fuzzy c-means (SV-GKFCM) as a kind of the support vector-based kernel fuzzy clustering are designed to determine connections (weights) between the input and hidden layers of the proposed model. SV-GKFCM helps effectively reduce the number of redundant data to re-modify the partitioning of clusters in the DP-RBFNNs. In addition, the cluster centers can be accurately updated from the non-linear partitioned data with the aid of Gaussian kernel distance in SV-GKFCM; b) least absolute shrinkage deviations (LASD) as a robust estimation are designed to update connection weights between the hidden and output layers. The SAE (sum of absolute error) function in the LASD method is used as a cost function to reduce the noise interference in the procedure of weight estimation as well as enhance the robustness of the DP-RBFNNs. The superiority of the proposed model is demonstrated through the experimental results. [ABSTRACT FROM AUTHOR]

Abstract: Liaw proposed a broadcasting cryptosystem [H.T. Liaw, Broadcasting cryptosystem in computer networks, Computers & Mathematics with Applications 37 (Mar. 1999) 85–87] which claims to involve fewer broadcasting messages, and has attracted quite some research efforts on iterative analysis and improvement [H.M. Sun, Security of broadcasting cryptosystem in computer networks, Electronics Letters 35 (Nov. 1999) 2108–2109; Y.M. Tseng, J.K. Jan, Cryptanalysis of Liaw’s broadcasting cryptosystem, Computers & Mathematics with Applications 41 (Jun. 2001) 1575–1578; J.M. Masque, A. Peinado, Cryptanalysis of improved Liaw’s broadcasting cryptosystem, Journal of Information Science and Engineering 22 (Mar. 2006) 391–399]. We show that the redefined Liaw’s broadcasting cryptosystem recently presented in [J.M. Masque, A. Peinado, Cryptanalysis of improved Liaw’s broadcasting cryptosystem, Journal of Information Science and Engineering 22 (Mar. 2006) 391–399] is still insecure in that an unauthorized user is able to obtain the shared secret, which is only intended for certain privileged users. [Copyright &y& Elsevier]

In recent years, classical fuzzy clustering-based neural networks (FCNNs) have been successfully applied to regression tasks. The determination of the parameters such as cluster centers of the existing hard c-means (HCM) or fuzzy c-means (FCM), leads to the performance deterioration of the model because of the sensitivity of HCM or FCM to noise and outliers. Moreover, there are also several factors for over-fitting and degradation of the robustness of the ensuing model. To solve such problems, two improved clustering techniques and L 2 norm-regularization are considered in the proposed robust fuzzy clustering-based neural networks (RFCNNs) modeling. SVs-based hard c-means (SVs-based HCM) and SVs-based fuzzy c-means (SVs-based FCM) designed with support vectors (SVs) can reduce the interference of uncorrelated data, including noise and outliers, thereby enhancing the main data characteristics effectively, as well as leading to the construction on the improved network model. L 2 norm-regularization can be used to alleviate the degradation of robustness caused by overfitting. In terms of improving the performance of the model through SVs-based HCM or SVs-based FCM, as well as robustness completed through L 2 norm-regularization, the superiority of RFCNNs was verified by experimenting with synthetic data and publicly available data from machine learning datasets. [ABSTRACT FROM AUTHOR]