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Due to the high demands of data communication, the broadcasting system streams the data daily. This service not only sends out the message to the correct participant but also respects the security of the identity user. In addition, when delivered, all the information must be protected for the party who employs the broadcasting service. Currently, Attribute-Based Broadcast Encryption (ABBE) is useful to apply for the broadcasting service. (ABBE) is a combination of Attribute-Based Encryption (ABE) and Broadcast Encryption (BE), which allows a broadcaster (or encrypter) to broadcast an encrypted message, including a predefined user set and specified access policy to install the authorization mechanism. It is desirable to hide all the information when producing in the ciphertext, which has not been considered in the previous works of ABBE. Motivated by the above issue, we devise a solution to achieve anonymity for the ABBE scheme, which not only hides the access structures but also anonymizes the user's identity. In this work, we propose two schemes as Anonymous Key Policy (AKP)-ABBE and Anonymous Ciphertext Policy (ACP)-ABBE with supporting multiple access structures by using OR / AND gates. Specifically, we present the generic constructions of AKP/ACP-ABBE on the building block of the Inner Product Encryption (IPE ), which enables the hidden user's identity and complex OR / AND -Gate access structure. We show that our proposed schemes are secured under the standard models. [ABSTRACT FROM AUTHOR]

Objectives: The main objective of this work is to design an efficient numerical scheme is proposed for solving singularly perturbed time delayed parabolic problems with two parameters. Results: The scheme is constructed via the implicit Euler and non-standard finite difference method to approximate the time and space derivatives, respectively. Besides, to enhance the accuracy and order of convergence of the method Richardson extrapolation technique is employed. Intensive numerical experimentation has been done on some model examples. Further, the layer behavior of the solutions is presented using graphs and observed to agree with the existing theories. Finally, error analysis of the scheme is done and observed that the proposed method is parameter uniform convergent with the order of convergence (Δ t) 2 + h 2 [ABSTRACT FROM AUTHOR]

In this paper, a new numerical method for solving a class of stochastic partial differential equations is presented. The proposed method is based on a non-polynomial cubic spline algorithm with an O(h4) local truncation error. The new approach has the advantage of simultaneously including ten non-polynomial cubic spline schemes. The proposed approach is also tested on three stochastic heat equations. The current results are compared to solutions obtained using the B-spline wavelet approximation method. The provided solutions demonstrate the proposed method's accuracy and applicability.