Eihab Bashier

A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation

Abstract We design a robust fitted operator finite difference method for the numerical solution of a singularly perturbed delay parabolic partial differential equation. This method is unconditionally stable and is convergent with order O ( k + h 2 ) , where k and h are respectively the time and space step-sizes, which is better than the one obtained by Ansari et al. [A.R. Ansari, S.A. Bakr, G.I. Shishkin, A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations, J. Comput. Appl. Math. 205 (2007) 552–566] where they have used a fitted mesh finite difference method. Their method was of the order O N t - 1 + N x - 2 ln 2 N x , where Nt and Nx denote the total number of sub-intervals in the time and space directions. The performance of our method is illustrated through some numerical experiments. We also compare our results with those obtained by a standard finite difference method as well as other works seen in the literature. In addition, we provide a novel proof for the bounds on partial derivatives of the solution of the continuous problem.

Speech scrambling based on chaotic maps and one time pad

This paper presents a chaos-based speech scrambling system. Chaotic maps have been successfully used for large-scale data encryption such as image, audio and video data, due to their good properties such as pseudo-randomness, sensitivity to changes in initial conditions and system parameters and aperiodicity. This paper uses two chaotic maps, circle map and logistic map for speech confusion and diffusion, respectively. In the confusion stage, speech samples are divided into small segments. Then, indices of ordered generated sequence of circle map are used to shuffle the positions of the speech signal segments. Then, a one-time pad generated by the logistic map is used for the diffusion stage. Several experimental results, signal-to-noise ratio, key space, key sensitivity tests, statistical analysis, chosen/known plaintext attack and time analysis show that the proposed method for speech scrambling performs efficiently and can be applied for secure real time speech communications.

Detection of Zero-Day Polymorphic Worms Using Principal Component Analysis

Polymorphic worms pose a big challenge to the Internet security. The difficulty of detection of such a polymorphic worm is that it has more than one instance and very large efforts are needed to capture all these instances and to generate signatures. This paper proposes automatic system for signature generation for zero-day polymorphic worms. We have designed a novel double-honeynet system, which is able to detect new worms that have not been seen before. We apply Principal Component Analysis (PCA) to determine the most significant substrings that are shared between polymorphic worm instances and to use them as signatures. The system is able to generate signatures to match most polymorphic worm instances with low false positives and low false negatives.

A fitted numerical method for a system of partial delay differential equations

We consider a system of two coupled partial delay differential equations (PDDEs) describing the dynamics of two cooperative species. The original system is reduced to a system of ordinary delay differential equations (DDEs) obtained by applying the method of lines. Then we construct a fitted operator finite difference method (FOFDM) to solve this resulting system. The model considered in this paper is very sensitive to small changes in the parameters associated in with the model. Depending on the values of these parameters, the solution can be stable, periodic and/or aperiodic. Such behavior of the solution is exploited via the proposed FOFDM. This FOFDM is analyzed for convergence and it is seen that this method is unconditionally stable and has the accuracy of O(k+h^2), where k and h denote time and space step-sizes, respectively. Some numerical results confirming theoretical observations are also presented. These results are comparable with those obtained in the literature.

A second-order fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation

We design a parameter robust fitted operator finite difference method for the numerical solution of a singularly perturbed delay parabolic partial differential equation. The method is constructed by replacing the classical differential operator with a fitted operator based on Crank–Nicolsons discretization. The proposed method is analysed for stability and convergence and it is found that this method is unconditionally stable and is convergent with order , where k and h are respectively the time and space step sizes. The performance of this method is illustrated through a numerical example.

Accurate signature generation for polymorphic worms using principal component analysis

Internet worms pose a major threat to Internet infrastructure security, and their destruction causes loss of millions of dollars. Therefore, the networks must be pro-tected as much as possible to avoid losses. In this paper we propose accurate system for signature generation for Zero-day polymorphic worms. We have designed a novel double-honeynet system, which is able to detect new worms that have not been seen before. We apply Princi-pal Component Analysis (PCA) to determine the most significant substrings that are shared between po-lymorphic worm instances. The experimental results show that the PCA has successfully detected polymorphic worms with zero false positives and zero false negatives.

Optimal control of an epidemiological model with multiple time delays

In this paper, we consider an optimal control model governed by a system of delay differential equations representing an SIR model. We extend the model of Kaddar (2010) by incorporating the suitable controls. We consider two control strategies in the optimal control model, namely: the vaccination and treatment strategies. The model has three time delays that represent the incubation period, and the times taken by the vaccine and treatment to be effective. We derive the first-order necessary conditions for the optimal control and perform numerical simulations to show the effectiveness as well as the applicability of the model for different values of the time delays. These numerical simulations show that the model is more sensitive to the delays representing the incubation period and the treatment delay, whereas the delay associated with the vaccine is not significant.

Enhanced model for PKI certificate validation in the mobile banking

Mobile banking is a service that allows customers to do banking transactions on their mobile phone. Bank transactions, such as balance inquiry, money transfer, online payments and other mobile services usually require the transmission of critical information. Therefore, it is extremely necessary to provide the security services including the confidentiality, integrity, and authentication. The Public Key Infrastructure (PKI) system can be used to provide the four security services, in particular, the authentication service for mobile banking. Because the current PKI systems use the RSA asymmetric algorithm with key lengths of 1024-4096 bits and advanced web browsers to deal with the certificate validation, it is not appropriate for the mobile devices, which have limited resources and software. This paper proposes an efficient PKI system for mobile devices. In the improved model, the NTRU replaces the RSA algorithm and the Micalis NOVOMODO system has been use to provide efficient certificate validation. This new setup for PKI complies with the limited resources of the mobile devices and provides the four security services with cheap computational costs).

A New Level 3 Trust Hierarchal Certificateless Public Key Cryptography Scheme in the Random Oracle Model

Despite the fact that the traditional public key infrastructure provides Level 3 trusted authority, but its two major problems of scalability and certificate management raised the need to an alternative security infrastructure. That motivated the appearance of new technologies to replace the traditional PKI, such as the Identity based encryption, the certificateless encryption, etc. But all those new technologies are yet immature and could not introduce a trust level more than Level 2, except few trials at the level of the authority. This paper aims at introducing an integrated hierarchal certificateless scheme with a Level 3 trust authority. This is done through merging the traditional PKI hierarchy and the certificateless technology in one scheme. The new scheme employs the X509 certificate format and is free of the scalability and certificate management problems of the PKI. We also describe how our new hierarchal certificateless PKC, can be integrated with a traditional PKI through a bridge model.

A Secure Mobile Banking Scheme Based on Certificateless Cryptography in the Standard Security Model

Providing the security services (authenticity, integrity, confidentiality and non-repudiation) all together in mobile banking has remained a problematic issue for both banks and their customers. Both the public key infrastructure (PKI) and the identity-based public key cryptography (IB-PKC) which have been thought to provide solutions to these security services, have their own limitations. While the PKI suffers the scalability and certificate management problems, the identity-based cryptography suffers the key escrow problem. This paper proposes a secure web-based mobile banking scheme using certificateless public key cryptography. Within this scheme, the key generating center(KGC) has an offline connection with a public directory server. Both of the client and the bank’s web-server use the identities of each other to obtain the public key of each from the KGC’s public directory server. Then, each party computes an authenticated per-session shared secret symmetric key. By using this shared secret key the client can encrypt his username and password to access his banking account and carry out signed banking transactions. As a result, the proposed scheme is secure in the standard model and provides authentication, confidentiality, integrity and nonrepudiation. Moreover, the scheme is secure against known key attack, resilient against unknown key share and key-compromise impersonation, and secure against weak perfect forward secrecy.