Muhammad Asif Gondal

A new comparative study between homotopy analysis transform method and homotopy perturbation transform method on a semi infinite domain

Abstract The aim of this article is to introduce a new approximate method, namely homotopy analysis transform method (HATM) which is a combination of homotopy analysis method (HAM) and Laplace decomposition method (LDM) to provide an analytical approximate solution to Blasius flow equations. The proposed scheme finds the solutions of nonlinear problems without any discretization, restrictive assumptions and avoids the rounding-off errors. The proposed technique solves the nonlinear problems without using Adomian polynomials and He’s polynomials which can be considered as a clear advantage of this new algorithm over decomposition and the homotopy perturbation transform method (HPTM). A good agreement between the obtained solution and some well-known results has been demonstrated.

A group theoretic approach to construct cryptographically strong substitution boxes

In this paper, we present a method to construct a substitution box used in encryption applications. The proposed algorithm for the construction of substitution box relies on the linear fractional transform method. The design methodology is simple, while the confusion-creating ability of the new substitution box is complex. The strength of the proposed substitution box is evaluated, and an insight is provided to quantify the confusion-creating ability. In addition, tests are performed to assess the vulnerability of the encrypted data to algebraic and statistical attacks. The substitution box is critically analyzed by strict avalanche criterion, bit independent criterion, differential approximation probability test, linear approximation probability test, non-linearity test, and majority logic criterion. The performance of the proposed substitution box is also compared with those of some of the well-known counterparts including AES, APA, Gray, S8, Skipjack, Xyi, and prime of residue substitution boxes. It is apparent that the performance, in terms of confusion-creating ability, of the new substitution box is better than those of some of the existing non-linear components used in encryption systems. The majority logic criterion is applied to these substitution boxes to further evaluate the strength and usefulness.

A new analytical solution procedure for nonlinear integral equations

The chief aim of the present article is to introduce a new analytical technique, two-step Laplace decomposition method (TSLDM) for nonlinear Volterra integral equations. The newly proposed method efficiently find exact solution with less computation as compared with standard Laplace decomposition method (LDM). The proposed algorithm is used to solve nonlinear Volterra integral equations effectively and overcome the deficiencies in Laplace decomposition method (LDM) easily.

Homotopy Perturbation Method for Nonlinear Exponential Boundary Layer Equation using Laplace Transformation, He's Polynomials and Pade Technology He's Polynomials and Pade Technology

In this article, we proposed a new reliable combination of homotopy perturbation method, Laplace transformation and Pade approximation to obtain the series solution of nonlinear exponential boundary layer equation. The propose method is called homotopy perturbation transform Pade method (HPTPM). The nonlinear term can easily be handled with the help of Hes polynomials based on homotopy perturbation method. The proposed method solve exponential boundary layer equation without restrictions on the nonlinear behavior and use Pade approximants to accelerate the convergence of obtained series solution which can be considered as a significant features of the new algorithm over decomposition method.

A reliable treatment of Abel’s second kind singular integral equations

Abstract The central idea of this paper is to construct a new mechanism for the solution of Abel’s type singular integral equations that is to say the two-step Laplace decomposition algorithm. The two-step Laplace decomposition algorithm (TSLDA) is an innovative adjustment in the Laplace decomposition algorithm (LDA) and makes the calculation much simpler. In this piece of writing, we merge the Laplace transform and decomposition method and present a novel move toward solving Abel’s singular integral equations.

A novel solution procedure for fuzzy fractional heat equations by homotopy analysis transform method

In this paper, we designed a reliable recipe of homotopy analysis method and Laplace decomposition method namely homotopy analysis transform method to solve fuzzy fractional heat and wave equations. This method overcomes the difficulties arise in other analytical method and removes the restrictive condition of nonlinearity and assumptions of small and large parameters.

Generalized Majority Logic Criterion to Analyze the Statistical Strength of S-Boxes

The majority logic criterion is applicable in the evaluation process of substitution boxes used in the advanced encryption standard (AES). The performance of modified or advanced substitution boxes is predicted by processing the results of statistical analysis by the majority logic criteria. In this paper, we use the majority logic criteria to analyze some popular and prevailing substitution boxes used in encryption processes. In particular, the majority logic criterion is applied to AES, affine power affine (APA), Gray, Lui J, residue prime, S8 AES, Skipjack, and Xyi substitution boxes. The majority logic criterion is further extended into a generalized majority logic criterion which has a broader spectrum of analyzing the effectiveness of substitution boxes in image encryption applications. The integral components of the statistical analyses used for the generalized majority logic criterion are derived from results of entropy analysis, contrast analysis, correlation analysis, homogeneity analysis, energy analysis, and mean of absolute deviation (MAD) analysis.

Image encryption algorithm based on total shuffling scheme and chaotic S-box transformation

This paper presents an image encryption scheme based on complete shuffling algorithm: limited in the skew tent-map-predicated image cryptosystem and chaotic substitution box transformation. The proposed image encryption algorithm provides extra confusion due to the inclusion of a chaotic S-box. It is well known from the literature that simple image encryption based on a total shuffling scheme is not secure against a chosen cipher text attack. We then projected an extended algorithm which does well against a chosen cipher text attack. Furthermore we analyze the proposed technique for unified average changing intensity (UACI) and NPCR analysis to determine its strength.

Analysis of optimized signal processing algorithms for smart antenna system

By the exponential increase in cellular communication area, the user demands and with their side problems also tend to increase. Several techniques such as cell splitting, frequency reuse, diversity and so on have already been applied to overcome these problems. In all these procedures, smart antenna is one of the best techniques used to boost capacities, enlarge bandwidth, raise the SIR ratios, minimize the effects of fading and improve MIMO communications. An ordinary antenna array which can turn up into a smart antenna array is due to the signal processing algorithms, which consists of angle of arrival (AOA) estimations and Beamforming. In this paper, I will discuss and analyse about the MUSIC algorithm for AOA estimation and least mean squares algorithm for Beamforming.

Application of Mean of Absolute Deviation Method for the Selection of Best Nonlinear Component Based on Video Encryption

The aim of this work is to make use of the mean of absolute deviation (MAD) method for the evaluation process of substitution boxes used in the advanced encryption standard. In this paper, we use the MAD technique to analyze some popular and prevailing substitution boxes used in encryption processes. In particular, MAD is applied to advanced encryption standard (AES), affine power affine (APA), Gray, Lui J., Residue Prime, S8 AES, SKIPJACK, and Xyi substitution boxes.