Open Access Short Research Article

Extending Wiener's Extension to RSA-Like Cryptosystems over Elliptic Curves

P. Anuradha Kameswari, L. Jyotsna

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2016/23036

The studies on Wiener's attack on RSA with small deciphering exponents led to the refinement of attack bounds on the deciphering exponent in the paper \Revisiting Wiener's Attack - New Weak Keys in RSA" by Subhamoy Maitra and Santanu Sarkar. Further in the paper \ Extending The Wiener's Attack to RSA-Type Cryptosystem" by R. G. E. Pinch, it is proved that Wiener's attack on RSA Cryptosystem with small deciphering exponent may be extended to RSA-like Cryptosystems on elliptic curves. Now in this paper we show that the Wiener's extension on RSA that refines the attack bound on deciphering exponent can also be extended to RSA-like Cryptosystems on elliptic curves.

Open Access Original Research Article

RAM-RSA and RBM-RSA: A New Fast Hybrid RSA Variants

Yossria M. Elhassan, Noureldien A. Noureldien

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/22196

Since the development of RSA in 1977, many RSA variants are developed. The objectives behind these variants are either to improve RSA decryption time, to accelerate RSA encryption time or to rebalance RSA encryption and decryption time. The Mprime RSA variant is a well known variant that improve standard RSA decryption time, while Rebalanced RSA-CRT variant lowered decryption time. Later, the Rebalanced RSA-CRT Scheme A and Scheme B variants are developed to improve encryption cost in Rebalanced RSA-CRT variant.

The Rprime RSA variant was proposed in 2002, as a hybrid variant that use the key generation algorithm of Rebalanced RSA (modified for k primes) together with the decryption algorithm of Mprime RSA in order to further improve decryption time.

In this paper, we combine the achievements of Mprime variant and RSA Rebalanced Scheme A and Scheme B variants to develop two RSA variants that improve both the encryption and decryption time. We call these variants RAM-RSA (Rebalanced Scheme A with Mprime) and RBM-RSA (Rebalanced Scheme B with Mprime).

The experimental tests show that; for decryption RAM-RSA and RBM-RSA are respectively 3.4 and 2.8 times faster than Rprime RSA, and for encryption they are respectively 4.5 and 5.8 times faster than Rprime RSA.

Open Access Original Research Article

Arabic Isolated Word Speaker Dependent Recognition System

Amer El Kourd, Kaouther El Kourd

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2016/23034

This paper describes the development of a new Arabic isolated word speaker dependent recognition system based on a combination of several features extraction and classifications techniques. Where, the system combines the methods outputs using a voting rule. The dataset used in this system include 40 Arabic words recorded in a calm environment with 5 different speakers. We compared 5 different methods which are pairwise Euclidean distance with Mel-Frequency cepstral coefficients (MFCC), Dynamic Time Warping (DTW) with Formants features, Gaussian Mixture Model (GMM) with  MFCC, Dynamic Time Warping (DTW) with MFCC features and  Itakura distance with Linear Predictive Coding  features (LPC) and we got a recognition rate of 85.23%, 57%  , 87%, 90%, 83%  respectively. In order to improve the accuracy of the system, we tested several combinations of these 5 methods. We find that the best combination is MFCC | Euclidean + Formant | DTW + MFCC | DTW + LPC | Itakura with an accuracy of 94.39% but with large computation time of 2.9 seconds. In order to reduce the computation time of this hybrid, we compare several subcombination of it and find that the best performance in trade off computation time is by first combining MFCC | Euclidean + LPC | Itakura and only when the two methods do not match the system will add Formant | DTW + MFCC | DTW methods to the combination, where the average computation time is reduced to the half to 1.56 seconds and the system accuracy is improved to 94.56%.

Open Access Original Research Article

Test Cases Minimization and Prioritization Based on Requirement, Coverage, Risk Factor and Execution Time

Wasiur Rhmann, Taskeen Zaidi, Vipin Saxena

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2016/23269

Large numbers of test cases are designed for effectively testing the quality of the developed software products. Due to limited resource and time constraint it is not possible to test the software with large number of test cases. Test case minimization selects the test cases from test suites which have higher probability of finding errors. Test case prioritization effectively improves various performance goals by executing test cases in appropriate order. This paper presents a test case minimization and prioritization approach based on several factors related to the software projects. Proposed approach prioritizes the test cases based on faults exposed by test cases, requirement coverage, risk, statement coverage and test case execution time. In the present work, test cases are selected and prioritized within the given time constraint.

Open Access Original Research Article

On the Endomorphism Ring of a Noetherian Chain Module

Hanan A. Alolaiyan, Ahmad M. Alghamdi

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/BJMCS/2016/23383

The aim of this paper is to further develop the theory of the well-known Schur's lemma on endomorphism rings for application to wider structures. We show that for a commutative Noetherian chain ring R and Noetherian chain modules M and N, the left R-module HomR (M,N) will be a chain module. Then, we conclude that the endomorphism ring EndR (M) of the Noetherian chain module M over such R is a Noetherian chain ring. As a special case, we consider that the dual R- module M * = HomR (M,R) of the Noetherian chain R-module M is a Noetherian chain module.

Open Access Original Research Article

Mathematical Modelling of Typhoid Fever Disease Incorporating Protection against Infection

J. K. Nthiiri, G. O. Lawi, C. O. Akinyi, D. O. Oganga, W. C. Muriuki, M. J. Musyoka, P. O. Otieno, L. Koech

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2016/23325

In this study, we have formulated a mathematical model based on a system of ordinary differential equations to study the dynamics of typhoid fever disease incorporating protection against infection. The existence of the steady states of the model are determined and the basic reproduction number is computed using the next generation matrix approach. Stability analysis of the model is carried out to determine the conditions that favour the spread of the disease in a given population. Numerical simulation of the model carried showed that an increase in protection leads to low disease prevalence in a population.

Open Access Original Research Article

On Approximate Solution of Fractional Differential Equations with Variable Coefficients

Hammad Khalil, Rahmat Ali Khan

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/BJMCS/2016/23568

In this paper we study some interesting properties of shifted Jacobi polynomials and based on these properties a new operational matrix is derived. The new matrix is then used along with some previous results to provide a theoretical treatment to approximate the solution of fractional differential equations with variable coefficients. The scheme is then extended to solve coupled system of fractional differential equations with variable coefficients. The scheme is simple and provides a very high accurate estimate of solution. The accuracy of the scheme is shown with some test problems. The results are displayed graphically. We use MatLab to carry out the necessary calculation.