Abstract In this study, we propose a method in order to estimate the strength of a cryptographic algorithm. The method combines the evaluation of the cryptographic key length and the evaluation of the success rate of the randomness tests in the algorithm output samples. In the first step, the algorithm is classified into one of four general categories, according to its key size, taking into account the current computer power which a cryptanalyst can use for exhaustive key search. In the second step, we examine the success rate of the tests on the output samples. For this, the maximum accepted number of the rejected samples is calculated, taking as parameters the total number of samples (which depends from the selected sampling error) and the desired significance level and confidence interval for the success rate of the tests. If the rejected samples do not exceed the maximum number, the algorithm is considered as “random” and it is rated in the initial strength category due to its key size. If the rejected samples exceed the maximum number, the algorithm is submitted to further tests under certain conditions. Keywords: Cryptography, Data encryption, Communication security, Computer security, Data security, Information security.
Abstract In this communication, we study the existence of nonnegative solutions of a nonlinear system in Banach spaces. These maps involved in the system defined on cone do not necessarily take values in the cone. Using fixed point theorems just established for this type of mappings, nonnegative solutions of the system are obtained and used to investigate elliptic boundary value problems (BVPs). MSC(2010): 47H10, 35J57. Keywords: Nonlinear system, Nonnegative solutions, Nowhere normal-outward maps, Fixed point, Elliptic BVPs.
Abstract The human circulatory system is one of the admirable rhythms of nature. The heart and the vasculature are constitutive structures. The vasculature consists of arterial and venous appurtenances which are arranged in an idealized network capable of enhancing circulation. The crux of this study is the representation of the cardiovascular system as a network in which electrical constraints apply. As a network, the system is amenable to graph analytic treatment; as edge-nodal parameters ensue, topological constraints apply. In virtue of cardiac auto-rhythmicity, electrical impulses are driven through the vessels to the body cells. As a rule, the vessels must elicit a modicum of resistance. This work weaponized the elements of graph theory and electrical properties of the heart in elucidating the flow mechanism associated with the cardio-vascular system. The voltage drop across the connecting vessels (idealized as wires) was carefully depicted and analyzed by the method of matrices. When the cardiac function is within physiological definition a vascular compartment may be a liability in the event of poor circulation. Therefore the knowledge of vascular resistive capacities, which this work portrayed, is a sine-qua-non to the assessment of flow integrity of the system under consideration. MSC 2010 No.: 05C21, 92C42, 92B25. Keywords: Cardiovascular, Network, Matrices, Flow, Circuit, Edges and Nodes, Wave propagation, Bifurcation.
Abstract In this article, a new kind of finite difference scheme that is exponentially fitted, inspired from Fourier analysis, for a fourth space derivative was developed for solving diffusion problems. Dispersion relation and local truncation error of the method were discussed. Stability analysis of the method revealed that it is conditionally stable. Compared to the corresponding fourth order classical scheme in the literature, the proposed scheme is efficient and accurate. Mathematics Subject Classification (2020): 65M06, 65N06. Keywords: Exponential fitting, Finite difference, Local truncation error, Heat equations.
