On Modelling and Simulation of Electric Circuit Problems

Differential equations are of fundamental importance in Mathematics, Physical Sciences and Engineering Mathematics. Many mathematical relations and physical laws appeared in the form of such equations. This paper reviewed an application of these equations in solving mathematical model on electric circuit problems using the First order linear differential equation. The analytical approached in solving the equations confirmed that solving electric circuits using first order linear ordinary differential equations gives accurate and reliable result. Therefore, the application is of importance and great need. However, complex problems need higher order differential equations, which are nonlinear and have entirely different approach in finding their solutions.

Modified Conjugate Gradient Method via DFP Update for Solving Systems of Nonlinear Equations

In this study, a fully derivative-free method for solving large scale nonlinear systems of equations via memoryless DFP update is presented. The new proposed method is an enhanced DFP (Davidon-FletcherPowell) update which is matrix and derivative free thereby require low memory storage. Under suitable conditions, the proposed method converges globally. Numerical comparisons using a set of large-scale test problems showed that the proposed method is efficient.

A Different Encryption System Based on the Integer Factorization Problem

We present a new computational problem in this paper, namely the order of a group element problem which is based on the factorization problem, and we analyze its applications in cryptography. We present a new one-way function and from this function we propose a homomorphic probabilistic scheme for encryption. Our scheme, provably secure under the new computational problem in the standard model.

Efficient GeMSS Based Ring Signature Scheme

The ring signature scheme has an important usage area of public key crypto-system. It can be used for e-voting, as well as leaking information without revealing identity within a group. However, most of these systems relies on traditional crypto-systems which are not secure against quantum computing related attacks. Multivariate cryptography is one of the most popular research areas on quantum resilient crypto-systems. In this work, we propose an efficient ring signature scheme based on GeMSS, where we achieve smaller signature size and faster verification time with respect to other alternatives.

A Novel Image Encryption Approach Using Polar Decomposition and Orthogonal Matrices

Information security is one of the important issues in the information age, image encryption algorithms have been increasingly studied to guarantee the secure image transmission over the internet and through wireless networks. In this article, we propose a new approach for image encryption based on polar decomposition and orthogonal matrices. This scheme offers good confusion and diffusion qualities. The proposed algorithm is shown to be secure against important cryptanalytic attacks (statistical attacks, sensitivity dependence, differential attacks, brute force attacks...), theoretical analysis and computer simulations both confirm that it has a high security level.

Secure Hybrid Crypto-system AES/RSA on FPGA for Data Communication

With the development of information technologies, our environment is surrounded by digital data that transit via networks. When data are important, they become vulnerable to external attacks which can be avoided by using cryptography which provides confidentiality, integrity and availability required to secure digital data transactions such as e- commerce, mobile telephony and Internet. This paper deals with securing data transmitted over a network composed by a server and several clients, where a security platform has been integrated into the server and embedded on an FPGA circuit. The protection of data transfer between clients is provided by hybrid cryptography combining symmetric and asymmetric cryptographies. The security of client-server communication is ensured by the AES protocol and the Diffie-Hellman key exchange protocol. To offer a good management of keys and their sharing, a dedicated system for generating keys is designed to fit with public key infrastructures. This system is a part of the server and has been implemented using JAVA language and executed on a computer. This communication system provides a Graphical User Interface (GUI) offering to clients ease and flexibility in transferring their data.

Efficient FPGA Implementation of Modular Multiplication and Exponentiation

This paper presents an FPGA implementation of the most critical operations of Public Key Cryptography (PKC), namely the Modular Exponentiation (ME) and the Modular Multiplication (MM). Both operations are integrated in Hardware (HW) as Programmable System on Chip (PSoC). The processor Microblaze of Xilinx is used for flexibility. Our objective is to achieve a best trade-off between execution time, occupied area and flexibility. In order to satisfy this constraint, Montgomery Power Ladder and Montgomery Modular Multiplication (MMM) algorithms are utilized for the ME and for the MM implementations as HW accelerators, respectively. Our implementation approach is based on the digit-serial method for performing the basic arithmetic operations. Efficient parallel and pipeline strategies are developed at the digit level for the optimization of the execution time. The application for 1024-bits data length shows that the MMM run in 6.24 µs and requires 647 slices. The ME is executed in 6.75 ms, using 2881 slices.

A New Approach to Verifying and Sharing a Secret QR Code using Elliptic Curves

One of the modern applications of cryptography is the sharing of secrets in occurrence keys. Indeed, the need to establish a shared secret key in a multi-user system clearly remains a major problem of trust between users. Therefore, one solution is to share this secret key between users seamlessly. New technologies embedded systems such as sensor networks provide an ideal platform for sharing secrets. In addition, elliptic curves offer an adequate solution for reducing the size of keys, which is suitable for embedded systems. In this article, we propose an approach for sharing a secret leaked in a QR code adapted for a multiuser system, where each user has the ability to verify its share by an access structure. The system allows a recovery without loss of data in this case the QR code used.