Double Mersenne number in maximum and minimum matrices

Maximum Load and Minimum Volume Structural Optimization

A bi-criteria optimization is considered whose objectives are the maximization of the load sustained by a structure and the minimization of the structure's volume. As the objectives are conflicting, the solution to the problem is of the Pareto type. The problem is elaborated for a thin-walled column of cruciform cross-section, prone to flexural and torsional buckling. A numerical example is als...

New Mersenne Number Transform Diffusion Power Analysis

Problem statement: Due to significant developments in the processing power and parallel processing technologies, the existing encryption algorithms are increasingly susceptible to attacks, such as side-channel attacks, for example. Designing new encryption algorithms that work efficiently on different platforms and security levels to protect the transmitted data from any possible attacks is one...

Tricyclic and Tetracyclic Graphs with Maximum and Minimum Eccentric Connectivity

Let $G$ be a connected graph on $n$ vertices. $G$ is called tricyclic if it has $n + 2$ edges, and tetracyclic if $G$ has exactly $n + 3$ edges. Suppose $mathcal{C}_n$ and $mathcal{D}_n$ denote the set of all tricyclic and tetracyclic $n-$vertex graphs, respectively. The aim of this paper is to calculate the minimum and maximum of eccentric connectivity index in $mathcal{C}_n$ and $mathcal{D}_n...

Modular Number Systems: Beyond the Mersenne Family

In SAC 2003, J. Chung and A. Hasan introduced a new class of specific moduli for cryptography, called the more generalized Mersenne numbers, in reference to J. Solinas’ generalized Mersenne numbers proposed in 1999. This paper pursues the quest. The main idea is a new representation, called Modular Number System (MNS), which allows efficient implementation of the modular arithmetic operations r...

Bounds on the maximum number of minimum dominating sets