Integer factorization is an important problem in modern cryptography as it is the basis of RSA encryption. I have implemented two integer factorization algorithms: Pollard’s rho algorithm and Dixon’s factorization method. While the results are not revolutionary, they illustrate the software design difficulties inherent to integer factorization. The code for this project is available at https://...

A recently developed PLUS factorization holds great promise in image coding due to its simplicity and integer reversibility. However, existing PLUS factorizations did not consider stability and optimality. To address these problems, we propose methodologies to design stable and optimal PLUS factorization algorithms. Firstly, we propose three stable PLUS factorization algorithms, prove the stabi...

The security of public key encryption such as RSA scheme relied on the integer factoring problem. The security of RSA algorithm is based on positive integer N, because each transmitting node generates pair of keys such as public and private. Encryption and decryption of any message depends on N. Where, N is the product of two prime numbers and pair of key generation is dependent on these prime ...

Triple arrays are considered in which 10 symbols each appear 3 times in a 5 × 6 arrangement of symbols. These triple arrays fall into seven isomorphism classes. The orders of the automorphism groups of the arrays in these classes are 60, 12, 12, 6, 4, 3 and 3, respectively. © 2005 Elsevier B.V. All rights reserved.

This research paper describes key information technology (IT) project management activities in terms of project scope, time, and cost management, namely the triple constraint. The authors contend that the ability to properly manage and execute these activities are the quintessential components that oftentimes drives whether projects succeed or fail. The literature shows that IT projects have a ...

We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an quadratic upper and lower bound on the length of the shortest word not in uf(L). We observe that uf(L) need not be context-free if L is context-free. Next, we con...

this study focused on triple-negative breast cancer (tnbc) that is characterized by the lack of expression of estrogen receptor (er), progesterone receptor (pr), and human epidermal growth factor receptor 2 (her-2). the primary goal of this study was to describe the relation between triple-negative receptor status and survival. this is the first study about triple-negative breast cancer in our ...

on the onset of triple-diffusive convection in a horizontal layer of nanofluid heated from below and salted from above and below is studied both analytically and numerically. the effects of thermophoresis and brownian diffusion parameters are also introduced through buongiorno model in the governing equations. by using linear stability analysis based on perturbation theory and applying normal m...