In this paper, a new modification was proposed to enhance the security level in the Blowfish algorithm by increasing the difficulty of cracking the original message which will lead to be safe against unauthorized attack. This algorithm is a symmetric variable-length key, 64-bit block cipher and it is implemented using gray scale images of different sizes. Instead of using a single key in cipher operation, another key (KEY2) of one byte length was used in the proposed algorithm which has taken place in the Feistel function in the first round both in encryption and decryption processes. In addition, the proposed modified Blowfish algorithm uses five Sboxes instead of four; the additional key (KEY2) is selected randomly from additional Sbox

The advancements in Information and Communication Technology (ICT), within the previous decades, has significantly changed people’s transmit or store their information over the Internet or networks. So, one of the main challenges is to keep these information safe against attacks. Many researchers and institutions realized the importance and benefits of cryptography in achieving the efficiency and effectiveness of various aspects of secure communication.This work adopts a novel technique for secure data cryptosystem based on chaos theory. The proposed algorithm generate 2-Dimensional key matrix having the same dimensions of the original image that includes random numbers obtained from the 1-Dimensional logistic chaotic map for given con

     In this paper, we define and study z-small quasi-Dedekind as a generalization of small quasi-Dedekind modules. A submodule  of -module  is called z-small (  if whenever  , then . Also,  is called a z-small quasi-Dedekind module if for all  implies  . We also describe some of their properties and characterizations. Finally, some examples are given.

New types of modules named Fully Small Dual Stable Modules and Principally Small Dual Stable are studied and investigated. Both concepts are generalizations of Fully Dual Stable Modules and Principally Dual Stable Modules respectively. Our new concepts coincide when the module is Small Quasi-Projective, and by considering other kind of conditions. Characterizations and relations of these concepts and the concept of Small Duo Modules are investigated, where every fully small dual stable R-module M is small duo and the same for principally small dual stable.

Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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In this paper, we introduce the concept of e-small M-Projective modules as a generalization of M-Projective modules.

The reliance damages for depending upon the contract are considered as a type of damages arising from the breach of the contract, which are included within the common law remedies for the damage and loss suffered by the non-breaching party. It is worth-bearing in mind that the reliance damages are monetary in nature, and different from such equitable remedies as the specific performance and the injunction which are of real nature. It is to be noted that this piece of research is dedicated to study the concept of the reliance damages in the English law, as well as their states, the judicial doctrines upon which this type of damages is based, and the manner how the courts estimate them. Compared with situation of the Iraqi civil law No. (4

Numerical study of separation control on symmetrical airfoil, four digits (NACA

0012) by using rotating cylinder with double steps on its upper surface based on the computation of Reynolds-average Navier- Stokes equations was carried out to find the optimum configuration of unconventional airfoil for best aerodynamics performance. A model based on collocated Finite Volume Method was developed to solve the governing equations on a body-fitted coordinate system. A revised (k-w) model was proposed as a known turbulence model. This model was adapted to simulate the control effects of rotating cylinder. Numerical solutions were performed for flow around unconventional airfoil with cylinder to main stream velocities ratio in the range