هيام خزعل حسن الخياط

The main purpose of utilizing s-box (static, or dynamic) is to encrypt data with/without decrypt cipher-data, s-box may be a public in the cipher method, but if it’s private and included with steps of the cipher method, and depended it on the key cipher method. This work used the integer chaos data which are generated from the tent chaos map and symmetric group Sn in order to generate the private dynamic s-box between the sender and the receiver. An initial n × m s-box constructed by utilizing the random mixed between integer chaos sequence, and key method, with random element of symmetric group. The generation of s-box depend on the sequence Ics, where Ics generated from chaos sequence called Tent map is a simple linear function T(xn) such that to convert Tent chaos sequence x1, x2, …, xn to integer sequence d1, d2, …, dn. When the proposed method analyzed provide high randomness and high sensitivity to any simple changes of the initial used values.

This paper introduces and investigate a new subclasses of the class Σμ of analytic functions that both ℊ and ℊ−1are μ-fold symmetric

Algebraic topology is a branch of mathematics which use the concepts of abstract algebra to study topological spaces in which to find algebraic invariants that classify topological spaces up to homeomorphism. In this paper. First, the basic properties of some concepts on algebraic topology such as the topological ring, the topological module, and the topological free module were recalled, which were helped to define new concepts and proof some of there properties as a new results, which we will show in our work. Then we introduce some results related to the relation between the free topological module and homomorphism topology. As in any application, we choose the tensor concept in order to explain new results about the topological module.

To prevent sensitive images shared on social media from being stolen, researchers are seeking to find and innovate image encryption algorithms. Since attackers attempt to exploit it to access encrypted images, the problem of generating keys as the first stage of any encryption algorithm is regarded as a critical problem. This issue was dealt with in this paper through the use of the logistic map. This map must be calculated using specific conditions and special parameters to maintain its chaos. The Diffie-Hellman key exchange algorithm was modified to address this problem since the shared keys now consist of a 16-element vector. The first two elements will be used for a logistic map. The entire vector was used to create a self-invertible matrix. The encryption level entails two operations: the first is matrix multiplication with a vector, and the second is a bitwise XOR operation between two matrices. A proposed encryption algorithm is capable of producing encrypted images that are challenging to decrypt through the use of stringent security tests. The outcomes of each test showhowwell the proposed encryption algorithm performs compared with other algorithms and how to resist the attacks.

الغرض الرئيسي من استخدام s-box (ثابت أو ديناميكي) هو التشفير البيانات مع/بدون فك تشفير البيانات المشفرة، قد يكون s-box عامًا في طريقة التشفير، أما إذا كانت خاصة ومتضمنة مع خطوات طريقة التشفير، ومعتمدة ذلك على طريقة التشفير الرئيسية. استخدم هذا العمل بيانات الفوضى الصحيحة التي هي تم إنشاؤها من خريطة فوضى الخيمة والمجموعة المتماثلة Sn من أجل إنشاء صندوق s ديناميكي خاص بين المرسل والمستقبل. صندوق أولي n × m s تم إنشاؤها باستخدام العشوائي المختلط بين تسلسل الفوضى الصحيح و الطريقة الرئيسية، مع عنصر عشوائي من مجموعة متماثلة. جيل s-box تعتمد على تسلسل Ics، حيث يتم توليد Ics من تسلسل فوضوي يسمى Tent الخريطة هي دالة خطية بسيطة T(xn) بحيث يمكن تحويل تسلسل فوضى الخيمة x1، x2,..., xn إلى تسلسل صحيح d1, d2,..., dn.عندما تم تحليل الطريقة المقترحة توفر عشوائية عالية وحساسية عالية لأية تغييرات بسيطة في البداية القيم المستخدمة.