On Two Novel Generalized Versions of Diffie-Hellman Key Exchange Algorithm Based on Neutrosophic and Split-Complex Integers and their Complexity Analysis

Dima Alrwashdeh^1,*, Talat Alkhouli², Ahmed Soiman Rashed Alhawiti³, Ali Allouf⁴, Hussein Edduweh⁵, Abdallah Al-Husban⁶

¹Department of Information Technology, School of Information Technology and System, the University of Jordan, Aqaba, Jordan

²Applied Science Department, Aqaba University College, Balqa Applied University, Jordan

³Department of General Studies, Technical College of Haql, Tabuk, Kingdom of Saudi Arabia

⁴Tishreen University, Faculty Of computer engineering and automation, Latakia, Syria

⁵Department of Mathematics, the University of Texas at Arlington, Arlington, TX 76019-0407, USA

⁶Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan

Emails: d.rawashdeh@ju.edu.jo; Talat.khouli@bau.edu.jo; ahmed.a13@tvtc.gov.sa; Ali.allouf@gmail.com; Husseinsaid.edduweh@mavs.uta.edu; dralhosban@inu.edu.jo

 Abstract

The objective of this paper is to build the Split-Complex version of Diffie-Hellman key Exchange Algorithm, where we use the mathematical foundations of Split-Complex Number Theory and Integers, such as congruencies, raising a split-complex integer to a power of split-complex integer to build novel algorithms for key Exchange depending of famous Diffie-Hellman algorithm. Additionally, we present the proposed version of the Diffie-Hellman algorithm based on neutrosophic number theory. Also, we analyze the complexity of the novel algorithms with many examples that explain their applied validity.

Keywords: Split-Complex Cryptography; Split-Complex Diffie-Hellman; Hellman key Exchange Algorithms; Neutrosophic Diffie-Hellman