INTRODUCTION TO DOMINO KLEIN-4 GROUP CRYPTOGRAPHY

Abstract

As a type of simple group in mathematics, the concept of the Klein-4 group finds applications in various fields such as biology, 2D materials, games, and more. This research combines the idea of the Klein-4 group with the rules of domino cards to create a binary operation. This binary operation serves as the encryption key, and its inverse serves as the decryption key. The comprehensive process in this study represents a novel application of the Klein-4 group in cryptography. By leveraging the structural properties of the Klein-4 group, this method introduces a unique approach to securing information. The combination of group theory and modular forms in this study enhances the complexity of the encryption and decryption processes, making it more difficult for unauthorized parties to access or interpret the data. As a result, the security of the data is significantly improved. The encryption algorithm is not only efficient but also resistant to common cryptographic attacks. This study demonstrates the potential of abstract algebraic concepts in developing practical solutions for modern-day cryptographic challenges. The research methods and proposed hypotheses in this study have been validated through the proof of the given theorems. However, this study limits the data to alphabet. Researchers interested in the field of cryptography can further develop this idea to apply cryptographic processes to other types of data.