Applications of Eisenstein Rings and Elliptic Curves in Cryptography

Abstract

The ease of access and simplicity in handling digital content, such as electronic advertising, videos, audios, digital repositories, electronic libraries, and web de sign, raise several security concerns. With the widespread availability of digital information through the internet and other sources, researchers have been focusing on developing secure solutions to protect data security. Digital images play a crucial role in communication between different locations. Secure communication occurs when two entities exchange information without the need for a third party to eavesdrop. Keeping this in mind, experts have proposed various techniques for ensuring the secure transmission of digital data. While there are numerous secure technical methods documented in literature, there is always room for improvement in safeguarding data security. The important component of modern cryptographic systems are S-boxes. They make the cryptosystem nonlinear and ensure its crypto graphic security. This thesis delves into the intricate realm of Eisenstein rings and Elliptic curve-based S-boxes, unveiling their potential applications in the domain of image encryption. As we navigate through the theoretical foundations, practical implementations, and experimental validations, this work strives to contribute to the advancement of cryptographic methodologies. The convergence of algebraic structures, elliptic curves, and image encryption not only underscores the significance of interdisci plinary research but also presents an opportunity to enhance the robustness of cryptographic systems. This thesis is a testament to the pursuit of knowledge, aiming to bridge theoretical concepts with practical implications in the pursuit of secure and efficient image encryption techniques