Secured Digital Healthcare system using Noetherian Rings and SHA Algorithm

In the digital health era, safeguarding medical data is of utmost importance to ensure confidentiality, integrity, and availability. This paper presents a mathematical approach to encryption and secure data management, leveraging vector spaces and matrix operations to enhance the security of medical records. By integrating advanced encryption techniques rooted in linear algebra, we propose a framework that fortifies data protection while maintaining authorized accessibility. Furthermore, we explore the mathematical underpinnings of the Secure Hash Algorithm (SHA), with a particular emphasis on its cryptographic security. Our analysis dissects SHA's structural components through mathematical constructs such as vector spaces, linear transformations, and permutation matrices. By establishing correlations between these mathematical principles and SHA’s operational processes, we gain deeper insights into its robustness against cryptographic attacks. The proposed framework not only reinforces the security of medical records but also provides a systematic approach to analyzing cryptographic techniques through a mathematical lens. This study underscores the pivotal role of linear algebra in contemporary encryption methods and highlights its potential in securing sensitive medical information in an increasingly digital landscape