Non-Homogeneous Differential Equations to A Laplace Transform – Based on Cryptographic Process

Non-Homogeneous Differential Equations to A Laplace Transform – Based on Cryptographic Process

Ramya DR1, Prashantha R2

1, Department of Mathematics, GMIT, Bharathinagara, Mandya-571422

email ID: ramyadr.gmitmat@gmail.com

2, Department of Mathematics, GMIT, Bharathinagara, Mandya-571422

email ID: rprashanth3@gmail.com

Abstract: The study of non-homogeneous differential equations is crucial in various scientific and engineering applications. This paper explores the application of the Laplace Transform method in solving such equations, particularly in the context of cryptographic processes. The Laplace Transform simplifies the solution process by converting differential equations into algebraic equations in the frequency domain, making it an effective tool for cryptographic algorithm design and security analysis. By leveraging this approach, we aim to enhance encryption mechanisms, ensuring robust data protection. This research highlights the significance of mathematical transformations in modern cryptographic systems, offering insights into secure communication protocols.