Cryptography Security of Digital Signals using Golden Matrix with Recurrence Relations

Abstract

Modern cryptography is a field of study and practice that involves creating secure communication and data protection systems. Its primary goal is to ensure authenticity, integrity, and confidentiality of information in the presence of adversaries or potential attackers. Digital signatures are a crucial component of modern cryptography, providing validation, data privacy protection in digital communication. These are used to verify the authenticity of a digital message or document and ensure that no changes have been made to it since the signature was applied. . We can explore new methods for safeguarding digital signals using the Golden Matrix. The golden matrix, constructed using mathematical principles of the golden ratio, exhibits self-similarity and deterministic complexity, making it a robust foundation for encryption. Recurrence relations, such as those found in Fibonacci sequences, add an additional layer of security by introducing dynamic and pseudo-random transformations. We want to compare the time complexity in FP transform and Vigenere Cipher. Time complexity of the proposed algorithms is better than Vigenere Cipher also proposed algorithms have multilevel security so it’s more secure and authenticate for networks. Furthermore, the method's efficiency makes it suitable for real-time digital signal encryption, such as video streaming, audio communication, and data transfer. Experimental results demonstrate the robustness, scalability, and computational efficiency of this technique, proving its viability for securing digital communication in modern networks.