Comparative analysis to security of digital signals using Fibonacci – Pell transform and Vigenere Cipher

Abstract

In the modern era of digital communication, the need for secure data transmission is critical. This paper proposes a novel cryptographic technique that integrates the mathematical properties of Fibonacci and Pell sequences to encrypt digital signals. By leveraging the Fibonacci-Pell Transform (FPT), the method enhances the complexity of signal encryption while maintaining computational efficiency. The proposed method is evaluated against conventional cryptographic methods with regard to security strength, computational overhead, and robustness against common attacks. Conversely, the Vigenere Cipher, a classical poly alphabetic substitution cipher, employs a repeating key to encrypt plaintext, offering simplicity and ease of implementation. However, its susceptibility to frequency analysis and known-plaintext attacks, especially when short keys are used, raises concerns about its robustness in modern applications. Through simulations and security assessments, this paper compares the two methods in terms of key sensitivity, resistance to statistical attacks, and computational efficiency. The findings suggest that while the Vigenere Cipher provides a foundational understanding of encryption techniques, the Fibonacci–Pell Transform offers enhanced security features suitable for contemporary digital signal protection.