Application of Walsh Transformations for Encryption and Decryption of Audio Signals

<p><strong><span>This paper explores using the Walsh-Hadamard Transform (WHT) to encrypt and decrypt audio signals. WHT, known for its computational efficiency and orthogonality properties, enables the decomposition of a signal into spectral coefficients, which can then be securely masked using a random key. Additionally, the article investigates the application of the Discrete Cosine Transform (DCT) alongside WHT and their combined variant (DCT-WHT) for encrypting and decrypting audio signals. WHT, characterized by its high computational speed, and DCT, known for its high accuracy, demonstrate significant efficiency in the encryption and decryption process [1], [2]. The study provides a detailed algorithm for preprocessing signals, including normalization, padding signal lengths to the nearest power of two, and applying forward and inverse WHT transformations. A novel masking technique is introduced, leveraging the properties of Walsh basis functions to enhance data security. Practical implementation involves converting input audio signals into WAV format, applying the WHT or the combined DCT-WHT approach, encrypting the coefficients with a random key, and reconstructing the original signal using inverse transformations. The proposed methods ensure reconstruction accuracy exceeding 99.9%, maintaining high fidelity while providing robust attack resistance. This approach efficiently transmits audio data securely in communication systems, multimedia applications, and other areas requiring robust encryption mechanisms. Additionally, the study explores the possibility of combining WHT with other signal processing algorithms, such as DCT or the Fourier Transform, to further enhance security features. The combined use of these methods improves resistance to attacks through multi-layer spectral transformation of the signal while retaining computational efficiency and noise resilience [1], [2]. The study highlights the promise of the DCT-WHT approach as a versatile and adaptable tool within modern cryptographic frameworks, offering a simple yet effective solution for the secure transmission and processing of audio data<span>  </span>[2].</span></strong></p>