The Impact of the Largest Lyapunov Exponent and Complexity of a Hyperchaotic System on the Secure Speech Communication

The magnitude of the largest Lyapunov exponent (LE) is used as a metric of chaoticity. The Kaplan-Yorke dimension is utilized to measure the complexity of a hyperchaotic system. A system having higher largest Lyapunov exponent has more chaoticity, and a higher Lyapunov dimension exhibits more complexity. We have performed a comparative analysis considering six different hyperchaotic systems to know the impact of Lyapunov exponents and complexity on the secure speech communication system. Each hyperchaotic system is used to generate the secure encrypted and decrypted speech signals by using the proposed two steps (masking and modulation) secure speech communication technique. The degree of security of the encrypted speech signal is analyzed by some available performance measures, such as encryption correlation coefficient, Segmental Spectral Signal to Noise Ratio (SSSNR), and peredogram. The performance measures resulted by using the considered six hyperchaotic systems (two systems with higher positive LE, two with medium and the rest two with low positive LE) are compared and observed that the largest positive Lyapunov exponent and Kaplan-Yorke dimension impact the performance of the secure speech communication. A higher value of the largest Lyapunov exponent and complexity of chaotic systems result in more security in the speech communication system.