Secure Communication Scheme Based on Projective Synchronization of Hyperchaotic Systems

Abstract

AbstractThis chapter develops a secure communication scheme based on the synchronization of two hyperchaotic systems, including key statistical, dynamical, and security analyses. First, the scheme is based on the projective synchronization between two hyperchaotic systems applied to image encryption. The encryption process comprises the generation and discretization of chaotic sequences, the transformation of the sequence elements into the image domain, and the modulo operation as encryption transformation. Second, the reliability and robustness of the proposed scheme are evaluated through the primary dynamical, statistical, and security analyses such as spectral and dynamical complexity, sensitivity, unpredictability, chaotic range, elements distribution, and randomness characteristics, key space definition, and resistance to distortion analysis, return map analysis, differential attack, decryption, and brute force attacks. Finally, the experimental results give evidence of the feasibility and robustness of the chaotic scheme. They show that using high-dimensional chaotic systems such as hyperchaotic systems combined with projective synchronization improves the confusion and diffusion properties, increases the key space, and limits the effectiveness of decryption, distortion, differential, generalized and adaptive synchronization, return map and brute force attacks.