Full states pseudo-random projective synchronization of hyperchaotic system and corresponding secure communication algorithm

This paper proposes a more general and complicated synchronization scheme, termed full states pseudo-random projective synchronization (FSPRPS). In this synchronization scheme, the scaling factor is a function matrix composed of external pseudo-random sequences. It makes many existing synchronization schemes special cases of FSPRPS. Via modified active control, the proposed synchronization is realized efficiently between hyperchaotic systems. Meanwhile, based on FSPRPS, a novel secure communication algorithm who overcomes several shortcomings of many existing algorithms is constructed. In this algorithm, two systems are utilized to implement encryption. The information signal is inserted into these two systems to participate the generation of several chaotic signals. Then, the transmitted signals are masked and scrambled twice by these chaotic signals to enhance the security. In simulations, RGB color images are taken as the information signal to exhibit the feasibility and validity of the proposed algorithm. In performance analyses that followed, this algorithm is proved as huge size of key space ( \(\ge {2}^{1020}\) $\ge 2^{1020}$ ), high sensitivity to keys and plaintexts (PSNR is about 99.62%), excellent statistical properties (information entropy is about 7.9993), strong robustness and high processing efficiency (encryption time for a \(512\times 512\) $512\times 512$ RGB image is about 1.6 s). These all demonstrate the feasibility, robustness, high security and effectiveness of the algorithm, which can serve as an effective reference for constructing other synchronization schemes and secure communication algorithms.