Contribution to chaotic encryption methods for digital data

Abstract

In this thesis, we investigate the development process of chaos-based image encryption algorithms from various perspectives, including the serious challenge of generating secure random number sequences for use as dynamic encryption keys. First, at the aim of improving the randomness and non-periodicity qualities of the basic pseudo-random number generators (PRNG) used as key-stream generators, we exploit the unique attributes of the logistic map (LM), logistic-sine system(LSS), linear feedback shift registers (LFSR), and nonlinear feedback shift register (NLFSR) to design new key-stream generators (namely: LSS-LFSR-PRNG, LM-NLFSR-PRNG, and LSS-NLFSR-PRNG). Therefore, our generators succeed in generating unlimited, random, and nonlinear sequences by passing the totality of the National Institute of Standard and Technology (NIST) statistical tests, and displayed strong cryptographic security, resulting in high entropy, high key sensitivity, and large key space exceeding 2^100. The second goal highlights the importance of selecting an appropriate chaos-based architecture for confusion and diffusion. The dimensions of the chaos-based confusion-diffusion architecture vary depending on the specific chaotic map being used. Hence, we design three confusion-diffusion algorithms of various levels (1D LM-based cryptosystem, 1D LM-Chebyshev-based cryptosystem, and 3D intertwining logistic map-cosine (ILM) based cryptosystem), to discuss and demonstrate the impact of choosing the appropriate dimension of the chaotic map on the vulnerability of a cryptosystem. It has been proven that higher-dimensional chaotic maps, such as 3D-ILM, can enhance the ability to resist exhaustive and statistical attacks by achieving desirable values of the number of pixels change rate (NPCR) and unified average changing intensity (UACI), while these maps are unable to maintain encryption speed. The third goal of this thesis is to improve the core of the mathematical model of chaos-based cryptosystems by boosting the chaotic complexity and chaotic range of basic one-dimensional chaotic maps. Where, we propose a new nonlinear chaotification system capable of producing 1D enhanced discrete chaotic maps (enhanced tangent-Logistic map T-LM, enhanced tangent-Sine map T-SM, and enhanced tangent-Chebyshev system T-CH), by applying tangent nonlinear transforms to the outputs of the existing chaotic maps. This strategy improves the performance of basic 1D chaotic maps by exhibiting better dynamical behavior, Lyapunov exponent, bifurcation, and larger chaotic intervals