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Currently, low-dimensional chaotic maps have many disadvantages, such as narrow chaotic regions, numerous cycle windows, and weak chaotic representations. Based on this issue, an n -dimensional non-degenerate chaotic system (n D - NDCS) is constructed. By setting the control parameters of the system, we can obtain dimensionally adjustable non-degenerate chaotic systems with desired Lyapunov exponents. Compared with existing methods, the proposed n D - NDCS has a simple structure with few control parameters, which is suitable for resource-constrained scenarios, such as small embedded devices and mobile devices. To demonstrate the practicality of the proposed method, we construct a 3D - NDCS and a 4D - NDCS as two examples. Performance evaluations show better randomness and complexity than other methods in terms of sample entropy, permutation entropy and other indicators. Since both chaotic systems can produce pseudo-random sequences with sensitive initial values and strong randomness, we further design an efficient pseudo-random number generator (PRNG) on the FPGA. The experiment results show that the proposed PRNG occupies merely 3.13 % of the effective resources of the target FPGA. In addition, the throughput of the PRNG which obtained from post-processing is up to 15 Gb/s, and successfully passed the NIST SP800-22 test. Finally, an FPGA-based hardware implementation platform is developed to realize the proposed PRNG. [ABSTRACT FROM AUTHOR]

Lyapunov exponents (LEs) characterize the average exponential rate of convergence or divergence between adjacent orbits in phase space. Thus, the number of positive LEs can reflect the complexity of chaotic systems from a certain point of view. To resist the dynamic degradation of digital chaos, we propose a novel universal method that is based on QR decomposition for constructing non-degenerate hyperchaotic maps. A large number of positive LEs can be generated to increase the complexity of chaotic systems. Furthermore, we construct a 4-D discrete non-degenerate hyperchaotic map as an example to demonstrate the adaptability and efficacy of the proposed scheme. For the proposed method, the related control parameters can not only effectively adjust Lyapunov exponents, but also carry out chaotic regulation on the discrete map, such as amplitude control and offset boosting. In addition, a pseudorandom number generator (PRNG) is designed with desirable statistical properties. Then, a microcontroller-based platform was developed to implement the proposed chaotic map. This study is interesting and has a potential for real-world applications, such as secure communication and cryptography. [ABSTRACT FROM AUTHOR]

Digital chaotic maps are severely hampered by the finite calculation accuracy of the hardware device that is used to implement them, and their applications in cryptography and information assurance are seriously degraded. To resolve this issue, we put forward a universal iterative model to construct non-degenerate polynomial chaotic maps with any desired number of positive Lyapunov exponents. In addition, we innovatively propose the geometric control methods of polynomial chaotic maps, including amplitude control, offset boosting, plane rotation, shape control, and combined regulation. Furthermore, to assess the effectiveness and feasibility of the proposed method, a microcontroller-based platform was developed to demonstrate the hardware implementation and geometric control of the proposed polynomial chaotic map. Finally, a PRNG is constructed by interval quantization. Numerical experiments are performed to verify the desirable statistical properties of the PRNG in terms of local weak random test, discrete Fourier transform test, linear complexity and NIST SP800-22 test. [ABSTRACT FROM AUTHOR]

Due to the limited machine word length of hardware devices, the dynamics of digital chaotic systems will degenerate. To combat this issue, we proposed a universal method that is based on singular value decomposition (SVD), which can reversely construct non-degenerate hyperchaotic systems with any desired number of positive Lyapunov exponents by controlling pre-specified singular values. To assess the practicability and effectiveness of the method, we construct a 6-dimensional non-degenerate hyperchaotic system as an example. Furthermore, based on the hyperchaotic system, a pseudorandom number generator (PRNG) with desirable statistical characteristics is designed for image encryption. Numerical simulations were performed to evaluate the security of the image encryption algorithm in terms of histogram, information entropy, differential attack test, etc. The proposed non-degenerate hyperchaotic system can be effectively applied in the field of multimedia data encryption and information security. [ABSTRACT FROM AUTHOR]