Chaotic systems have been extensively applied in image encryption as a source of randomness. However, dynamical degradation has been pointed out as an important limitation of this procedure. To overcome this limitation, this paper presents a novel image encryption scheme based on the pseudo-orbits of 1D chaotic maps. We use the difference of two pseudo-orbits to generate a random sequence. The generated sequence has been successful in all NIST tests, which implies it has adequate randomness to be employed in encryption process. Confusion and diffusion requirements are also effectively implemented. The usual low key space of 1D maps has been improved by a novelty procedure based on multiple perturbations in the transient time. A factor using the plain image is one of the perturbation conditions, which ensures a new and distinct secret key for each image to be encrypted. The proposed encryption scheme has been efficaciously verified using the Lena, Baboon, and Barbara test images.

This work presents an architecture to compute matrix inversions in a hardware reconfigurable FPGA with single-precision floating-point representation, whose main unit is the processing component for Gauss-Jordan elimination. This component consists of other smaller arithmetic units, organized to maintain the accuracy of the results without the need to internally normalize and de-normalize the floating-point data. The implementation of the operations and the whole unit take advantage of the resources available in the Virtex-5 FPGA. The performance and resource consumption of the implementation are improvements in comparison with different more elaborated architectures whose implementations are more complex for low cost applications. Benchmarks are done with solutions implemented previously in FPGA and software, such as Matlab.

Chaos-based image encryption schemes have been extensively employed over the past few years. Many issues such as the dynamical degradation of digital chaotic systems and information security have been explored, and plenty of successful solutions have also been proposed. However, the impact of finite precision in different hardware and software setups has received little attention. In this work, we have shown that the finite precision error may produce distinct cipher-images on different devices. In order to overcome this problem, we introduce an efficient cryptosystem, in which the chaotic logistic map and the Galois field theory are applied. Our approach passes in the ENT test suite and in several cyberattacks. It also presents an astonishing key space of up to $2^{4096}$ . Benchmark images have been effectively encrypted and decrypted using dissimilar digital devices.

Chaotic systems have been applied in many applications involving instrumentation and measurements, such as in sensors and control systems, due to their pseudo-random proprieties. However, reproducing chaos in digital systems is challenging because of the dynamical degradation of chaotic digital systems and, consequently, their intrinsic periodic orbits. Many techniques have been employed to guarantee a sufficiently large period, making them suitable for such applications. Nevertheless, few papers pay attention to the effects of using different numerical representations on chaos degradation and, at the same time, keeping key design parameters, such as few logical resources and power consumption. Thus, this paper aims to provide a new hardware architecture for a chaos-based PRNG using the Half-Unit-Biased (HUB) format for fixed-point numbers by bi-coupling the tent map in conjunction with the Bernoulli map, causing a significant impact on its logical resources and performance. Results show that the HUB format is more effective than the standard fixed-point numerical representation and that the proposed approach is chaotic, with pseudo-randomness.