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Pseudorandom encoders represent a significant type of absolute position encoders that can be implemented using only a single code track on a code disk and a single reading head, making them especially suitable for high-resolution position measurements. Since pseudorandom code words used for encoding positions are not compatible with other electronics, pseudorandom encoders include a converter that translates the pseudorandom code into the natural binary code. This paper proposes an improved implementation of the serial Fibonacci pseudorandom/natural code converter used in pseudorandom position encoders. The improvement is based on modifying the way bits are written into the converter’s shift register, which reduces the propagation delay inside the code converter, thus enabling an increase in the clock frequency. Simulations of the proposed solution, performed in Multisim software, provide a realistic picture of its behaviour and performance. Based on the simulation results, the proposed solution enables a significant increase in the clock frequency of the code converter by 180.54% or 57.56%, depending on the encoder resolution. This significantly boosts the speed of code conversion and enhances the overall performance of the position encoder. The proposed solution is highly valuable for numerous position measurement applications, especially in the increasingly relevant high-resolution applications.

A change in neuronal-action potential can generate a magnetically induced current during the release and propagation of intracellular ions. To better characterize the electromagnetic-induction effect, this paper presents an improved discrete Rulkov (ID-Rulkov) neuron model by coupling a discrete model of a memristor with sine memductance into a discrete Rulkov neuron model. The ID-Rulkov neuron model possesses infinite invariant points, and its memristor-induced stability effect is evaluated by detecting the routes of period-doubling and Neimark-Sacker bifurcations. We investigated the memristor-induced dynamic effects on the neuron model using bifurcation plots and firing patterns. Meanwhile, we theoretically expounded the memristor initial-boosting mechanism of infinite coexisting patterns. The results show that the ID-Rulkov neuron model can realize diverse neuron firing patterns and produce hyperchaotic attractors that are nondestructively boosted by the initial value of the memristor, indicating that the introduced memristor greatly benefits the original neuron model. The hyperchaotic attractors initially boosted by the memristor were verified by hardware experiments based on a hardware platform. In addition, pseudorandom number generators are designed using the ID-Rulkov neuron model, and their high randomness is demonstrated based onstrict test results.

Recently, chaotic maps have been considered to design pseudorandom number generator (PRNG). However, some chaotic maps present security disadvantages, such as low uniformity and low randomness properties. Nowadays, chaos-based PRNGs are used as the main source for the development of cryptographic algorithms. In this work, to overcome such weaknesses, a novel 2D hyperchaotic map is proposed based on discrete-time feedback by using Hénon map and Sine map. In addition, the dynamics of the hyperchaotic map are enhanced by using the remainder after division function ( ), where better random statistical properties are obtained. A comparison is made between the enhanced Hénon-Sine hyperchaotic map (EHSHM) and the Hénon-Sine hyperchaotic map through Lyapunov exponent analysis, attractor trajectory, histograms and sensitivity at initialization. Then, 8-bit pseudorandom number generator based on the proposed hyperchaotic map (PRNG-EHSHM) is designed and the initial seed of the PRNG is calculated by a secret key of 60 hexadecimal characters. It is implemented in both MATLAB and Arduino Mega microcontroller for experimental results. A complete security analysis is presented from a cryptographic point of view, such as key space, floating frequency, histograms and entropy of the information. Moreover, the randomness is verified with the tests of the National Institute of Standards and Technology (NIST 800-22). Based on the security results obtained, the proposed PRNG-EHSHM can be implemented in embedded cryptographic applications based on chaos.

The paper addresses the challenge of enhancing the resilience of stream ciphers against attacks. It reviews existing approaches to stream cipher creation and proposes new methods that incorporate time delays to introduce gaps in the original message and embed additional bits. These methods result in a ciphertext that is longer than the original message, potentially altering the frequency if the overall transmission time is equalized. The paper explores methods that generate ciphers with varying lengths of bit insertion, enabling the creation of different length ciphers from a single input message. A method featuring frequent insertion of single bits, generated by additional pseudo-random number generators (PRNG), is implemented. The study examines both variable-length ciphergrams and fixed maximum insertion bit methods. A pseudo-random control bit sequence is employed to determine random insertion points or groups of additional bits, which are also generated pseudo-randomly. To facilitate controlled delays, specialized hardware has been developed for both the transmitting and receiving ends, ensuring synchronous message transmission. The additional stability of these stream ciphers, enhanced through time delays, is further reinforced by bitwise mixing using the initial key gamma. These methods not only increase resistance to decryption but also introduce new challenges for cryptanalysts.

We study the problem of constructing strong approximate unitary \\(k\\)-designs on \\(D\\)-dimensional grids (and more generally on Cartesian products of graphs), building on the work of Schuster et al. arXiv:2509.26310 which establishes strong unitary designs in 1D and in all-to-all connectivity. We provide two constructions. The first construction leverages the existing all-to-all connectivity result with general routing theory to provide flexible (but slightly suboptimal) strong \\(k\\)-designs in arbitrary connectivities. The second construction is more direct, requires no auxiliaries and has provably optimal depth (in the number of qubits \\(n\\)) for \\(D\\)-dimensional grids with constant dimension. Combining these techniques also allows us to construct strong pseudorandom unitaries on \\(D\\)-dimensional grids with provably optimal depth.

A multiple-image encryption algorithm based on single-channel scrambling, diffusion and chaotic system is presented in this paper. The initial values of the chaotic system are associated with the pixel values of each set of encrypted images as the key for each set of image encryption. The pseudo-random sequences and matrixes generated by the chaotic system are obtained by the corresponding keys, and then, the whole set of images are fused across-image and transferred from the RGB channel to the HSV channel after fusion. For single-channel encryption, select one of the HSV channels is extracted and encryption operations of scrambling and diffusion are performed. The index sequences generated by the chaotic sequences with zero frequency shifting rearrange the pixel positions of the encrypted channel. Combining data splitting, stack storage, and chaotic matrixes, the diffusion operation is achieved. Analyses of the performance show that the algorithm has both excellent encryption speed and security performance.

Most discrete neuron models have simple algebraic structures with easy digital implementation. However, they cannot show the abundant firing regimes of neurons. To address this issue, in this paper, we propose an improved discrete tabu learning neuron (IDTLN) model using sine nonlinearity as the activation function. Using this model, the fixed points and their stability are analyzed theoretically, the parameter-related bifurcation and regime transition behaviors as well as heterogeneous multistability are investigated by numerical tools, and the multi-scroll hyperchaotic behaviors are revealed according to the dynamics distribution in the parameter plane. It is shown that the IDTLN model has two types of fixed points, stable and unstable, and their number and stability types change with the parameters, which leads to the formation of multistability and the generation of multi-scroll hyperchaotic attractors. Besides, we design six pseudorandom number generators (PRNGs) using multi-scroll hyperchaotic sequences provided by the IDTLN model and evaluate their randomness using TestU01. The evaluation results show that this proposed neuron model has high randomness without chaos degradation, which is particularly suitable for PRNG application. Finally, we develop a digital hardware platform to verify the regime transition and multi-scroll hyperchaos of the IDTLN model.

We provide a construction of binary pseudorandom sequences based on Hardy fields H as considered by Boshernitzan. In particular we give upper bounds for the well distribution measure and the correlation measure defined by Mauduit and Sárközy. Finally we show that the correlation measure of order s is small only if s is small compared to the “growth exponent” of H .

Nonreciprocal transmission is essential in a wide range of applications due to its unique ability to control the flow of signals or energy in a specific direction without allowing for its reversal. This letter proposes a novel ultra‐wideband magnetless transmission line using pseudorandom noise (PN) sequence modulation. By applying the properties of strong autocorrelation for PN sequences, two PN sequences with the same elements but different delays are utilised to achieve synchronised forward transmitting propagation and unsynchronised backward isolating propagation. A pair of double‐sideband mixers are applied for the modulation. An experiment is performed to demonstrate the proposed nonreciprocal transmission line. The experimental results show that a ultra‐wideband from 0.5 to 3.5 GHz forward propagation and more than 13 dB backward isolation are achieved. The proposed nonreciprocal transmission line is compatible with silicon‐based integration. This manuscript proposes a novel ultra‐wideband magnetless transmission line that utilises pseudorandom noise (PN) sequence modulation. By leveraging the strong autocorrelation properties of PN sequences, we employ two PN sequences with identical elements but different delays to achieve synchronised forward transmitting propagation and unsynchronised backward isolating propagation. Experimental results demonstrate that the proposed nonreciprocal transmission line exhibits an ultra‐wideband isolating bandwidth with relatively low insertion loss.

In order to overcome the disadvantages of logistic map in designing chaos-based cipher, the piecewise logistic map (PLM) is presented. Some properties related to cryptography of the PLM, such as ergodicity, Lyapunov exponent, and bifurcation, are analyzed and compared with the logistic map. From the view of cryptography, the PLM owns better properties than the logistic map. Then, a novel pseudorandom number generator (PRNG) based on the PLM is proposed. Since the cryptographic properties of the PLM are enhanced, the presented PRNG achieves a trade-off between efficiency and security. Both performance analysis and simulation test confirm that our scheme is simple, secure, and efficient, with high potential to be adopted as a stream cipher for secure communication.