In the public key cryptography infrastructure of electronic commerce (E-commerce), use of the Rivest, Shamir, and Adleman (RSA) algorithm is very common. Due to the security requirements, the necessary key size of RSA is increasing exponentially. Because of this large key size, it is not convenient to use RSA in resource-constrained applications where computational speed, storage and bandwidth are limited. Elliptic Curve Cryptography (ECC) is the best alternative to the traditional RSA. ECC provides the same level of security as RSA but with reduced key size. The most important factor in the use of ECC is the selection of the correct elliptic curve. There are different types of elliptic curves suggested by various standards. The selection of the curve is dependent on various parameters, such as prime field size, the shape of the curve, etc. In this paper, sets of elliptic curves recommended by different standards for cryptography are selected, and the selected curves are analysed, focusing on the performance and security features. The performance of each curve is measured in terms of computation time. The analysis is performed by considering each curve for the implementation of the Elliptic Curve Diffie-Hellman (ECDH) algorithm and the Elliptic Curve Digital Signature Algorithm (ECDSA). The comparative table of selected curves is arranged according to the computation time taken by each curve to perform various operations when used for the ECC algorithms.

One major influence on the future deployment of cellular networks will be a continuous increase in traffic inside mobile broadband systems. Moreover, traditional macrocell-based mobile communication networks will struggle to keep up with the enormous expansion in the demand for communications services in the future. Densification of networks is required if we are to meet the comprehensive needs for end terminals for a wide range of applications. One of the leading concepts in this competitive environment is the Ultra-Dense Network (UDN) where the access nodes and/or the communication links per unit area are densified, with the aim of improving overall network performance. The location of the UDN nodes meets the criteria for symmetry with a high probability. Ultra-dense cell deployment aims to reduce the physical distance between the transmitter and receiver in order to boost system performance and generally optimize the values of a wide variety of key performance indicators (KPIs). This paper aims to provide a taxonomy of UDNs and specifically of UDN-related KPIs. Initially, we address the complex questions “What is the current understanding of what ultra-dense networks are and what they should be, and how can we measure their performance?” by shedding light on the fundamental characteristics of UDNs.

Nowadays, Low-power Wide Area Networks (LPWANs) hold much promise, due to their low-power, low-cost, and low throughput nature. The very long range of LPWA technologies enables devices to spread and move over large geographical areas, thus creating excellent opportunities for new IoT technologies and for Wireless Sensor Networks (WSNs) in general. In this context, LoRa (Long Range) technology represents a highly important example of wireless technology working in high-density networks. LoRa Wide-Area Networks (LoRaWANs) are characterised by low data rate requirements per device, large cells and heterogeneous application domains, which can lead to extremely high numbers of devices coexisting in the same cell. The coexistence of other technologies operating in the same ISM (Industrial Scientific and Medical) band may lead to increased interference. In this paper an overview of interference management in LoRaWANs is performed, encompassing different approaches, methods and algorithms to deal with interference in the ISM band. We focus on the so-called Co-Spreading Factor Interference (CSFI) and Inter-Spreading Factor Interference (ISFI) occurring when the useful and interference signal use the same or different SFs. We aim to show via link-level simulations the impact of coding rate and bandwidth on this imperfect orthogonality-based CSFI and ISFI.

In this paper, a new method for designing orthogonal bicomplex digital signal processing (DSP) algorithms is developed. In contrast to those previously reported on, the method proposed is universal, since it is not affected by the order or the type of the real digital processing algorithm employed as a prototype. The method is based on a transformation starting with either real or complex orthogonal DSP algorithms represented in the z-domain, and transforming them into orthogonal bicomplex algorithms. The proposed new method is applied in the design of bilinear orthogonal bicomplex DSP systems with a canonical number of elements, the main advantage of which is that the order of the digital system is reduced by a factor of four. As well as being canonical, the orthogonal bicomplex digital systems are also symmetrical structures, as a result of which they offer parallelism and subsequent unification. It is experimentally shown that bicomplex orthogonal DSP algorithms acquire the properties of the initial algorithm prototype, irrespective of whether it is real or complex. Since the new design method is universally applicable, it can be used to develop bicomplex orthogonal digital algorithms of any order and type. Being simple, canonical, and symmetrical—and, thus, leading to lower equipment cost, reduced complexity, and higher energy efficiency—these structures may well be appropriate for the enhancement of the implementation of intelligent algorithms in next-generation radio access networks.

Mathematics is the wide-ranging solid foundation of the engineering sciences which ensures their progress by providing them with its unique toolkit of rules, methods, algorithms and numerical systems. In this paper, an overview of the numerical systems that have currently found an application in engineering science and practice is offered, while also mentioning those systems that still await full and comprehensive applicability, recognition, and acknowledgment. Two possible approaches for representing hypercomplex numbers are proposed—based on real numbers and based on complex numbers. This makes it possible to justify the creation and introduction of numerical systems specifically suited to digital signal processing (DSP), which is the basis of all modern technical sciences ensuring the technological progress of mankind. Understanding the specifics, peculiarities, and properties of the large and diverse family of hypercomplex numbers is the first step towards their more comprehensive and thorough study, and hence their use in a number of high-tech intelligent applications in various engineering and scientific fields, such as information and communication technologies (ICT), communication and neural networks, cybersecurity and national security, artificial intelligence (АI), space and military technologies, industrial engineering and machine learning, astronomy, applied mathematics, quantum physics, etc. The issues discussed in this paper are, however, far from exhausting the scientific topics related to both hypercomplex numbers in general and those relevant to DSP. This is a promising scientific area, the potential of which has not yet been fully explored, but research already shows the enhanced computational efficiency and intelligent performance of hypercomplex DSP.

Jamming attacks present a major challenge for the physical layer security of wireless communication systems. Among the large number of existing methods for jamming mitigation, filtering is a simple but promisingly effective solution that can be applied in resource-constrained and low-power wireless networks. In this article, a first-order adaptive complex narrowband notch filter is proposed for use against high-power narrowband jamming attacks. The central frequency of the filter is adaptively adjustable to match the interfering frequency. This enables the proposed solution to perform effectively in the presence of a jammer whose frequency varies in fixed or random time periods. The simulation results demonstrate the filter's behavior and the efficiency of the proposed technique.