Today’s communication systems are in need of spectrally efficient and high throughput techniques more than ever because of high data rate applications and the scarcity and expense of bandwidth. To cope with increased data rate demands, more base stations are needed which is not cost and energy efficient in cellular networks. It has been shown that wireless relay networks can provide higher network throughput and increase power efficiency with low complexity and cost. Furthermore, network resources can be utilized more efficiently by using network coding in relay networks. A wireless relay network in which multiple nodes exchange information with the help of relay node(s) is called a multi-way relay channel (MWRC). MWRCs are expected to be an integral part of next generation wireless standards. The main focus of this dissertation is the investigation of transmission schemes in an MWRC to improve the throughput and error performance. An MWRC with full data exchange is assumed in which a half-duplex relay station (RS) is the enabler of communication. One of the challenges with signal demodulation in MWRCs is the existence of ambiguous points in the received constellation. The first part of this dissertation investigates a transmission scheme for full data exchange in MWRC that benefits from these points and improves its throughput by 33% compared to traditional relaying. Then an MWRC is considered where a RS assists multiple nodes to exchange messages. A different approach is taken to avoid ambiguous points in the superposition of user symbols at the relay. This can be achieved by employing complex field network coding (CFNC) which results in full data exchange in two communication phases. CFNC may lead to small Euclidean distances between constellation points, resulting in poor error performance. To improve this performance, the optimal user precoding values are derived such that the power efficiency of the relay constellation is highest when channel state information is available at the users. The error performance of each user is then analyzed and compared with other relaying schemes. Finally, focusing on the uplink of multi-way relay systems, the performance of an MWRC is studied in which users can employ arbitrary modulation schemes and the links between the users and the relay have different gains, e.g. Rayleigh fading. Analytical expressions for the exact average pairwise error probability of these MWRCs are derived. The probability density function (PDF) and the mean of the minimum Euclidean distance of the relay constellation are closely approximated, and a tight upper bound on the symbol error probability is developed. / Graduate

Dans cette thèse, nous étudions les problèmes de la factorisation d'entier et de calcul de logarithme discret dans les corps finis. Dans un premier temps, nous nous intéressons à l'algorithme de factorisation d'entier ECM et présentons une méthode pour analyser les courbes elliptiques utilisées dans cet algorithme en étudiant les propriétés galoisiennes des polynômes de division. Ensuite, nous présentons en détail l'algorithme de factorisation d'entier NFS, et nous nous intéressons en particulier à l'étape de sélection polynomiale pour laquelle des améliorations d'algorithmes existants sont proposées. Puis, nous présentons les algorithmes NFS-DL et FFS pour le calcul de logarithme discret dans les corps finis. Nous donnons aussi des détails sur deux calculs de logarithme discret effectués durant cette thèse, l'un avec NFS-DL et l'autre avec FFS. Enfin, nous étudions une étape commune à l'algorithme NFS pour la factorisation et aux algorithmes NFS-DL et FFS pour le calcul de logarithme discret: l'étape de filtrage. Nous l'étudions en détail et nous présentons une amélioration dont nous validons l'impact en utilisant des données provenant de plusieurs calculs de factorisation et de logarithme discret / In this thesis, we study the problems of integer factorization and discrete logarithm computation in finite fields. First, we study the ECM algorithm for integer factorization and present a method to analyze the elliptic curves used in this algorithm by studying the Galois properties of division polynomials. Then, we present in detail the NFS algorithm for integer factorization and we study in particular the polynomial selection step for which we propose improvements of existing algorithms. Next, we present two algorithms for computing discrete logarithms in finite fields: NFS-DL and FFS. We also give some details of two computations of discrete logarithms carried out during this thesis, one with NFS-DL and the other with FFS. Finally, we study a common step of the NFS algorithm for integer factorization and the NFS-DL and FFS algorithms for discrete logarithm computations: the filtering step. We study this step thoroughly and present an improvement for which we study the impact using data from several computations of discrete logarithms and factorizations

Data security will play a central role in the design of future IT systems. The PC has been a major driver of the digital economy. Recently, there has been a shift towards IT applications realized as embedded systems, because they have proved to be good solutions for many applications, especially those which require data processing in real time. Examples include security for wireless phones, wireless computing, pay-TV, and copy protection schemes for audio/video consumer products and digital cinemas. Most of these embedded applications will be wireless, which makes the communication channel vulnerable. The implementation of cryptographic systems presents several requirements and challenges. For example, the performance of algorithms is often crucial, and guaranteeing security is a formidable challenge. One needs encryption algorithms to run at the transmission rates of the communication links at speeds that are achieved through custom hardware devices. Public-key cryptosystems such as RSA, DSA and DSS have traditionally been used to accomplish secure communication via insecure channels. Elliptic curves are the basis for a relatively new class of public-key schemes. It is predicted that elliptic curve cryptosystems (ECCs) will replace many existing schemes in the near future. The main reason for the attractiveness of ECC is the fact that significantly smaller parameters can be used in ECC than in other competitive system, but with equivalent levels of security. The benefits of having smaller key size include faster computations, and reduction in processing power, storage space and bandwidth. This makes ECC ideal for constrained environments where resources such as power, processing time and memory are limited. The implementation of ECC requires several choices, such as the type of the underlying finite field, algorithms for implementing the finite field arithmetic, the type of the elliptic curve, algorithms for implementing the elliptic curve group operation, and elliptic curve protocols. Many of these selections may have a major impact on overall performance. In this dissertation a finite field from a special class called the Optimal Extension Field (OEF) is chosen as the underlying finite field of implementing ECC. OEFs utilize the fast integer arithmetic available on modern microcontrollers to produce very efficient results without resorting to multiprecision operations or arithmetic using polynomials of large degree. This dissertation discusses the theoretical and implementation issues associated with the development of this finite field in a low end embedded system. It also presents various improvement techniques for OEF arithmetic. The main objectives of this dissertation are to --Implement the functions required to perform the finite field arithmetic operations. -- Implement the functions required to generate an elliptic curve and to embed data on that elliptic curve. -- Implement the functions required to perform the elliptic curve group operation. All of these functions constitute a library that could be used to implement any elliptic curve cryptosystem. In this dissertation this library is implemented in an 8-bit AVR Atmel microcontroller. / Dissertation (MEng (Computer Engineering))--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / unrestricted

Telemetry system, Optimisation, Sensoric networks, Smart Grid, Internet of Things, Sensors, Information security, Cryptography, Cryptography algorithms, Cryptosystem, Confidentiality, Integrity, Authentication, Data freshness, Non-Repudiation.