A generalisation of the Diffie-Hellman protocol is studied in this dissertation. In the generalisation polynomials are used to reduce the representation size of a public key and linear shift registers for more efficient computations. These changes are important for the implementation of the protocol in con- strained environments. The security of the Diffie-Hellman protocol and its generalisation is based on the same computations problems. Lastly three examples of the generalisation and their implementation are discussed. For two of the protocols, models are given to predict the execution time and it is determined how well these model predictions are. / Dissertation (MSc (Applied Mathematics))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / MSc / unrestricted

In this thesis, we consider how to reduce the communication cost of the key exchange procedures as many as possible, while the secure group communication can still be achieved. Due to the energy consumption is usually proportional to the distance, we use the shortest paths algorithm to find the shortest communication paths between any pair of the secure group members. We first propose a straightforward heuristic named Minimum-Energy First-Selected ( MEFS ). MEFS tries to select the pair of group members which has less communication cost than all other pairs have at every time. Though MEFS performs better than random selecting, it still has some weakness in solving the energy-aware key management problem. So we use the concept of the minimum cost flow problem, and by appropriate transformation, then we get the optimal solution of the energy-aware key management problem under some constraints. At last, the simulation results proves that the minimum cost flow approach actually works better than MEFS does.

Diploma thesis deals with an anonymous transmit of messages using protocol for anonymous authentication. In first part, we introduce theoretical familiarization to the issues and description protocol for anonymous authentication. Further, it describes the suggestion of the communication between the client and the server. Finally, contains a description of the created system for anonymous transmit of messages, which consists of the server and clients, who can leave challenges on the server for other users and they obtains challenges from the server. The thesis explains how to start and control program. There are also discussed methods of computing verification values, encryption keys and messages and authentication of receivers.

Current needs of human communication came to status, when most of transferred messages are considered as private and transition over non-secured communication lines in open form is not possible. That originated a lot of different methods for securing of messages and transfers in ciphered form. Two mainstreams were established, symmetric cryptography and asymmetric cryptography. Second of mentioned groups is based on usage of two information – keys, when one of then is broadly known and is public and second, well protected and private. Using a public key it is possible to establish a cryptogram of message, but for deciphering it is necessary to know private key. Asymmetric methods are based on mathematical problems, for which there is not an effective computing algorithm. This thesis are focused for asymmetric cryptosystems based on discrete logarithm problem, where ciphering of message using public key is very easy and quick, but deciphering without knowledge of private key is extremely time consuming process. Work describes a mathematical base of discrete logarithm problem, its’ properties and methods developed for solving of this problem. Descriptions of particular cryptosystems are given, i.e. ElGamal cryptosystem, Diffie-Hellman protocol and DSA. Second part of thesis is focused for web application developed as study support of discrete logarithm problem and of cryptosystems using this problem. It describes functional and graphical interface, work with it and options given to user working with application. Mentions also lessons for user which should help with understanding of described problems and practicing.