Electronic commerce and the internet provide greater opportunities for companies and individual person to be involved in commercial activities; the involved parties may not know or trust each other or may even be mutually suspicious of each other. The issue of fairness becomes more critical and must be well addressed. The aim of this thesis is to investigate security solutions with fairness for on-line transactions. A fair trading protocol with credit payment is proposed. The proof of equivalence of discrete logarithm to discrete loglogarithm is employed as the main tool to construct the protocol. The scheme provides a unique link between payment and gambling outcome so that the winner can be ensured to get the payment. Since an optimal fair exchange method is used in gambling message exchange, the proposed system guarantees that no one can successfully cheat during a gambling process. Our system requires an off-line Trusted Third Party (TTP). If cheating occurs, the TTP can resolve the problem and make the gambling process fair. An efficient and secure poker scheme is proposed. It is based on multiple encryption and decryption of individual cards. The protocol satisfies all major security requirements of a real mental poker. It gets rid of the Card Salesman and guarantees minimal effect due to collusion. The protocol is secure and more efficient compared with other known protocols. The strategies of players can be kept confidential with the introduction of a Dealer. The protocol is suitable to be implemented in an on-line gambling card game. The implementation of the fair on-line gambling protocol has been demonstrated and all utility classes for the implementation have been defined. / Master of Science (Hons)