Group signature schemes and payment systems based on the discrete logarithm problem

The security of many cryptographic systems relies on the difficulty of computing discrete logarithms in certain finite groups. This dissertation studies existing cryptographic protocols which are based on this problem. These protocols are then unified and extended to create a framework for designing cryptographic systems. Using this framework, new and efficient realizations of digital group signature schemes and digital payment systems are developed. Group signature schemes allow a member of a group to sign messages anonymously on the group’s behalf. In the case of later dispute, a designated group manager can reveal the signer’s identity. An efficient realization of this concept is proposed. Furthermore, the concept of generalized group signatures is developed and realized. This type of scheme allows the definition of sets of group members which can jointly sign on the group’s behalf. Anonymous digital payment systems allow a customer to pay digitally and anonymously. Unfortunately, anonymity also opens the path to criminal misuse, for instance to launder money. As a compromise between the protection of privacy and the possibility of surveillance for crime inspection, the concept of revocable anonymity has been proposed. It introduces a trustworthy third-party which can reveal the identity of a payer in cases of misuse. From an operational point of view, it can be an important requirement that this third-party is not involved in ordinary transactions, but only in anonymity revocation. In this work we present an efficient anonymous digital payment systems satisfying this requirement.