Anonymous credit cards and their collusion analysis

Communications networks are traditionally used to bring information together. They can also be used to keep information apart in order to protect personal privacy. A cryptographic protocol specifies a process by which some information is transferred among some users and hidden from others. We show how to implement anonymous credit cards using simple cryptographic protocols. We pose, and solve, a collusion problem which determines whether it is possible for a subset of users to discover information that is designed to be hidden from them during or after execution of the anonymous credit card protocol.