Communications networks are traditionally used to bring information to
gether. They can also be used to keep information apart in order to pr
otect personal privacy, A cryptographic protocol specifies a process b
y which some information is transferred among some users and hidden fr
om others. We show how to implement anonymous credit cards using simpl
e cryptographic protocols, We pose, and solve, a collusion problem whi
ch determines whether it is possible for a subset of users to discover
information that is designed to be hidden from them during or after e
xecution of the anonymous credit card protocol.