We use the concept of designated 2-verifier proofs to design simple and sec
ure electronic payment systems. Two on-line protocols which link securely C
ustomers, Merchants and Banks are presented. in the first the identity of t
he Customer is traceable. This protocol can be used for general electronic
payment systems. The second protocol can be used for anonymous electronic c
ash payments. Both protocols have a simple structure and are provably secur
e. (C) 2000 Published by Elsevier Science B.V. All rights reserved.