Credit-based electronic payment systems are considered to play important ro
les in future automated payment systems. Like most other types of payment s
ystems, however, credit-based systems proposed so far generally involve com
putationally expensive cryptographic operations. Such a relatively heavy co
mputational load is preventing credit-based systems from being used in appl
ications which require very East processing. A typical example is admission
-fee payment at the toll gate of an expressway without stopping a vehicle t
hat travels at a high speed. In this article, we propose a very fast credit
-based electronic payment protocol for admission-fee payment. More specific
ally, we propose a payment system between a high-speed vehicle and a toll g
ate which uses only very simple and fast computations. The proposed system
makes use of an optimized Key Pre-distribution System (or KPS) to obtain hi
gh resistance against collusion attacks.