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2 Weiliang Zhao et al.
of fairness must be carefully addressed. There is no fairness for involved parties in the
existing popular payment protocols. One target of this paper is to address the fairness
issue in the credit card payment process. In the existing credit card protocols, the finan-
cial institution that provides the credit card service plays a role of on-line authority and
will be actively involved in a payment. To avoid the involvement of financial institution
in normal transactions and reduce running costs, some credit card based schemes with
off-line financial authority has been proposed [12]. Another target of this paper is to
avoid the on-line financial institution for credit card service in the normal transactions.
In this paper, we propose a fair trading protocol with off-line anonymous credit card
payment. The protocol addresses the fairness and privacy of the trading process and its
associated payment. The credit card is anonymous and an on-line credit card service
from a financial institution is not necessary during the processing of a payment. The
TTP and financial institution for credit card can be both off-line, the proposed proto-
col has better availability and reliability and is more efficient than other solutions with
more on-line components. The technique of proof of equivalence of discrete logarithm
to discrete log-logarithm [13] is the essential tool in the constructing of our fair trad-
ing protocol. In section 2, the electronic payment with off-line anonymous credit card
is discussed. In section 3, we propose a fair exchange protocol with off-line anony-
mous credit card based payment. Finally, section 4 concludes the paper with some final
remarks.
2 Electronic Payment With Anonymous Off-line Credit Card
Credit card payment is currently the most popular of all on-line payment methods.
There are at least three parties involved in this kind of payments: Client, Merchant and
Bank. The client is the buyer or service user who will make the payment. The merchant
is the goods or service provider who will receive the payment. The bank is the financial
institution that provides credit card service and guarantees the transfer of money value
from the client to the merchant. The bank acts as the issuer of credit cards to clients and
acquirer of payment records from merchants. For one payment, the issuer and acquirer
can be same or different, clearing between the issuer and the acquirer will be done
using existing financial networks. There is an on-line financial authority in the existing
electronic credit card protocols [8–11]. The authors in [12] have proposed a credit based
payment scheme in which the financial institution is not necessary on-line. Merchant
can ensure the authenticity of the credit cards without the help of an on-line authority
organization. Firstly, the client applies for a digital credit card from the bank. After the
credit check, if the client is approved to have it, the digital credit card is delivered to the
client through a secure channel. The credit information of the client is anonymous with
the technique of no-interactive equality proof [16].
The digital credit card contains at least the following information:
– client’s ID
– h
i
= g
x
i
mod q, i =1, 2,...,l, where g
i
∈ Z
∗
p
are the common generators, x
contains the credit card number, PIN number, other confidential information and
salt.
– credit amount A
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