Communication Environment
Definition 3.3 (Communication environment) Communication environment CE is defined as the following set:
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CE = {G, D, N } (3.2)
In CE, the engaging parties in G, using a set of Internet-accessible payment devices D, communicate to one another over a set of communication networks N. Generally, CE can be classified into fixed environment F E and wireless environment W E, where
CE = F E ? W E (3.3)
Fixed Environment: the fixed environment F E is defined as the following set:
F E = {G, F D, F N } (3.4)
Where F E ? CE, F D ? D, and F N ? N . Note that F D stands for a set of Internet-accessible payment devices operating over a fixed network F N held by engaging parties in G. The examples of F D are personal computers (PCs) and Internet KIOSKs. F N represents a set of communication infrastructure which is composed of a number of wired links among the devices in F D. The examples of F N are Local Area Networks (LANs) and Wide Area Networks (WANs).
Wireless Environment: the wireless environment W E is defined as the following set:
W E = {G, W D, W N } (3.5)
Where W E ? CE, W D ? D, and W N ? N . Note that W D stands for a set of Internet-accessible wireless payment devices e.g. cellular phones or Personal Digital Assistants (PDAs), held by engaging parties in G.
From the definitions of fixed and wireless devices described above, we can state the relationship between them as follows:
D = F D ? W D (3.6)
W N represents a set of wireless communication infrastructure in which the members in G communicate to one another. W N is composed of a number of wireless links among the devices in W D. The examples of W N are wireless LANs and cellular networks.
From the definitions of fixed and wireless networks described above, we can state the following relationship between them:
N = F N ? W N (3.7)
Payment Token
Definition 3.4 (Payment token) A payment token T is a form of electronic money that is transferred among engaging parties in G in a payment system
S. T represents physical money in traditional payment transactions. T has the following properties:
1. T is valid if T can be proven by I.
2. A party Q accepts T sent from a party R if T is proven valid.
Referred to various kinds of payment systems outlined in chapter 2, the examples of T are electronic coins in micropayment systems, such as ci in PayWord RS96 and wi in PayFair Yen01, and P rice in SET Mas97 and iKP BGH+00 protocols.
Payment Information
Definition 3.5 (Payment information) Payment information P I refers to the validity of a payment token T to its issuer I. P I has the following proper- ties:
1. Any party’s P I is known only to her financial institution and herself.
• P IC is known only to I and C.
• P IM is known only to A and M .
2. Any party’s P I is valid if it can be proven by her financial institution.
3. T is valid if P I is proven valid.
Referred to the payment systems outlined in chapter 2, the examples of P I are PayWord certificate in PayWord and P I which contains credit-card information of a client in SET and iKP protocols. An issuer can use this information to identify its clients.
Payment Transaction
Definition 3.6 (Payment transaction) A payment transaction P T is de- fined as a set of actions ACT regarding fund transfer performed by engaging parties in G over a set of communication networks N . P T can be represented as the following:
P T = {G, D, ACT, N } (3.8)
Figure 3.2 demonstrates the directions of payment token transfer. Payment Ordering represents payment token transfer from C to M , even though, in fact, the actual transfer of payment token is processed from I to A in Payment Clearing. Debit represents the deduction of the value of the payment token from C to I, although, in fact, this action is performed at I itself because C’s account has been established with I. Credit represents money deposit from A to M even though, actually, this action is performed at A itself because M has an account established with A.
Figure 3.2: Payment transaction
Note that, from Figure 3.2, the arrows represent the directions of actual transactions. As P SP acts as a medium between C-M and I-A, all actual transactions relevant to Debit and Credit are performed through P SP . The broken arrows represent the directions of actions performed by originators of the actions to their intended recipients.
Goals of Engaging Parties for Payment Transactions
On designing a payment protocol, we focus on the information related to a payment transaction that should be transferred to engaging parties at the end of the transaction. This information must deliver its sender’s intention and purpose regarding the payment transaction to its intended recipient. Such information is considered as goals of engaging parties. We provide reasoning about the goals of engaging parties by using an accountability logic proposed by Kungpisdan et al. (KP) KP02. KP’s logic not only reasons about provability of payment transactions, performed by engaging parties, to a verifier, but it also infers sending and receiving information relevant to fund transfer. We deploy modal operators in KP’s logic to state the goals of engaging parties that contain payment token T , payment information P I, and identities of engaging parties in particular payment transactions.
Definition 3.7 (Goals of engaging parties) Goals of engaging parties re- garding a payment transaction (Goals) are defined as the following set:
