ANÁLISIS DE SENSIBILIDAD DE LAS PROVISIONES MATEMÁTICAS A LOS

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 ac- countability logic proposed by Kungpisdanet al. (KP) [KP02]. KP’s logic not only reasons about provability of payment transactions, performed by engag- ing 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 tokenT, payment information P I, and identities of engaging parties in particular payment transactions.

Based on the notations similar to the ones in [Her01, KP02], the following modal operators are used throughout this thesis:

• Q authorized X: a party Q has authorization on performing an action X, where X ∈ACT.

• Q CanProve X to R: a party Q is able to prove to a party R that the statement X is true without revealing any information which is consid- ered to be secret to R.

Referred to the Definition 3.2, P SP acts on behalf of I and A over the Internet side. Thus, in the proposed mobile payment model, we focus on three main parties communicating to one another over the Internet: C, M, and P SP. Based on SET protocol requirements analyzed by Meadows et al.

[MS98], the following definition presents the goals of engaging parties regarding the payment transaction.

Definition 3.7 (Goals of engaging parties) Goals of engaging parties re- garding a payment transaction(Goals) are defined as the following set:

Client’s Goal (CG): C can ensure that M has delivered or committed to deliver the goods or services requested by C.

C CanProve ( M authorized payment-order(M, C, TC) ) to V

From the above statement, C must be able to prove to a verifier V, who does not involve in the transaction, that M has authorized the transaction regardingPayment Ordering which has been requested byC. Such authoriza- tion may be contained in the message sent to C. This message or its parts must be provable that it has been originated byM and it hasC as its intended recipient. Moreover, this message must contain authorized amountTC as a re- ceipt of the payment to C.

Merchant’s Goal (MG): M can ensure thatAhas transferred or committed to transfer the amount equivalent toTM to M.

M CanProve ( PSP authorized credit(PSP, M, TM) ) to V

From the above statement, M must be able to prove to a verifier V that P SP authorized the transaction regarding Credit which has been requested byM. In other words, M has to receive the message originated by P SP (on behalf ofA) and the message must contain the amountTM authorized byP SP.

Payment System Provider’s Goal (P SP G): P SP, on behalf of I and A, has successfully performed Payment Clearing.

R CanProve (

where,

C CanProve ( PSP authorized debit(PSP, C, TC)) to V ∧

M CanProve ( PSP authorized credit(PSP, M, TM) ) to V →P CanProve ( PSP authorized payment-clearing(

PSP, C, M, TC, TM) ) to V (3.19)

where P stands for any party. It can be seen that achieving P SP’s goal cannot be proven by onlyP SP itself, but by the cooperation with C and M. To achieve this goal, P SP has to collect the results of two proofs performed by C and M; one is performed by C to prove that P SP has deducted or committed to deduct the amountTC requested byC and the other isM’s goal (MG).

Moreover, based on [KP02], we define the goal of actions which are per- formed in each protocol message as follows:

Definition 3.8 (Message goal) Each message transferred in a protocol sho- uld deliver its sender’s intention regarding an action in ACT regarding a pay- ment transaction P T to its intended recipient.

Q CanP rove ( Q authorized act(Q, R, X) ) to R

where Q and R stand for any party and X stands for the message com- ponent containing Q’s intention regarding performing the action act, where

As a message goal, P SP G can be represented as the following:

PSP CanProve ( PSP authorized debit(PSP, C, TC)) to C ∧

PSP CanProve ( PSP authorized credit(PSP, M, TM) ) to M →PSP CanProve ( PSP authorized payment-clearing(

PSP, C, M, TC, TM) ) to Q (3.20)

where R stands for C or M. To achieve this goal, P SP has to prove that the message originated by itself contains necessary information to be used as evidence to prove toC andM regarding its tasks. Such evidence must contain at least the provable identities of both the sender and the intended recipient of the message and authorized amountTC and TM. In this case, it can be seen that the verifiers are internal parties who involve in the transaction.

3.1.8

Party’s Requirements for Payment Transactions