Abstract: E-commerce is buying and selling through the Internet where the payment process is electronic. Electronic payment (e-payment) is the critical support phase of e-commerce contains sensitive data in transactions and consequently, it must be secure. Therefore, a security protocol (cryptographic protocol) is used in the transaction between parties, and it must be satisfy security properties. In this paper, we study e-payment phase in SET protocol. We found it still has problems of huge and complex transactions processes and not fully satisfy security properties. We introduced an enhanced model that represent the all participants in e-payment phase and functions for each, our model presented sequence diagram for transactions, which reduce the numbers of transactions steps from thirty five to fifteen steps. The functions of removed steps are handled by a “controller agent" working in parallel with these transactions. Such control agent is able to make decisions in an automated way according to the interactions and capable of terminating the process in case of fraud or attack.

Abstract: Fixed DP curve is a recent representation of the polynomial curves, proposed by Delgado and Pena in 2003. They introduced a new curve representation with linear computational complexity. An algorithmic approach to degree reduction of interval DP curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed DP curves) associated with the original interval DP curve are obtained. These four fixed DP curves are transformed into four fixed Bezier curves. The degree of the four fixed Bezier curves is reduced based on the matrix representations of the degree reduction process. The process of degree reduction k times are applied to the four fixed Bezier curves of degree n to obtain the four fixed Bezier curves of degree n-k without changing their shapes. The four fixed reduced Bezier curves are converted into DP curves of the same degree. Finally the reduced interval DP control points are obtained from the four fixed reduced DP control points. An illustrative example is included in order to demonstrate the effectiveness of the proposed method.

Abstract: Most of cryptographic protocols are subjects to very subtle attacks. Therefore, many researchers have developed tools to model and analyze protocols to guarantee their security properties. The spi calculus has proved to be useful for analyzing and reasoning on cryptographic protocols. However, current works assumed that the spi calculus dealt with transferring a single unstructured message for sending each message in a single action, which is mostly needed in implementing real protocols with an open environment, such case cause a problem in proving the freshness of generated keys for each output action. In this paper, we introduced an improved version of spi calculus called the Tspi calculus that provides the ability for solving the problem of tuple of messages using nested partial map function and guarantee the freshness of generated keys by the use of an evolution function for each action in the running processes for making suitable decision during interaction with an open environment such as e-commerce protocols.