A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

Using coloured petri nets to simulate DoS-resistant protocols

In this work, we examine unbalanced computation between an initiator and a responder that leads to resource exhaustion attacks in key exchange protocols. We construct models for two cryp-tographic protocols; one is the well-known Internet protocol named Secure Socket Layer (SSL) protocol, and the other one is the Host Identity Protocol (HIP) which has built-in DoS-resistant mechanisms. To examine such protocols, we develop a formal framework based on Timed Coloured Petri Nets (Timed CPNs) and use a simulation approach provided in CPN Tools to achieve a formal analysis. By adopting the key idea of Meadows' cost-based framework and re¯ning the de¯nition of operational costs during the protocol execution, our simulation provides an accurate cost estimate of protocol execution compar- ing among principals, as well as the percentage of successful connections from legitimate users, under four di®erent strategies of DoS attack.

Modelling Denial of Service Attacks on JFK with Meadow's Cost-Based Framework

We present the first detailed application of Meadows’s cost-based modelling framework to the analysis of JFK, an Internet key agreement protocol. The analysis identifies two denial of service attacks against the protocol that are possible when an attacker is willing to reveal the source IP address. The first attack was identified through direct application of a cost-based modelling framework, while the second was only identified after considering coordinated attackers. Finally, we demonstrate how the inclusion of client puzzles in the protocol can improve denial of service resistance against both identified attacks.