Biblio
In this article, we introduce a new method for computing fixed points of a class of iterated functions in a finite time, by exponentiating linear multivalued operators. To better illustrate this approach and show that our method can give fast and accurate results, we have chosen two well-known applications which are difficult to handle by usual techniques. First, we apply the exponentiation of linear operators to a digital filter in order to get a fine approximation of its behavior at an arbitrary time. Second, we consider a PID controller. To get a reliable estimate of its control function, we apply the exponentiation of a bundle of linear operators. Note that, our technique can be applied in a more general setting, i.e. for any multivalued linear map and that the general method is also introduced in this article.
Low-latency anonymity systems such as Tor rely on intermediate relays to forward user traffic; these relays, however, are often unreliable, resulting in a degraded user experience. Worse yet, malicious relays may introduce deliberate failures in a strategic manner in order to increase their chance of compromising anonymity. In this paper we propose using a reputation metric that can profile the reliability of relays in an anonymity system based on users' past experience. The two main challenges in building a reputation-based system for an anonymity system are: first, malicious participants can strategically oscillate between good and malicious nature to evade detection, and second, an observed failure in an anonymous communication cannot be uniquely attributed to a single relay. Our proposed framework addresses the former challenge by using a proportional-integral-derivative (PID) controller-based reputation metric that ensures malicious relays adopting time-varying strategic behavior obtain low reputation scores over time, and the latter by introducing a filtering scheme based on the evaluated reputation score to effectively discard relays mounting attacks. We collect data from the live Tor network and perform simulations to validate the proposed reputation-based filtering scheme. We show that an attacker does not gain any significant benefit by performing deliberate failures in the presence of the proposed reputation framework.