A wide variety of privacy metrics have been proposed in the literature to evaluate the level of protection offered by privacy enhancing-technologies. Most of these metrics are specific to concrete systems and adversarial models, and are difficult to generalize or translate to other contexts. Furthermore, a better understanding of the relationships between the different privacy metrics is needed to enable more grounded and systematic approach to measuring privacy, as well as to assist systems designers in selecting the most appropriate metric for a given application. In this work we propose a theoretical framework for privacy-preserving systems, endowed with a general definition of privacy in terms of the estimation error incurred by an attacker who aims to disclose the private information that the system is designed to conceal. We show that our framework permits interpreting and comparing a number of well-known metrics under a common perspective. The arguments behind these interpretations are based on fundamental results related to the theories of information, probability and Bayes decision.
Several metrics have been proposed in the literature to assess the level of anonymity provided by anonymous communication systems (ACSs). Reiter and Rubin @cite_11 define the degree of anonymity as a probability @math , where @math is the probability assigned by an attacker to the potential initiators of a communication. In this model, users are more anonymous as they appear (towards a certain adversary) to be less likely of having sent a message, and the metric is thus computed individually for each user and for each communication. @cite_32 on the other hand define the degree of anonymity as the binary logarithm of the number of users of the system, which may be regarded as a Hartley entropy. This metric only depends on the number of users of the system, and does not take into account that some users might appear as more likely senders of a message than others.
@cite_32 @cite_11
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There are different methods to build an anonymity service using MIXes. A substantial decision for doing so is the method of choosing the MIX route. In this paper we compare two special configurations: a fixed MIX route used by all participants and a network of freely usable MIXes where each participant chooses his own route. The advantages and disadvantages in respect to the freedom of choice are presented and examined. We'll show that some additional attacks are possible in networks with freely chosen MIX routes. After describing these attacks, we estimate their impact on the achievable degree of anonymity. Finally, we evaluate the relevance of the described attacks with respect to existing systems like e.g. Mixmaster, Crowds, and Freedom. In this paper we introduce a system called Crowds for protecting users' anonymity on the world-wide-web. Crowds, named for the notion of “blending into a crowd,” operates by grouping users into a large and geographically diverse group (crowd) that collectively issues requests on behalf of its members. Web servers are unable to learn the true source of a request because it is equally likely to have originated from any member of the crowd, and even collaborating crowd members cannot distinguish the originator of a request from a member who is merely forwarding the request on behalf of another. We describe the design, implementation, security, performance, and scalability of our system. Our security analysis introduces degrees of anonymity as an important tool for describing and proving anonymity properties.