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.
Mixes were proposed by Chaum @cite_41 in 1981, and are a basic building block for implementing high-latency anonymous communications. A mix takes a number of input messages, and outputs them in such a way that it is infeasible to link an output to its corresponding input. In order to achieve this goal, the mix changes the appearance (by encrypting and padding messages) and the flow of messages (by delaying and reordering them). Mixmaster @cite_14 and Mixminion @cite_25 are more advanced versions of the Chaumian mix @cite_41 , and they haven been deployed to provide anonymous email services.
@cite_41 @cite_14 @cite_25
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A technique based on public key cryptography is presented that allows an electronic mail system to hide who a participant communicates with as well as the content of the communication - in spite of an unsecured underlying telecommunication system. The technique does not require a universally trusted authority. One correspondent can remain anonymous to a second, while allowing the second to respond via an untraceable return address. The technique can also be used to form rosters of untraceable digital pseudonyms from selected applications. Applicants retain the exclusive ability to form digital signatures corresponding to their pseudonyms. Elections in which any interested party can verify that the ballots have been properly counted are possible if anonymously mailed ballots are signed with pseudonyms from a roster of registered voters. Another use allows an individual to correspond with a record-keeping organization under a unique pseudonym, which appears in a roster of acceptable clients. We present Mixminion, a message-based anonymous remailer protocol with secure single-use reply blocks. Mix nodes cannot distinguish Mixminion forward messages from reply messages, so forward and reply messages share the same anonymity set. We add directory servers that allow users to learn public keys and performance statistics of participating remailers, and we describe nymservers that provide long-term pseudonyms using single-use reply blocks as a primitive. Our design integrates link encryption between remailers to provide forward anonymity. Mixminion works in a real-world Internet environment, requires little synchronization or coordination between nodes, and protects against known anonymity-breaking attacks as well as or better than other systems with similar design parameters.