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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As more of our daily activities are carried out online, it becomes important to develop technologies to protect our online privacy. Anonymity is a key privacy technology, since it serves to hide patterns of communication that can often be as revealing as their contents. This motivates our study of the use of large scale peer-to-peer systems for building anonymous systems. We first develop a novel methodology for studying the anonymity of peer-to-peer systems, based on an information-theoretic anonymity metric and simulation. We use simulations to sample a probability distribution modeling attacker knowledge under conservative assumptions and estimate the entropy-based anonymity metric using the sampled distribution. We then validate this approach against an analytic method for computing entropy. The use of sampling introduces some error, but it can be accurately bounded and therefore we can make rigorous statements about the success of an entire class of attacks. We next apply our methodology to perform the first rigorous analysis of Freenet, a peer-to-peer anonymous publishing system, and identify a number of weaknesses in its design. We show that a targeted attack on high-degree nodes can be very effective at reducing anonymity. We also consider a next generation routing algorithm proposed by the Freenet authors to improve performance and show that it has a significant negative impact on anonymity. Finally, even in the best case scenario, the anonymity levels provided by Freenet are highly variable and, in many cases, little or no anonymity is achieved. To provide more uniform anonymity protection, we propose a new design for peer-to-peer anonymous systems based on structured overlays. We use random walks along the overlay to provide anonymity. We compare the mixing times of random walks on different graph structures and find that de Bruijn graphs are superior to other structures such as the hypercube or butterfly. Using our simulation methodology, we analyze the anonymity achieved by our design running on top of Koorde, a structured overlay based on de Bruijn graphs. We show that it provides anonymity competitive with Freenet in the average case, while ensuring that worst-case anonymity remains at an acceptable level. We also maintain logarithmic guarantees on routing performance. In secure multiparty computation, mutually distrusting users in a network want to collaborate to compute functions of data which is distributed among the users. The users should not learn any additional information about the data of others than what they may infer from their own data and the functions they are computing. Previous works have mostly considered the worst case context (i.e., without assuming any distribution for the data); Lee and Abbe (2014) is a notable exception. Here, we study the average case (i.e., we work with a distribution on the data) where correctness and privacy is only desired asymptotically. For concreteness and simplicity, we consider a secure version of the function computation problem of K "orner and Marton (1979) where two users observe a doubly symmetric binary source with parameter p and the third user wants to compute the XOR. We show that the amount of communication and randomness resources required depends on the level of correctness desired. When zero-error and perfect privacy are required, the results of (2014) show that it can be achieved if and only if a total rate of 1 bit is communicated between every pair of users and private randomness at the rate of 1 is used up. In contrast, we show here that, if we only want the probability of error to vanish asymptotically in block length, it can be achieved by a lower rate (binary entropy of p) for all the links and for private randomness; this also guarantees perfect privacy. We also show that no smaller rates are possible even if privacy is only required asymptotically. Measures for anonymity in systems must be on one hand simple and concise, and on the other hand reflect the realities of real systems. Such systems are heterogeneous, as are the ways they are used, the deployed anonymity measures, and finally the possible attack methods. Implementation quality and topologies of the anonymity measures must be considered as well. We therefore propose a new measure for the anonymity degree, which takes into account possible heterogeneity. We model the effectiveness of single mixes or of mix networks in terms of information leakage and measure it in terms of covert channel capacity. The relationship between the anonymity degree and information leakage is described, and an example is shown The ability to locate random relays is a key challenge for peer-to-peer (P2P) anonymous communication systems. Earlier attempts like Salsa and AP3 used distributes hash table lookups to locate relays, but the lack of anonymity in their lookup mechanisms enables an adversary to infer the path structure and compromise used anonymity. NISAN and Torsk are state-of-the-art systems for P2P anonymous communication. Their designs include mechanisms that are specifically tailored to mitigate information leak attacks. NISAN proposes to add anonymity into the lookup mechanism itself, while Torsk proposes the use of secret buddy nodes to anonymize the lookup initiator. In this paper, we attack the key mechanisms that hide the relationship between a lookup initiator and its selected relays in NISAN and Torsk. We present passive attacks on the NISAN lookup and show that it is not as anonymous as previously thought. We analyze three circuit construction mechanisms for anonymous communication using the NISAN lookup, and show that the information leaks in the NISAN lookup lead to a significant reduction in user anonymity. We also propose active attacks on Torsk that defeat its secret buddy mechanism and consequently compromise user anonymity. Our results are backed up by probabilistic modeling and extensive simulations. Our study motivates the search for a DHT lookup mechanism that is both secure and anonymous.