Mixnets are widely believed to hide communication metadata of individuals. We show that there are various pitfalls when designing mixnet topologies and routing strategies, in particular when choosing mixnets with low delays. We introduce a tool that empirically evaluates such leakage in mixnets and show that this tool precisely estimates this leakage for recipient anonymity, up to an error introduced by sampling. First, we introduce a novel generic attack strategy that we even prove to be optimal for breaking recipient anonymity. In contrast to prior work, our attack strategy incorporates the severity of each observation's leakage, via its so-called privacy loss. Second, our tool provides a lower bound on an attacker's advantage against recipient anonymity by sampling a large set of observations; if a significant number of observations with high privacy loss is observed, the tool outputs a lower bound on the leakage by providing a lower bound on the mass of the tail of the distribution of privacy losses. From the literature, we study the topology and routing strategies of the Karaoke and Atom protocols, provide bounds on their leakage, and recommend design choices based on the analysis.

While many anonymous communication (AC) protocols have been proposed to provide anonymity over the internet, scaling to a large number of users while remaining provably secure is challenging. We tackle this challenge by proposing a new scaling technique to improve the scalability/anonymity of AC protocols that distributes the computational load over many nodes without completely disconnecting the paths different messages take through the network. We demonstrate that our scaling technique is useful and practical through a core sample anonymous broadcast protocol, Streams, that offers provable security guarantees and scales for a million messages. The scaling technique ensures that each node in the system does the computation-heavy public key operation only for a tiny fraction of the total messages routed through the Streams network while maximizing the mixing/shuffling in every round. Our experimental results show that Streams can scale well even if the system has a load of one million messages at any point in time, with a latency of 16 seconds while offering provable “one-in-a-billion” unlinkability, and can be leveraged for applications such as anonymous microblogging and network-level anonymity for blockchains. We also illustrate by examples that our scaling technique can be useful to other AC protocols to improve their scalability and privacy, and can be interesting to protocol developers.

Abstract For anonymous communication networks (ACNs), Das et al. recently confirmed a long-suspected trilemma result that ACNs cannot achieve strong anonymity, low latency overhead and low bandwidth overhead at the same time. Our paper emanates from the careful observation that their analysis does not include a relevant class of ACNs with what we call user coordination where users proactively work together towards improving their anonymity. We show that such protocols can achieve better anonymity than predicted by the above trilemma result. As the main contribution, we present a stronger impossibility result that includes all ACNs we are aware of. Along with our formal analysis, we provide intuitive interpretations and lessons learned. Finally, we demonstrate qualitatively stricter requirements for the Anytrust assumption (all but one protocol party is compromised) prevalent across ACNs.

Abstract Quantifying the privacy loss of a privacy-preserving mechanism on potentially sensitive data is a complex and well-researched topic; the de-facto standard for privacy measures are ε-differential privacy (DP) and its versatile relaxation (ε, δ)-approximate differential privacy (ADP). Recently, novel variants of (A)DP focused on giving tighter privacy bounds under continual observation. In this paper we unify many previous works via the privacy loss distribution (PLD) of a mechanism. We show that for non-adaptive mechanisms, the privacy loss under sequential composition undergoes a convolution and will converge to a Gauss distribution (the central limit theorem for DP). We derive several relevant insights: we can now characterize mechanisms by their privacy loss class, i.e., by the Gauss distribution to which their PLD converges, which allows us to give novel ADP bounds for mechanisms based on their privacy loss class; we derive exact analytical guarantees for the approximate randomized response mechanism and an exact analytical and closed formula for the Gauss mechanism, that, given ε, calculates δ, s.t., the mechanism is (ε, δ)-ADP (not an over-approximating bound).

Many applications, such as anonymous communication systems, privacy-enhancing database queries, or privacy-enhancing machine-learning methods, require robust guarantees under thousands and sometimes millions of observations. The notion of r-fold approximate differential privacy (ADP) offers a well-established framework with a precise characterization of the degree of privacy after r observations of an attacker. However, existing bounds for r-fold ADP are loose and, if used for estimating the required degree of noise for an application, can lead to over-cautious choices for perturbation randomness and thus to suboptimal utility or overly high costs. We present a numerical and widely applicable method for capturing the privacy loss of differentially private mechanisms under composition, which we call privacy buckets. With privacy buckets we compute provable upper and lower bounds for ADP for a given number of observations. We compare our bounds with state-of-the-art bounds for r-fold ADP, including Kairouz, Oh, and Viswanath's composition theorem (KOV), concentrated differential privacy and the moments accountant. While KOV proved optimal bounds for heterogeneous adaptive k-fold composition, we show that for concrete sequences of mechanisms tighter bounds can be derived by taking the mechanisms' structure into account. We compare previous bounds for the Laplace mechanism, the Gauss mechanism, for a timing leakage reduction mechanism, and for the stochastic gradient descent and we significantly improve over their results (except that we match the KOV bound for the Laplace mechanism, for which it seems tight). Our lower bounds almost meet our upper bounds, showing that no significantly tighter bounds are possible.

Computing differential privacy guarantees is an important task for a wide variety of applications. The tighter the guarantees are, the more difficult it seems to be to compute them: naive bounds are simple additions, whereas modern composition theorems require either a search over a potentially confusing parameter space (for the composition theorem of Kairouz, Oh, and Visvanath), require computing many moments (for Rényi DP) or finding parameters of a function that limits the privacy loss (for concentrated DP). The best known approach for tight differential privacy bounds, called Privacy Buckets, provides requires running a fairly complex implementation of numerical approximations. In this work, we provide an easy-to-use interface for computing state-of-the-art differential privacy guarantees by simply accessing a website. Guarantees for the widely used Laplace mechanism and for the similarly popular Gauss mechanism can be computed by simply stating the scale parameter of the noise, the sensitivity, and the number of compositions. Privacy guarantees for more complex distributions can be computed by uploading two histograms. This work bridges the gap between the best known theoretical results for computing differential privacy guarantees and privacy analysts and users benefiting from such guarantees.

This work investigates the fundamental constraints of anonymous communication (AC) protocols. We analyze the relationship between bandwidth overhead, latency overhead, and sender anonymity or recipient anonymity against the global passive (network-level) adversary. We confirm the trilemma that an AC protocol can only achieve two out of the following three properties: strong anonymity (i.e., anonymity up to a negligible chance), low bandwidth overhead, and low latency overhead. We further study anonymity against a stronger global passive adversary that can additionally passively compromise some of the AC protocol nodes. For a given number of compromised nodes, we derive necessary constraints between bandwidth and latency overhead whose violation make it impossible for an AC protocol to achieve strong anonymity. We analyze prominent AC protocols from the literature and depict to which extent those satisfy our necessary constraints. Our fundamental necessary constraints offer a guideline not only for improving existing AC systems but also for designing novel AC protocols with non-traditional bandwidth and latency overhead choices.

The authors introduce delegatable functional signatures (DFS) which support the delegation of signing capabilities to another party, called the evaluator , with respect to a functionality . In a DFS, the signer of a message can choose an evaluator, specify how the evaluator can modify the signature without voiding its validity, allow additional input, and decide how the evaluator can further delegate its capabilities. Technically, DFS unify several seemingly different signature primitives, including functional signatures and policy‐based signatures, sanitisable signatures, identity‐based signatures, and blind signatures. The authors characterise the instantiability of DFS with respect to the corresponding security notions of unforgeability and privacy. On the positive side, they show that privacy‐free DFS can be constructed from one‐way functions. Furthermore, they show that unforgeable and private DFS can be constructed from doubly‐enhanced trapdoor permutations. On the negative side, they show that the previous result is optimal regarding its underlying assumptions. Their impossibility result shows that unforgeable private DFS cannot be constructed from one‐way permutations.

Abstract In this paper, we present a rigorous methodology for quantifying the anonymity provided by Tor against a variety of structural attacks, i.e., adversaries that corrupt Tor nodes and thereby perform eavesdropping attacks to deanonymize Tor users. First, we provide an algorithmic approach for computing the anonymity impact of such structural attacks against Tor. The algorithm is parametric in the considered path selection algorithm and is, hence, capable of reasoning about variants of Tor and alternative path selection algorithms as well. Second, we present formalizations of various instantiations of structural attacks against Tor and show that the computed anonymity impact of each of these adversaries indeed constitutes a worst-case anonymity bound for the cryptographic realization of Tor. Third, we use our methodology to conduct a rigorous, largescale evaluation of Tor’s anonymity which establishes worst-case anonymity bounds against various structural attacks for Tor and for alternative path selection algorithms such as DistribuTor, SelekTOR, and LASTor. This yields the first rigorous anonymity comparison between different path selection algorithms. As part of our analysis, we quantify the anonymity impact of a path selection transition phase, i.e., a small number of users decides to run an alternative algorithm while the vast majority still uses the original one. The source code of our implementation is publicly available.

Recently, the live-monitor MATor for formally analyzing user anonymity within the Tor network has been proposed (CCS'14). However, this monitor only considers adversaries that compromise part of the Tor network itself, not Internet infrastructural adversaries. In this work we present a formal technique for analyzing Tor against malicious or overly curious network infrastructure.

In this paper we present MATor: a framework for rigorously assessing the degree of anonymity in the Tor network. The framework explicitly addresses how user anonymity is impacted by real-life characteristics of actually deployed Tor, such as its path selection algorithm, Tor consensus data, and the preferences and the connections of the user. The anonymity assessment is based on rigorous anonymity bounds that are derived in an extension of the AnoA framework (IEEE CSF 2013). We show how to apply MATor on Tor's publicly available consensus and server descriptor data, thereby realizing the first real-time anonymity monitor. Based on experimental evaluations of this anonymity monitor on Tor Metrics data, we propose an alternative path selection algorithm that provides stronger anonymity guarantees without decreasing the overall performance of the Tor network.

Protecting individuals' privacy in online communications has become a challenge of paramount importance. To this end, anonymous communication (AC) protocols such as the widely used Tor network have been designed to provide anonymity to their participating users. While AC protocols have been the subject of several security and anonymity analyses in the last years, there still does not exist a framework for analyzing complex systems such as Tor and their different anonymity properties in a unified manner. In this work we present AnoA: a generic framework for defining, analyzing, and quantifying anonymity properties for AC protocols. AnoA relies on a novel relaxation of the notion of (computational) differential privacy, and thereby enables a unified quantitative analysis of well-established anonymity properties, such as sender anonymity, sender unlinkability, and relationship anonymity. While an anonymity analysis in AnoA can be conducted in a purely information theoretical manner, we show that the protocol's anonymity properties established in AnoA carry over to secure cryptographic instantiations of the protocol. We exemplify the applicability of AnoA for analyzing real-life systems by conducting a thorough analysis of the anonymity properties provided by the Tor network against passive attackers. Our analysis significantly improves on known anonymity results from the literature.