Abstract. We present Mixminion, a message-based anonymous remailer protocol that supports 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 allow users to maintain long-term pseudonyms using single-use reply blocks as a primitive. Our design integrates link encryption between remailers to provide forward anonymity. Mixminion brings together the best solutions from previous work to create a conservative design that protects against most known attacks. Keywords: anonymity, MIX-net, peer-to-peer, remailer, nymserver, reply block 1

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In many important applications, a collection of mutually distrustful parties must perform private computation over multisets. Each party’s input to the function is his private input multiset. In order to protect these private sets, the players perform privacy-preserving computation; that is, no party learns more information about other parties ’ private input sets than what can be deduced from the result. In this paper, we propose efficient techniques for privacy-preserving operations on multisets. By employing the mathematical properties of polynomials, we build a framework of efficient, secure, and composable multiset operations: the union, intersection, and element reduction operations. We apply these techniques to a wide range of practical problems, achieving more efficient results than those of previous work.

Abstract. This paper presents a secure and flexible Mix-net that has the following properties; it efficiently handles long plaintexts that exceed the modulus size of underlying public-key encryption as well as very short ones (length-flexible), input ciphertext length is not impacted by the number of mix-servers (length-invariant), and its security in terms of anonymity is proven in a formal way (provably secure). One can also add robustness i.e. it outputs correct results in the presence of corrupt servers. The security is proved in the random oracle model by showing a reduction from breaking the anonymity of our Mix-net to breaking a sort of indistinguishability of the underlying symmetric encryption scheme or solving the Decision Diffie-Hellman problem.

In order to design an exceptionally e#cient mix network, both asymptotically and in real terms, we develop the notion of almost entirely correct mixing, and propose a new mix network that is almost entirely correct. In our new mix, the real cost of proving correctness is orders of magnitude faster than all other mix nets. The trade-o# is that our mix only guarantees "almost entirely correct" mixing, i.e it guarantees that the mix network processed correctly all inputs with high (but not overwhelming) probability. We use a new technique for verifying correctness. This new technique consists of computing the product of a random subset of the inputs to a mix server, then require the mix server to produce a subset of the outputs of equal product. Our new mix net is of particular value for electronic voting, where a guarantee of almost entirely correct mixing may well be su#cient to announce instantly the result of a large election. The correctness of the result can later be verified beyond a doubt using any one of a number of much slower proofs of perfectcorrectness, without having to mix the ballots again.

We present a mix network that achieves efficient integration of public-key and symmetric-key operations. This hybrid mix network is capable of natural processing of arbitrarily long input elements, and is fast in both practical and asymptotic senses. While the overhead in the size of input elements is linear in the number of mix servers, it is quite small in practice. In contrast to previous hybrid constructions, ours has optimal robustness, that is, robustness against any minority coalition of malicious servers.

In 2005, Murdoch and Danezis demonstrated the first practical congestion attack against a deployed anonymity network. They could identify which relays were on a target Tor user’s path by building paths one at a time through every Tor relay and introducing congestion. However, the original attack was performed on only 13 Tor relays on the nascent and lightly loaded Tor network. We show that the attack from their paper is no longer practical on today’s 1500-relay heavily loaded Tor network. The attack doesn’t scale because a) the attacker needs a tremendous amount of bandwidth to measure enough relays during the attack window, and b) there are too many false positives now that many other users are adding congestion at the same time as the attacks. We then strengthen the original congestion attack by combining it with a novel bandwidth amplification attack based on a flaw in the Tor design that lets us build long circuits that loop back on themselves. We show that this new combination attack is practical and effective by demonstrating a working attack on today’s deployed Tor network. By coming up with a model to better understand Tor’s routing behavior under congestion, we further provide a statistical analysis characterizing how effective our attack is in each case. 1

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We propose a new mix network that is optimized to produce a correct output very fast when all mix servers execute the mixing protocol correctly (the usual case). Our mix network only produces an output if no server cheats. However, in the rare case when one or several mix servers cheat, we convert the inputs to a format that allows "back-up" mixing. This back-up mixing can be implemented using any one of a wide array of already proposed (but slower) mix networks. When all goes well, our mix net is the fastest, both in real terms and asymptotically, of all those that offer standard guarantees of privacy and correctness. In practice, this benefit far outweighs the drawback of a comparatively complex procedure to recover from cheating. Our new mix is ideally suited to compute almost instantly the output of electronic elections, whence the name "exit-poll" mixing.

Anonymity on the Internet is a property commonly identified with privacy of electronic communications. A number of different systems exist which claim to provide anonymous email and web browsing, but their effectiveness has hardly been evaluated in practice. In this thesis we focus on the anonymity properties of such systems. First, we show how the anonymity of anonymity systems can be quantified, pointing out flaws with existing metrics and proposing our own. In the process we distinguish the anonymity of a message and that of an anonymity system. Secondly, we focus on the properties of building blocks of mix-based (email) anonymity systems, evaluating their resistance to powerful blending attacks, their delay, their anonymity under normal conditions and other properties. This leads us to methods of computing anonymity for a particular class of mixes – timed mixes – and a new binomial mix. Next, we look at the anonymity of a message going through an entire anonymity system based on a mix network architecture. We construct a semantics of a network with threshold mixes, define the information observable by an attacker, and give a