As decentralized computing scenarios get ever more popular, unstructured topologies are natural candidates to consider running mix networks upon. We consider mix network topologies where mixes are placed on the nodes of an unstructured network, such as social networks and scale-free random networks. We explore the efficiency and traffic analysis resistance properties of mix networks based on unstructured topologies as opposed to theoretically optimal structured topologies, under high latency conditions. We consider a mix of directed and undirected network models, as well as one real world case study -- the LiveJournal friendship network topology. Our analysis indicates that mix-networks based on scale-free and small-world topologies have, firstly, mix-route lengths that are roughly comparable to those in expander graphs; second, that compromise of the most central nodes has little effect on anonymization properties, and third, batch sizes required for warding off intersection attacks need to be an order of magnitude higher in unstructured networks in comparison with expander graph topologies.
Borisov @cite_11 analyzes anonymous communications over a De Bruijn graph topology overlay network. He analyzes the deBruijn graph topology and comments on their successful mixing capabilities.
@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. We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013 This paper concerns the communication primitives of broadcasting (one-to-all communication) and gossiping (all-to-all communication) in radio networks with known topology, i.e., where for each primitive the schedule of transmissions is precomputed based on full knowledge about the size and the topology of the network.The first part of the paper examines the two communication primitives in general graphs. In particular, it proposes a new (efficiently computable) deterministic schedule that uses O(D+Δ log n) time units to complete the gossiping task in any radio network with size n, diameter D and max-degree Δ. Our new schedule improves and simplifies the currently best known gossiping schedule, requiring time O(D+√[i+2]DΔ logi+1 n), for any network with the diameter D=Ω(logi+4n), where i is an arbitrary integer constant i ≥ 0, see [17]. For the broadcast task we deliver two new results: a deterministic efficient algorithm for computing a radio schedule of length D+O(log3 n), and a randomized algorithm for computing a radio schedule of length D+O(log2 n). These results improve on the best currently known D+O(log4 n) time schedule due to Elkin and Kortsarz [12].The second part of the paper focuses on radio communication in planar graphs, devising a new broadcasting schedule using fewer than 3D time slots. This result improves, for small values of D, on currently best known D+O(log3n) time schedule proposed by Elkin and Kortsarz in [12]. Our new algorithm should be also seen as the separation result between the planar and the general graphs with a small diameter due to the polylogarithmic inapproximability result in general graphs due to Elkin and Kortsarz, see [11]. We consider the problem of diffusing information in networks that contain malicious nodes. We assume that each normal node in the network has no knowledge of the network topology other than an upper bound on the number of malicious nodes in its neighborhood. We introduce a topological property known as r-robustness of a graph, and show that this property provides improved bounds on tolerating malicious behavior, in comparison to traditional concepts such as connectivity and minimum degree. We use this topological property to analyze the canonical problems of distributed consensus and broadcasting, and provide sufficient conditions for these operations to succeed. Finally, we provide a construction for r-robust graphs and show that the common preferential-attachment model for scale-free networks produces a robust graph.