X-Vine: Secure and Pseudonymous Routing Using Social Networks

Distributed hash tables suffer from several security and privacy vulnerabilities, including the problem of Sybil attacks. Existing social network-based solutions to mitigate the Sybil attacks in DHT routing have a high state requirement and do not provide an adequate level of privacy. For instance, such techniques require a user to reveal their social network contacts. We design X-Vine, a protection mechanism for distributed hash tables that operates entirely by communicating over social network links. As with traditional peer-to-peer systems, X-Vine provides robustness, scalability, and a platform for innovation. The use of social network links for communication helps protect participant privacy and adds a new dimension of trust absent from previous designs. X-Vine is resilient to denial of service via Sybil attacks, and in fact is the first Sybil defense that requires only a logarithmic amount of state per node, making it suitable for large-scale and dynamic settings. X-Vine also helps protect the privacy of users social network contacts and keeps their IP addresses hidden from those outside of their social circle, providing a basis for pseudonymous communication. We first evaluate our design with analysis and simulations, using several real world large-scale social networking topologies. We show that the constraints of X-Vine allow the insertion of only a logarithmic number of Sybil identities per attack edge; we show this mitigates the impact of malicious attacks while not affecting the performance of honest nodes. Moreover, our algorithms are efficient, maintain low stretch, and avoid hot spots in the network. We validate our design with a PlanetLab implementation and a Facebook plugin.Comment: 15 page

Nonlocal PageRank

In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a \textit{long-range interaction} between them, does not exhibit concentration phenomena typical of spectral rankings which take into account just local interactions. We show that the predictive value of the rankings obtained using our proposals is considerably improved on different real world problems

d-Path Laplacians and Quantum Transport on Graphs

We generalize the Schrödinger equation on graphs to include long-range interactions (LRI) by means of the Mellin-transformed d-path Laplacian operators. We find analytical expressions for the transition and return probabilities of a quantum particle at the nodes of a ring graph. We show that the average return probability in ring graphs decays as a power law with time when LRI is present. In contrast, we prove analytically that the transition and return probabilities on a complete and start graphs oscillate around a constant value. This allowed us to infer that in a barbell graph-a graph consisting of two cliques separated by a path-the quantum particle get trapped and oscillates across the nodes of the path without visiting the nodes of the cliques. We then compare the use of the Mellin-transformed d-path Laplacian operators versus the use of fractional powers of the combinatorial Laplacian to account for LRI. Apart from some important differences observed at the limit of the strongest LRI, the d-path Laplacian operators produces the emergence of new phenomena related to the location of the wave packet in graphs with barriers, which are not observed neither for the Schrödinger equation without LRI nor for the one using fractional powers of the Laplacian

Efficient network exploration by means of resetting self-avoiding random walkers

The self-avoiding random walk (SARW) is a stochastic process whose state variable avoids returning to previously visited states. This non-Markovian feature has turned SARWs a powerful tool for modelling a plethora of relevant aspects in network science, such as network navigability, robustness and resilience. We analytically characterize self-avoiding random walkers that evolve on complex networks and whose memory suffers stochastic resetting, that is, at each step, with a certain probability, they forget their previous trajectory and start free diffusion anew. Several out-of-equilibrium properties are addressed, such as the time-dependent position of the walker, the time-dependent degree distribution of the non-visited network and the first-passage time distribution, and its moments, to target nodes. We examine these metrics for different resetting parameters and network topologies, both synthetic and empirical, and find a good agreement with simulations in all cases. We also explore the role of resetting on network exploration and report a non-monotonic behavior of the cover time: frequent memory resets induce a global minimum in the cover time, significantly outperforming the well-known case of the pure random walk, while reset events that are too spaced apart become detrimental for the network discovery. Our results provide new insights into the profound interplay between topology and dynamics in complex networks, and shed light on the fundamental properties of SARWs in nontrivial environments.Comment: 10 pages & 3 figures; Supp. Mat.: 11 pages & 15 figure

Long-range connections and mixed diffusion in fractional networks

Networks with long-range connections, obeying a distance-dependent power law of sufficiently small exponent, display superdiffusion, L´evy flights and robustness properties very different from the scale-free networks. It has been proposed that these networks, found both in society and in biology, be classified as a new structure, the fractional networks. Particular important examples are the social networks and the modular hierarchical brain networks where both short- and long-range connections are present. The anomalous superdiffusive and the mixed diffusion behavior of these networks is studied here as well as its relation to the nature and density of the long-range connections.info:eu-repo/semantics/publishedVersio