I study two privacy-preserving social network graphs to dis- close the types of relationships of connecting edges and provide flexible multigrained access control. To create such graphs, my schemes employ the concept of secretaries and types of relationships. It is significantly more efficient than those that using expensive cryptographic primitives. I also show how these schemes can be used for multigrained access control with various options. In addition, I describe how much these schemes are resilient to infer the types of connecting edges.
Hay @cite_14 defined @math -candidate anonymity model for social network such that for every structure query over the graph, there exist at least @math nodes that match the query. They then suggested a graph perturbation through modifying the graph by edge-deletions followed by edge-insertion. This approach could be an attacker's capability of re-identification of identities; however, it could not support @math -candidate anonymity.
@cite_14
1992286709 165003445 1998091733 2163598416
It is not uncommon in the data anonymization literature to oppose the "old" @math k -anonymity model to the "new" differential privacy model, which offers more robust privacy guarantees. Yet, it is often disregarded that the utility of the anonymized results provided by differential privacy is quite limited, due to the amount of noise that needs to be added to the output, or because utility can only be guaranteed for a restricted type of queries. This is in contrast with @math k -anonymity mechanisms, which make no assumptions on the uses of anonymized data while focusing on preserving data utility from a general perspective. In this paper, we show that a synergy between differential privacy and @math k -anonymity can be found: @math k -anonymity can help improving the utility of differentially private responses to arbitrary queries. We devote special attention to the utility improvement of differentially private published data sets. Specifically, we show that the amount of noise required to fulfill @math ? -differential privacy can be reduced if noise is added to a @math k -anonymous version of the data set, where @math k -anonymity is reached through a specially designed microaggregation of all attributes. As a result of noise reduction, the general analytical utility of the anonymized output is increased. The theoretical benefits of our proposal are illustrated in a practical setting with an empirical evaluation on three data sets. The Degree Anonymity problem arises in the context of combinatorial graph anonymization. It asks, given a graph (G ) and two integers (k ) and (s ), whether (G ) can be made k-anonymous with at most (s ) modifications. Here, a graph is k-anonymous if the graph contains for every vertex at least (k-1 ) other vertices of the same degree. Complementing recent investigations on its computational complexity, we show that this problem is very hard when studied from the viewpoints of approximation as well as parameterized approximation. In particular, for the optimization variant where one wants to minimize the number of either edge or vertex deletions there is no factor- (n^ 1- ) approximation running in polynomial time unless P = NP, for any constant (0 < 1 ). For the variant where one wants to maximize (k ) and the number (s ) of either edge or vertex deletions is given, there is no factor- (n^ 1 2 - ) approximation running in time (f(s) n^ O(1) ) unless W[1] = FPT, for any constant (0 < 1 2 ) and any function (f ). On the positive side, we classify the general decision version as fixed-parameter tractable with respect to the combined parameter solution size (s ) and maximum degree. The proliferation of network data in various application domains has raised privacy concerns for the individuals involved. Recent studies show that simply removing the identities of the nodes before publishing the graph social network data does not guarantee privacy. The structure of the graph itself, and in its basic form the degree of the nodes, can be revealing the identities of individuals. To address this issue, we study a specific graph-anonymization problem. We call a graph k-degree anonymous if for every node v, there exist at least k-1 other nodes in the graph with the same degree as v. This definition of anonymity prevents the re-identification of individuals by adversaries with a priori knowledge of the degree of certain nodes. We formally define the graph-anonymization problem that, given a graph G, asks for the k-degree anonymous graph that stems from G with the minimum number of graph-modification operations. We devise simple and efficient algorithms for solving this problem. Our algorithms are based on principles related to the realizability of degree sequences. We apply our methods to a large spectrum of synthetic and real datasets and demonstrate their efficiency and practical utility. 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.