Privacy-Preserving Quantum Two-Party Geometric Intersection

Privacy-preserving computational geometry is the research area on the intersection of the domains of secure multi-party computation (SMC) and computational geometry. As an important field, the privacy-preserving geometric intersection (PGI) problem is when each of the multiple parties has a private geometric graph and seeks to determine whether their graphs intersect or not without revealing their private information. In this study, through representing Alice's (Bob's) private geometric graph G_A (G_B) as the set of numbered grids S_A (S_B), an efficient privacy-preserving quantum two-party geometric intersection (PQGI) protocol is proposed. In the protocol, the oracle operation O_A (O_B) is firstly utilized to encode the private elements of S_A=(a_0, a_1, ..., a_(M-1)) (S_B=(b_0, b_1, ..., b_(N-1))) into the quantum states, and then the oracle operation O_f is applied to obtain a new quantum state which includes the XOR results between each element of S_A and S_B. Finally, the quantum counting is introduced to get the amount (t) of the states |a_i+b_j> equaling to |0>, and the intersection result can be obtained by judging t>0 or not. Compared with classical PGI protocols, our proposed protocol not only has higher security, but also holds lower communication complexity

Privacy-preserving proximity detection with secure multi-party computational geometry

Over the last years, Location-Based Services (LBSs) have become popular due to the global use of smartphones and improvement in Global Positioning System (GPS) and other positioning methods. Location-based services employ users' location to offer relevant information to users or provide them with useful recommendations. Meanwhile, with the development of social applications, location-based social networking services (LBSNS) have attracted millions of users because the geographic position of users can be used to enhance the services provided by those social applications. Proximity detection, as one type of location-based function, makes LBSNS more flexible and notifies mobile users when they are in proximity. Despite all the desirable features that such applications provide, disclosing the exact location of individuals to a centralized server and/or their social friends might put users at risk of falling their information in wrong hands, since locations may disclose sensitive information about people including political and religious affiliations, lifestyle, health status, etc. Consequently, users might be unwilling to participate in such applications. To this end, private proximity detection schemes enable two parties to check whether they are in close proximity while keeping their exact locations secret. In particular, running a private proximity detection protocol between two parties only results in a boolean value to the querier. Besides, it guarantees that no other information can be leaked to the participants regarding the other party's location. However, most proposed private proximity detection protocols enable users to choose only a simple geometric range on the map, such as a circle or a rectangle, in order to test for proximity. In this thesis, we take inspiration from the field of Computational Geometry and develop two privacy-preserving proximity detection protocols that allow a mobile user to specify an arbitrary complex polygon on the map and check whether his/her friends are located therein. We also analyzed the efficiency of our solutions in terms of computational and communication costs. Our evaluation shows that compared to the similar earlier work, the proposed solution increases the computational efficiency by up to 50%, and reduces the communication overhead by up to 90%. Therefore, we have achieved a significant reduction of computational and communication complexity

On Communication Protocols that Compute Almost Privately

A traditionally desired goal when designing auction mechanisms is incentive compatibility, i.e., ensuring that bidders fare best by truthfully reporting their preferences. A complementary goal, which has, thus far, received significantly less attention, is to preserve privacy, i.e., to ensure that bidders reveal no more information than necessary. We further investigate and generalize the approximate privacy model for two-party communication recently introduced by Feigenbaum et al.[8]. We explore the privacy properties of a natural class of communication protocols that we refer to as "dissection protocols". Dissection protocols include, among others, the bisection auction in [9,10] and the bisection protocol for the millionaires problem in [8]. Informally, in a dissection protocol the communicating parties are restricted to answering simple questions of the form "Is your input between the values \alpha and \beta (under a predefined order over the possible inputs)?". We prove that for a large class of functions, called tiling functions, which include the 2nd-price Vickrey auction, there always exists a dissection protocol that provides a constant average-case privacy approximation ratio for uniform or "almost uniform" probability distributions over inputs. To establish this result we present an interesting connection between the approximate privacy framework and basic concepts in computational geometry. We show that such a good privacy approximation ratio for tiling functions does not, in general, exist in the worst case. We also discuss extensions of the basic setup to more than two parties and to non-tiling functions, and provide calculations of privacy approximation ratios for two functions of interest.Comment: to appear in Theoretical Computer Science (series A

Privacy Preserving Multi-Server k-means Computation over Horizontally Partitioned Data

The k-means clustering is one of the most popular clustering algorithms in data mining. Recently a lot of research has been concentrated on the algorithm when the dataset is divided into multiple parties or when the dataset is too large to be handled by the data owner. In the latter case, usually some servers are hired to perform the task of clustering. The dataset is divided by the data owner among the servers who together perform the k-means and return the cluster labels to the owner. The major challenge in this method is to prevent the servers from gaining substantial information about the actual data of the owner. Several algorithms have been designed in the past that provide cryptographic solutions to perform privacy preserving k-means. We provide a new method to perform k-means over a large set using multiple servers. Our technique avoids heavy cryptographic computations and instead we use a simple randomization technique to preserve the privacy of the data. The k-means computed has exactly the same efficiency and accuracy as the k-means computed over the original dataset without any randomization. We argue that our algorithm is secure against honest but curious and passive adversary.Comment: 19 pages, 4 tables. International Conference on Information Systems Security. Springer, Cham, 201