Some Efficient Solutions to Yao's Millionaire Problem

We present three simple and efficient protocol constructions to solve Yao's Millionaire Problem when the parties involved are non-colluding and semi-honest. The first construction uses a partially homomorphic Encryption Scheme and is a 4-round scheme using 2 encryptions, 2 homomorphic circuit evaluations (subtraction and XOR) and a single decryption. The second construction uses an untrusted third party and achieves a communication overhead linear in input bit-size with the help of an order preserving function.Moreover, the second construction does not require an apriori input bound and can work on inputs of different bit-sizes. The third construction does not use a third party and, even though, it has a quadratic communication overhead, it is a fairly simple construction.Comment: 17 page

Efficient Secure Multiparty Computation Protocol for Sequencing Problem over Insecure Channel

As a powerful tool in solving privacy preserving cooperative problems, secure multiparty computation is more and more popular in electronic bidding, anonymous voting, and online auction. Privacy preserving sequencing problem which is an essential link is regarded as the core issue in these applications. However, due to the difficulties of solving multiparty privacy preserving sequencing problem, related secure protocol is extremely rare. In order to break this deadlock, this paper first presents an efficient secure multiparty computation protocol for the general privacy-preserving sequencing problem based on symmetric homomorphic encryption. The result is of value not only in theory, but also in practice

Lightweight secure integer comparison

We solve the millionaires problem in the semi-trusted model with homomorphic encryption without using intermediate decryptions. This leads to the computationally least expensive solution with homomorphic encryption so far, with a low bandwidth and very low storage complexity. The number of modular multiplications needed is less than the number of modular multiplications needed for one Pallier encryption. The output of the protocol can be either publicly known, encrypted, or secret-shared. The private input of the first player is computationally secure towards the second player, and the private input of the second player is even unconditionally secure towards the first player. We also introduce an efficient client-server solution for the millionaires problem with similar security properties

Improved Garbled Circuit Building Blocks and Applications to Auctions and Computing Minima

We consider generic Garbled Circuit (GC)-based techniques for Secure Function Evaluation (SFE) in the semi-honest model. We describe efficient GC constructions for addition, subtraction, multiplication, and comparison functions. Our circuits for subtraction and comparison are approximately two times smaller (in terms of garbled tables) than previous constructions. This implies corresponding computation and communication improvements in SFE of functions using our efficient building blocks. The techniques rely on recently proposed ``free XOR\u27\u27 GC technique. Further, we present concrete and detailed improved GC protocols for the problem of secure integer comparison, and related problems of auctions, minimum selection, and minimal distance. Performance improvement comes both from building on our efficient basic blocks and several problem-specific GC optimizations. We provide precise cost evaluation of our constructions, which serves as a baseline for future protocols

A Toolbox for privacy preserving distributed data mining

Distributed structure of individual data makes it necessary for data holders to perform collaborative analysis over the collective database for better data mining results. However each site has to ensure the privacy of its individual data, which means no information is revealed about individual values. Privacy preserving distributed data mining is utilized for that purpose. In this study, we try to draw more attention to the topic of privacy preserving data mining by showing a model which is realistic for data mining, and allows for very efficient protocols. We give two protocols which are useful tools in data mining: a protocol for Yaoѫs millionaires problem, and a protocol for numerical distance. Our solution to Yaoѫs millionaires problem is of independent interest since it gives a solution which improves on known protocols with respect to both computation complexity and communication overhead. This protocol can be used for different purposes in privacy preserving data mining algorithms such as comparison and equality test of data records. Our numerical distance protocol is also applicable to variety of algorithms. In this study we applied our numerical distance protocol in a privacy preserving distributed clustering protocol for horizontally partitioned data. We show application of our protocol over different attribute types such as interval-scaled,binary, nominal, ordinal, ratio-scaled, and alphanumeric. We present proof of security of our protocol, and explain communication, and computation complexity analysis indetail

Sorting and Searching Behind the Curtain: Private Outsourced Sort and Frequency-Based Ranking of Search Results Over Encrypted Data

We study the problem of private outsourced sorting of encrypted data. We start by proposing a novel sorting protocol that allows a user to outsource his data to a cloud server in an encrypted form and then request the server to perform computations on this data and sort the result. To perform the sorting the server is assisted by a secure coprocessor with minimal computational and memory resources. The server and the coprocessor are assumed to be honest but curious, i.e., they honestly follow the protocol but are interested in learning more about the user data. We refer to the new protocol as ``private outsourced sorting\u27\u27 since it guarantees that neither the server nor the coprocessor learn anything about user data as long as they are non-colluding. We formally define private outsourced sorting and provide an efficient construction that is based on semi-homomorphic encryption. As an application of our private sort, we present MSRE: the first scheme for outsourced search over encrypted data that efficiently answers multi-term queries with the result ranked using frequency of query terms in the data, while maintaining data privacy. To construct MSRE we use searchable encryption techniques combined with our new private sort framework. Finally, although not discussed in this work, we believe that our private sort framework can turn out to be an important tool for more applications that require outsourced sorting while maintaining data privacy, e.g., database queries

Proxy-secure computation model: application to k-means clustering implementation, analysis and improvements

Distributed privacy preserving data mining applications, where data is divided among several parties, require high amounts of network communication. In order to overcome this overhead, we propose a scheme that reduces remote computations in distributed data mining applications into local computations on a trusted hardware. Cell BE is used to realize the trusted hardware acting as a proxy for the parties. We design a secure two-party computation protocol that can be instrumental in realizing non-colluding parties in privacy-preserving data mining applications. Each party is represented with a signed and encrypted thread on a separate core of Cell BE running in an isolated mode, whereby its execution and data are secured by hardware means. Our implementations and experiments demonstrate that a significant speed up is gained through the new scheme. It is also possible to increase the number of non-colluding parties on Cell BE, which extends the proposed technique to implement most distributed privacy-preserving data mining protocols proposed in literature that require several non-colluding parties