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IEEE Information Theory Workshop (ITW)

On secure multiparty sampling for more than two parties

Manoj Prabhakaran, Vinod M. Prabhakaran

Published Sep 1, 2012• 12 citations
Publisher

Abstract

We investigate secure multi-party sampling problems involving more than two parties. In the public discussion model, we give a simple characterization of the distributions that can be sampled without any setup. In a model which allows private point-to-point communication, we reduce the problem of characterizing distributions that can be securely sampled using pairwise setups to the problem of characterizing distributions that can be sampled without any setups.

DOI
10.1109/itw.2012.6404773

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We investigate secure multi-party sampling problems involving more than two parties. In the public discussion model, we give a simple characterization of the distributions that can be sampled without any setup. In a model which allows private point-to-point communication, we reduce the problem of characterizing distributions that can be securely sampled using pairwise setups to the problem of characterizing distributions that can be sampled without any setups.
This work deals with the fundamental problem of characterizing which multiparty distributions can be securely sampled with information-theoretic security against passive corruption, when there is no setup or honest-majority. We focus on the case of 4-party distributions with boolean outputs for each party. We show that such a distribution is securely samplable if and only if every 2-party distribution derived from it by partitioning the parties into two sets is securely samplable. This extends a similar characterization previously known for 3-party distributions.
In the problem of secure multi-party sampling, n parties wish to securely sample an n-variate joint distribution, with each party receiving a sample of one of the correlated variables. The objective is to correctly produce the samples using a distributed message passing protocol, while maintaining privacy against a coalition of passively cheating parties. In the two-party case, we fully characterize the joint distributions that can be securely sampled under perfect correctness and privacy requirements as well as under weakened correctness and privacy requirements. Furthermore, we show that the distributions that can be securely sampled can be produced with a protocol that only uses one round of unidirectional communication. For the n-party case, any distribution can be securely sampled with privacy against a strict minority coalition, due to well-known results in secure multi-party computation. However, when privacy against a majority coalition is required, not all distributions can be securely sampled. We give necessary conditions and sufficient conditions for distributions that can be securely sampled. However, the exact characterization of the distributions that can be securely sampled remains open.
In the secure two-party sampling problem, two parties wish to generate outputs with a desired joint distribution via an interactive protocol, while ensuring that neither party learns more than what can be inferred from only their own output. For semi-honest parties and information-theoretic privacy guarantees, it is well-known that if only noiseless communication is available, then only the joint distributions, for which common information equals mutual information, can be securely sampled. We consider the problem where the parties may also interact via a given set of general communication primitives (multi-input/output channels). Our feasibility characterization of this problem can be stated as a zero-one law: primitives are either complete (enabling the secure sampling of any distribution) or useless (only enabling the secure sampling of trivial distributions). Our characterization of the complete primitives also extends to the more general class of secure two-party computation problems.
The Secure Multiparty computation is characterized by computation by a set of multiple parties each participating using the private input they have. There are different types of models for Secure Multiparty computation based on assumption about the type of adversaries each model is assumed to protect against including Malicious and Covert Adversaries. The model may also assume a trusted setup with either using a Public Key Infrastructure or a using a Common Reference String. Secure Multiparty Computation has a number of applications including Scientific Computation, Database Querying and Data Mining.
It is well known that, in theory, the general secure multi-party computation problem is solvable using circuit evaluation protocols. However, the communication complexity of the resulting protocols depend on the size of the circuit that expresses the functionality to be computed and hence can be impractical. Hence special solutions are needed for specific problems for efficiency reasons. The point inclusion problem in computational geometry is a special multiparty computation and has got many applications. Previous protocols for the secure point inclusion problem are not adequate. In this paper we modify some known solutions to the point inclusion problem in computational geometry to the frame work of secure two-party computation.