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IOS Press eBooks

Stateful Abstractions of Secure Multiparty Computation

Peeter Laud

Published Jan 1, 2015• 4 citations
Publisher

Abstract

In this chapter we present the Arithmetic Black Box (ABB) functionality. It is an ideal functionality that preserves the privacy of the data it stores and allows computations to be performed on the data stored, as well as retrieve certain pieces of data. We show that it is a very convenient abstraction of secure multiparty computation (SMC), which enables easy extensions and the construction of large privacy-preserving applications on top of it. In this chapter, we give a detailed definition of the ABB functionality and present different ways in which it can be implemented securely. We explain what extending an ABB means and how it is integrated into larger applications.

DOI
10.3233/978-1-61499-532-6-26

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In this chapter we present the Arithmetic Black Box (ABB) functionality. It is an ideal functionality that preserves the privacy of the data it stores and allows computations to be performed on the data stored, as well as retrieve certain pieces of data. We show that it is a very convenient abstraction of secure multiparty computation (SMC), which enables easy extensions and the construction of large privacy-preserving applications on top of it. In this chapter, we give a detailed definition of the ABB functionality and present different ways in which it can be implemented securely. We explain what extending an ABB means and how it is integrated into larger applications.
In this note we describe efficient protocols to perform in parallel many reads and writes in private arrays according to private indices. The protocol is implemented on top of the Arithmetic Black Box (ABB) and can be freely composed to build larger privacy-preserving applications. For a large class of secure multiparty computation (SMC) protocols, we believe our technique to have better practical performance than any previous ORAM technique that has been adapted for use in SMC. We also argue that for a significant class of SMC protocols, our technique has better asymptotic performance than previous approaches.
Secure multiparty computation (SMC) allows a set of parties to jointly compute a function on private inputs such that, they learn only the output of the function, and the correctness of the output is guaranteed even when a subset of the parties is controlled by an adversary. SMC allows data to be kept in an uncompromisable form and still be useful, and it also gives new meaning to data ownership, allowing data to be shared in a useful way while retaining its privacy. Thus, applications of SMC hold promise for addressing some of the security issues information-driven societies struggle with. In this thesis, we implement two SMC protocols. Our primary objective is to gain a solid understanding of the basic concepts related to SMC. We present a brief survey of the field, with focus on SMC based on secret sharing. In addition to the protocol im- plementations, we implement circuit randomization, a common technique for efficiency improvement. The implemented protocols are run on a simulator to securely evaluate some simple arithmetic functions, and the round complexities of the implemented protocols are compared. Finally, we attempt to extend the implementation to support more general computations.
In this paper, comparative study of different available Secure Multiparty Computation (SMC) protocols have been addressed. In SMC, a set of parties wishes to jointly compute some function on their inputs. This computation must preserve certain security properties, like privacy and correctness. The general approach for such kind of computation is to make use of trusted third party to do the computation and then announce the result publicly. The major problem with this approach is that it is difficult to find a third party which is trusted by all the parties providing the inputs. This implies that the data of parties must be secured. Security is meant to achieve correctness of the result of computation and keeping the party’s input private even if some of the parties are corrupted.
Secure Multiparty Computation (abrv. MPC) is a group of techniques that enable multiple entities to compute some function on their private inputs. Moreformally,itenablesasetofplayers{P1,...,Pn},eachofthemholding private inputs xi, where i is the index of the player, to evaluate a function f(x1,...,xn) = (y1,...,yn) so that every player Pi learns yi. Multiparty Computation has many application scenarios such as private auctioning, computation outsourcing, or private information retrieval. These and other applications make MPC a very appealing object of study, since it may be a solution to problems in different fields. The objective of this thesis is twofold. First, we aim to provide a comprehensive guide to the current state of multiparty computation protocols. Wedosobyinspectingthetwocategorieswheremostgeneralfunctionality secure function evaluation protocols are inserted - boolean or arithmetic circuit evaluation. Moreover, we show how to implement MPC protocols with current constructions, and what problems are inherently connected to the chosen representations. Second, we document some of the design choices behind a partial implementation of a concrete secure arithmetic circuit evaluation protocol - the SPDZ protocol by Damgård et al. [10]. We explain the protocol in general terms, and then go into the details of some subprotocols, namely those that were implemented.
As a fundamental part of cryptography, secure multiparty computation (SMC) is a building block of various cryptographic protocols, and it is also a hot topic in the international cryptographic community.In recent years, many SMC problems, such as secret information comparison, secret set problems and secure multiparty computational geometry, have been widely studied.As many practical problems need to be described by rational numbers, it is both theoretically and practically important to study the SMC problems in the rational number field.However, most of the existing researches focus on integers and the studied data are mainly one-dimensional data.There are few researches on secure multiparty computation of multi-dimensional data in the rational number field, but they can’t be generalized.Based on the fractional representation of rational numbers, the new encoding schemes about rational numbers and rational number vectors were proposed, which could encode multi-dimensional data in the rational number field and provided new solutions for other SMC problems in the rational number field.Based on the encoding scheme and one-way hash function, some protocols were designed for equality problems and set problems in the rational number field.These protocols used basic arithmetic operation and hash operation to guarantee efficiency than existing related protocols.And these protocols didn’t limit the range of research data and they were more widely applicable.It proves that these protocols are secure in the semi-honest model using simulation paradigm, and demonstrates the efficiency and the applicability of these protocols by theoretical analysis and experiment.A practical example was also given to illustrate that approaches are more versatile, and they could also be directly used to solve some secure multiparty computational geometry problems in the rational number field.