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Bit Decomposition Protocols in Secure Multiparty Computation

Peeter Laud, Alisa Pankova

Published Jan 1, 2018• 0 citations
Publisher

Abstract

We present improved protocols for the conversion of secret-shared bit-vectors into secret-shared integers and vice versa, for the use as subroutines in secure multiparty computation (SMC) protocols and for protocols verifying the adherence of parties to prescribed SMC protocols. The protocols are primarily designed for three-party computation with honest majority. We evaluate our protocols as part of the Sharemind three-party protocol set and see a general reduction of verification overheads, thereby increasing the practicality of covertly or actively secure Sharemind protocols.

DOI
10.1145/3267973.3267979

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We present improved protocols for the conversion of secret-shared bit-vectors into secret-shared integers and vice versa, for the use as subroutines in secure multiparty computation (SMC) protocols and for protocols verifying the adherence of parties to prescribed SMC protocols. The protocols are primarily designed for three-party computation with honest majority. We evaluate our protocols as part of the Sharemind three-party protocol set and see a general reduction of verification overheads, thereby increasing the practicality of covertly or actively secure Sharemind protocols.
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.
Secure multi-party computation (SMC) is an emerging topic which has been drawing growing attention during recent decades. There are many examples which show importance of SMC constructions in practice, such as privacy-preserving decision making and machine learning, auctions, private set intersection, and others. In this tutorial, we provide a comprehensive coverage of SMC techniques, starting from precise definitions and fundamental techniques. Consequently, a significant portion of the tutorial focuses on recent advances in general SMC constructions. We cover garbled circuit evaluation (GCE) and linear secret sharing (LSS) which are commonly used for secure two-party and multi-party computation, respectively. The coverage includes both standard adversarial models: semi-honest and malicious. For GCE, we start with the original Yao's garbled circuits construction [30] for semi-honest adversaries and consequently cover its recent optimizations such as the "free XOR,'' the garbled row reduction, the half-gates optimization, and the use of AES NI techniques. We follow with a discussion of techniques for making GCE resilient to malicious behavior, which includes the cut-and-choose approach and additional techniques to deter known attacks in the presence of malicious participants. In addition, we include the-state-of-the-art protocols for oblivious transfer (OT) and OT extension in the presence of semi-honest and malicious users. For LSS, we start from standard solutions for the semi-honest adversarial model including [5, 28] and consequently move to recent efficient constructions for semi-honest and malicious adversarial models. The coverage includes different types of corruption thresholds (with and without honest majority), which imply different guarantees with respect to abort.
Secure multiparty computation (SMC) has gained tremendous importance with the growth of the Internet and e-commerce, where mutually untrusted parties need to jointly compute a function of their private inputs. However, SMC protocols usually have very high computational complexities, rendering them practically unusable. In this paper, we tackle the problem of comparing two input values in a secure distributed fashion. We propose efficient secure comparison protocols for both the homomorphic encryption and secret sharing schemes. We also give experimental results to show their practical relevance.
Abstract. This paper presents a generic method for turning passively secure protocols into protocols secure against covert attacks, adding an offline preprocessing and a cheap post-execution verification phase. The execution phase, after which the computed result is already available to the parties, has only negligible overhead. Our method uses shared verification based on precomputed multiplica-tion triples. Such triples are often used to make the protocol execution itself faster, but in this work we make use of these triples especially for verification. The verification preserves the privacy guarantees of the original protocol, and it can be straightforwardly applied to protocols over finite rings, even if the same protocol performs its computation over several distinct rings at once.
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.