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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Constant-Round Client-Aided Two-Server Secure Comparison Protocol and Its Applications

Hiraku Morita, Nuttapong Attrapadung, Tadanori Teruya, Satsuya Ohata, Koji Nuida, Goichiro Hanaoka

Published Dec 31, 2019• 1 citation
Publisher

Abstract

We present an improved constant-round secure two-party protocol for integer comparison functionality, which is one of the most fundamental building blocks in secure computation. Our protocol is in the so-called client-server model, which is utilized in real-world MPC products such as Sharemind, where any number of clients can create shares of their input and distribute to the servers who then jointly compute over the shares and return the shares of the result to the client. In the client-aided client-server model, as mentioned briefly by Mohassel and Zhang (S&P'17), a client further generates and distributes some necessary correlated randomness to servers. Such correlated randomness admits efficient protocols since otherwise, servers have to jointly generate randomness by themselves, which can be inefficient. In this paper, we improve the state-of-the-art constant-round comparison protocols by Damgå rd et al. (TCC'06) and Nishide and Ohta (PKC'07) in the client-aided model. Our techniques include identifying correlated randomness in these comparison protocols. Along the way, we also use tree-based techniques for a building block, which deviate from the above two works. Our proposed protocol requires only 5 communication rounds, regardless of the bit length of inputs. This is at least 5 times fewer rounds than existing protocols. We implement our secure comparison protocol in C++. Our experimental results show that this low-round complexity benefits in high-latency networks such as WAN. We also present secure Min/Argmin protocols using the secure comparison protocol.

DOI
10.1587/transfun.2019cip0023

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Secure multi-party computation (MPC) provides provable security guarantees for many privacy critical applications. The semi-honest MPC protocols are secure against semi-honest adversaries who can only observe the protocol execution, while the maliciously secure MPC protocols are secure against malicious adversaries who can deviate from the protocol description arbitrarily. Many security sensitive applications tend to use semi-honest MPC protocols because malicious security comes with huge communication and/or computation costs. In this work, we show how to efficiently transform generic semi-honest two-party protocols into maliciously secure multi-party protocol in the server-aided setting. We further propose an optimized constant-round server-aided MPC protocol. The proposed protocols are secure when all but one parties are maliciously corrupted, while the remaining party and the server are corrupted by semi-honest and non-colluding adversaries. We implement and evaluate our constant-round protocol. For the 2-party case, our protocol is only 1.11× slower than thesemi-honestYao's Garbled Circuits protocol, and it is 9.16× faster than the maliciously secure authenticated garbling protocol and 4.96× faster than the state-of-the-art maliciously secure server-aided protocol of Wuet al.For the 8-party case, our protocol is 103.29× faster than the authenticated garbling protocol and 17.03× faster than the protocol of Wuet al.

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We present an improved constant-round secure two-party protocol for integer comparison functionality, which is one of the most fundamental building blocks in secure computation. Our protocol is in the so-called client-server model, which is utilized in real-world MPC products such as Sharemind, where any number of clients can create shares of their input and distribute to the servers who then jointly compute over the shares and return the shares of the result to the client. In the client-aided client-server model, as mentioned briefly by Mohassel and Zhang (S&P'17), a client further generates and distributes some necessary correlated randomness to servers. Such correlated randomness admits efficient protocols since otherwise, servers have to jointly generate randomness by themselves, which can be inefficient. In this paper, we improve the state-of-the-art constant-round comparison protocols by Damgå rd et al. (TCC'06) and Nishide and Ohta (PKC'07) in the client-aided model. Our techniques include identifying correlated randomness in these comparison protocols. Along the way, we also use tree-based techniques for a building block, which deviate from the above two works. Our proposed protocol requires only 5 communication rounds, regardless of the bit length of inputs. This is at least 5 times fewer rounds than existing protocols. We implement our secure comparison protocol in C++. Our experimental results show that this low-round complexity benefits in high-latency networks such as WAN. We also present secure Min/Argmin protocols using the secure comparison protocol.
A secure integer comparison protocol is one of the most fundamental building blocks to construct protocols of rich functionality in multi-party computation. It allows parties to compute the less-than functionality on shared values in privacy preserving manner. In this paper, we present a tree-based secure two-party comparison protocol in the client-aided client-server model, which outperforms existing approaches in terms of round complexity when it is used for 64-bit data. Our proposed protocol requires only 9 communication rounds to compare 64-bit data, which is at least 3 times fewer rounds than existing protocols. This suggests that our protocol is adequate to be used in low-latency networks such as WAN.
Integer division is one of the most fundamental arithmetic operators and is ubiquitously used. However, the existing division protocols in secure multi-party computation (MPC) are inefficient and very complex, and this has been a barrier to applications of MPC such as secure machine learning. We already have some secure division protocols working in ℤ2n. However, these existing results have drawbacks that those protocols needed many communication rounds and needed to use bigger integers than in/output. In this paper, we improve a secure division protocol in two ways. First, we construct a new protocol using only the same size integers as in/output. Second, we build efficient constant-round building blocks used as subprotocols in the division protocol. With these two improvements, communication rounds of our division protocol are reduced to about 36% (87 rounds → 31 rounds) for 64-bit integers in comparison with the most efficient previous one.
Secure multi-party computation (MPC) is a cryptographic tool that enables a set of parties to compute a function jointly while keeping each input secret. Since MPC based on secret sharing (SS) achieves high throughput and works fast, many applications have been developed. However, SS-based MPC requires many communication rounds in general, and this becomes a performance bottleneck in real-world applications under high-latency networks. In this paper, we propose SS-based secure three-party computation with almost no preprocessing based on our new (small-)constant-round fundamental gates, by revisiting a framework in a few previous works where a number of parties are assisted by another party who may partially learn secret information. Instead of ordinary logical gates, our fundamental gate is an efficient Equality, for which the result leaks to the third party, and we develop novel two-round constructions of secure building-block protocols (LessThan Comparison, RightShift, Table LookUp, etc.) from the insecure Equality. To show the practicality of our protocols, we implement a secure exact edit distance protocol for two genome strings. Our experiments show that in some network setting our protocol is about 2 times faster (14 times faster taking preprocessing into consideration) than the state-of-the-art SS-based protocol (Ohata and Nuida, FC 2020).
In this paper we are interested in efficient and secure constant round multi-party protocols which provide unconditional security against so called honest-but-curious adversaries. In particular, we design a novel constant round protocol that converts from shares over Z_q to shares over the integers working for all shared inputs from Z_q. Furthermore, we present a constant round protocol to securely evaluate a shared input on a public polynomial whose running time is linear in the degree of the polynomial. The proposed solution makes use of Chebyshev Polynomials. We show that the latter two protocols can be used to design efficient constant round protocols for the following natural problems: (i) Equality: Computing shares of the bit indicating if a shared input value equals zero or not. This provides the missing building blocks for many constant round linear algebra protocols from the work of Cramer and Damgård [CD01]. (ii) Comparison: Computing shares of a bit indicating which of two shared inputs is greater. (iii) Bits: Computing shares of the binary representation of a shared input value. (iv) Exponentiation: Computing shares of x^a mod q given shares of x, a and q. Prior to this paper, for all the above mentioned problems, there were in general no efficient constant round protocols known providing unconditional security.
Secure multi-party computation (MPC) allows a set of parties to compute a function jointly while keeping their inputs private. Compared with the MPC based on garbled circuits, some recent research results show that MPC based on secret sharing (SS) works at a very high speed. Moreover, SS-based MPC can be easily vectorized and achieve higher throughput. In SS-based MPC, however, we need many communication rounds for computing concrete protocols like equality check, less-than comparison, etc. This property is not suited for large-latency environments like the Internet (or WAN). In this paper, we construct semi-honest secure communication-efficient two-party protocols. The core technique is Beaver triple extension, which is a new tool for treating multi-fan-in gates, and we also show how to use it efficiently. We mainly focus on reducing the number of communication rounds, and our protocols also succeed in reducing the number of communication bits (in most cases). As an example, we propose a less-than comparison protocol (under practical parameters) with three communication rounds. This is less than a half compared with the previous work. Moreover, the number of communication bits is also 38.4%38.4\%38.4% fewer. As a result, total online execution time is 56.1%56.1\%56.1% shorter than the previous work adopting the same settings. Although the computation costs of our protocols are more expensive than those of previous work, we confirm via experiments that such a disadvantage has small effects on the whole online performance in the typical WAN environments.
Secure multi-party computation (MPC) provides provable security guarantees for many privacy critical applications. The semi-honest MPC protocols are secure against semi-honest adversaries who can only observe the protocol execution, while the maliciously secure MPC protocols are secure against malicious adversaries who can deviate from the protocol description arbitrarily. Many security sensitive applications tend to use semi-honest MPC protocols because malicious security comes with huge communication and/or computation costs. In this work, we show how to efficiently transform generic semi-honest two-party protocols into maliciously secure multi-party protocol in the server-aided setting. We further propose an optimized constant-round server-aided MPC protocol. The proposed protocols are secure when all but one parties are maliciously corrupted, while the remaining party and the server are corrupted by semi-honest and non-colluding adversaries. We implement and evaluate our constant-round protocol. For the 2-party case, our protocol is only 1.11× slower than thesemi-honestYao's Garbled Circuits protocol, and it is 9.16× faster than the maliciously secure authenticated garbling protocol and 4.96× faster than the state-of-the-art maliciously secure server-aided protocol of Wuet al.For the 8-party case, our protocol is 103.29× faster than the authenticated garbling protocol and 17.03× faster than the protocol of Wuet al.