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International Symposium on Computing and Networking Workshops (CANDARW)

New Approach to Dishonest-Majority Secure Multiparty Computation for Malicious Adversaries when n < 2k − 1

Shogo Ochiai, Keiichi Iwamura

Published Nov 1, 2020• 2 citations
Publisher

Abstract

In general, the (k, n) threshold secret sharing scheme (SSS) does not allow unconditionally secure multiparty computation (MPC) for n <; 2k - 1 . Therefore, Iwamura research team has been focusing on conditions under which the secure MPC can be performed securely for n <; 2k - 1, and found that their secure MPC protocol for n <; 2k - 1 is allowed under these three conditions against semi-honest adversaries: (1) the secret information does not contain 0 in the secure multiplication; (2) there is a set of distributed values for 1 using random numbers unknown to the adversaries; (3) the position of the values in the set of distributed values handled by each server is fixed during the sequence of computation. However, their protocol is not secure against malicious adversaries while SPDZ, which is representative secure MPC protocol, is secure against malicious adversaries. Therefore, we propose a secure MPC protocol against malicious adversaries based on the protocol of Iwamura research team.

DOI
10.1109/candarw51189.2020.00074

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In general, the (k, n) threshold secret sharing scheme (SSS) does not allow unconditionally secure multiparty computation (MPC) for n <; 2k - 1 . Therefore, Iwamura research team has been focusing on conditions under which the secure MPC can be performed securely for n <; 2k - 1, and found that their secure MPC protocol for n <; 2k - 1 is allowed under these three conditions against semi-honest adversaries: (1) the secret information does not contain 0 in the secure multiplication; (2) there is a set of distributed values for 1 using random numbers unknown to the adversaries; (3) the position of the values in the set of distributed values handled by each server is fixed during the sequence of computation. However, their protocol is not secure against malicious adversaries while SPDZ, which is representative secure MPC protocol, is secure against malicious adversaries. Therefore, we propose a secure MPC protocol against malicious adversaries based on the protocol of Iwamura research team.
We provide new two-round multiparty secure computation (MPC) protocols in the dishonest majority setting assuming the minimal assumption that two-round oblivious transfer (OT) exists. If the assumed two-round OT protocol is secure against semi-honest adversaries (in the plain model) then so is our two-round MPC protocol. Similarly, if the assumed two-round OT protocol is secure against malicious adversaries (in the common random/reference string model) then so is our two-round MPC protocol. Previously, two-round MPC protocols were only known under relatively stronger computational assumptions.
Secure multiparty computation (MPC) enables a set of parties to securely carry out a joint computation of their private inputs without revealing anything but the output. Protocols for semi-honest adversaries guarantee security as long as the corrupted parties run the specified protocol and ensure that nothing is leaked in the transcript. In contrast, protocols for malicious adversaries guarantee security in the presence of arbitrary adversaries who can run any attack strategy. Security for malicious adversaries is typically what is needed in practice (and is always preferred), but comes at a significant cost. In this paper, we present the first protocol for a two-thirds honest majority that achieves security in the presence of malicious adversariesat essentially the exact same cost as the best known protocols for semi-honest adversaries. Our construction is not a general transformation and thus it is possible that better semi-honest protocols will be constructed which do not support our transformation. Nevertheless, for the current state-of-the-art for many parties (based on Shamir sharing), our protocol invokes the best semi-honest multiplication protocol exactly once per multiplication gate (plus some additional local computation that is negligible to the overall cost). Concretely, the best version of our protocol requires each party to send on average of just 2 2/3 elements per multiplication gate (when the number of multiplication gates is at least the number of parties). This is four times faster than the previous-best protocol of Barak et al. (ACM CCS 2018) for small fields, and twice as fast as the previous-best protocol of Chida et al. (CRYPTO 2018) for large fields.
We present a new multiparty computation protocol secure against a static and malicious dishonest majority. Unlike most previous protocols that were based on working on MAC-ed secret shares, our approach is based on computations on homomorphic commitments to secret shares. Specifically we show how to realize MPC using any additively-homomorphic commitment scheme, even if such a scheme is an interactive two-party protocol. Our new approach enables us to do arithmetic computation over arbitrary finite fields. In addition, since our protocol computes over committed values, it can be readily composed within larger protocols, and can also be used for efficiently implementing committing OT or committed OT. This is done in two steps, each of independent interest: Black-box extension of any (possibly interactive) two-party additively homomorphic commitment scheme to an additively homomorphic multiparty commitment scheme, only using coin-tossing and a “weak” equality evaluation functionality. Realizing multiplication of multiparty commitments based on a lightweight preprocessing approach. Finally we show how to use the fully homomorphic commitments to compute any functionality securely in the presence of a malicious adversary corrupting any number of parties.
Protocols for secure multiparty computation enable a set of parties to compute a function of their inputs without revealing anything but the output. The security properties of the protocol must be preserved in the presence of adversarial behavior. The two classic adversary models considered are semi-honest (where the adversary follows the protocol specification but tries to learn more than allowed by examining the protocol transcript) and malicious (where the adversary may follow any arbitrary attack strategy). Protocols for semi-honest adversaries are often far more efficient, but in many cases the security guarantees are not strong enough.
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.