Committed MPC - Maliciously Secure Multiparty Computation from Homomorphic Commitments.

Anderson C. A. Nascimento, Joern Mueller-Quade, Akira Otsuka +2 more

Tore Kasper Frederiksen, Benny Pinkas B, Avishay Yanai

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.

T-H. Hubert Chan, Kai-Min Chung, Wei-Kai Lin +1 more

Eunkyung Kim, Hyang-Sook Lee, Jeongeun Park

Multikey fully homomorphic encryption (MFHE) allows homomorphic operations between ciphertexts encrypted under different keys. In applications for secure multiparty computation (MPC) protocols, MFHE can be more advantageous than usual fully homomorphic encryption (FHE) since users do not need to agree with a common public key before the computation when using MFHE. In EUROCRYPT 2016, Mukherjee and Wichs constructed a secure MPC protocol in only two rounds via MFHE which deals with a common random/reference string (CRS) in key generation. After then, Brakerski et al. replaced the role of CRS with the distributed setup for CRS calculation to form a four round secure MPC protocol. Thus, recent improvements in round complexity of MPC protocols have been made using MFHE. In this paper, we go further to obtain round-efficient and secure MPC protocols. The underlying MFHE schemes in previous works still involve the common value, CRS, it seems to weaken the power of using MFHE to allow users to independently generate their own keys. Therefore, we resolve the issue by constructing an MFHE scheme without CRS based on LWE assumption, and then we obtain a secure MPC protocol against semi-malicious security in three rounds. We also define a new security notion “multikey-CPA security” to prove that a multikey ciphertext cannot be decrypted unless all the secret keys are gathered and our scheme is multikey-CPA secure.

Arka Rai Choudhuri, Aarushi Goel, Matthew Green +2 more

Shogo Ochiai, Keiichi Iwamura

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.