Such protocols were only known assuming an honest majority. Protocols in the dishonest majority setting, such as the work of Ishai et al. (CRYPTO 2008), require communication complexity proportional to the circuit size. In addition, constant-round adaptively secure protocols assuming dishonest majority are known to be impossible in the stand-alone setting with black-box proofs of security in the plain model. Here, we solve the problem in the UC setting using a set-up assumption which was shown necessary in order to achieve dishonest majority.
The problem of constructing adaptively secure constant-round MPC protocols against arbitrary corruptions is considered a notorious hard problem. A recent line of works based on indistinguishability obfuscation construct such protocols with near-optimal number of rounds against arbitrary corruptions. However, based on standard assumptions, adaptively secure protocols secure against even just all-but-one corruptions with near-optimal number of rounds are not known. However, in this work we provide a three-round solution based only on LWE and NIZK secure against all-but-one corruptions.
In addition, Asharov et al. (EUROCRYPT 2012) and more recently Mukherjee and Wichs (ePrint 2015) presented constant-round protocols based on LWE which are secure only in the presence of static adversaries. Assuming NIZK and LWE their static protocols run in two rounds where the latter one is only based on a common random string. Assuming adaptively secure UC NIZK, proposed by Groth et al. (ACM 2012), and LWE as mentioned above our adaptive protocols run in three rounds.
Our protocols are constructed based on a special type of cryptosystem we call equivocal FHE from LWE. We also build adaptively secure UC commitments and UC zero-knowledge proofs (of knowledge) from LWE. Moreover, in the decryption phase using an AMD code mechanism we avoid the use of ZK and achieve communication complexity that does not scale with the decryption circuit.Category / Keywords: MPC, adaptive security, LWE, FHE Original Publication (with minor differences): IACR-PKC-2016 Date: received 12 Oct 2014, last revised 4 Jan 2016 Contact author: antigoni at cs au dk Available format(s): PDF | BibTeX Citation Version: 20160105:010415 (All versions of this report) Short URL: ia.cr/2014/830 Discussion forum: Show discussion | Start new discussion