### Promise Zero Knowledge and its Applications to Round Optimal MPC

Saikrishna Badrinarayanan, Vipul Goyal, Abhishek Jain, Yael Tauman Kalai, Dakshita Khurana, and Amit Sahai

##### Abstract

We devise a new partitioned simulation technique for MPC where the simulator uses different strategies for simulating the view of aborting adversaries and non-aborting adversaries. The protagonist of this technique is a new notion of promise zero knowledge (ZK) where the ZK property only holds against non-aborting verifiers. We show how to realize promise ZK in three rounds in the simultaneous-message model assuming polynomially hard DDH (or QR or N^{th}-Residuosity). We demonstrate the following applications of our new technique: -> We construct the first round-optimal (i.e., four round) MPC protocol for general functions based on polynomially hard DDH (or QR or N^{th}-Residuosity). -> We further show how to overcome the four-round barrier for MPC by constructing a three-round protocol for list coin-tossing'' -- a slight relaxation of coin-tossing that suffices for most conceivable applications -- based on polynomially hard DDH (or QR or N^{th}-Residuosity). This result generalizes to randomized input-less functionalities. Previously, four round MPC protocols required sub-exponential-time hardness assumptions and no multi-party three-round protocols were known for any relaxed security notions with polynomial-time simulation against malicious adversaries. In order to base security on polynomial-time standard assumptions, we also rely upon a leveled rewinding security technique that can be viewed as a polynomial-time alternative to leveled complexity leveraging for achieving non-malleability'' across different primitives.

Note: Improved assumptions and simplified analysis.

Available format(s)
Category
Cryptographic protocols
Publication info
Preprint. MINOR revision.
Keywords
Zero knowledgeMPCCoin Tossing
Contact author(s)
saikrishna @ cs ucla edu
History
2018-04-26: last of 5 revisions
See all versions
Short URL
https://ia.cr/2017/1088

CC BY

BibTeX

@misc{cryptoeprint:2017/1088,
author = {Saikrishna Badrinarayanan and Vipul Goyal and Abhishek Jain and Yael Tauman Kalai and Dakshita Khurana and Amit Sahai},
title = {Promise Zero Knowledge and its Applications to Round Optimal MPC},
howpublished = {Cryptology ePrint Archive, Paper 2017/1088},
year = {2017},
note = {\url{https://eprint.iacr.org/2017/1088}},
url = {https://eprint.iacr.org/2017/1088}
}

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