Saikrishna Badrinarayanan -- Promise Zero Knowledge and its Applications to Round Optimal MPC

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:

1) 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).

2) 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.

Based on joint work with Vipul Goyal, Abhishek Jain, Yael Tauman Kalai, Dakshita Khurana and Amit Sahai

Saikrishna Badrinarayanan is a 4th year PhD student at UCLA advised by Prof. Amit Sahai and Prof. Rafail Ostrovsky. His research interests are Secure Multiparty Computation and Functional Encryption.

Tuesday, August 7, 2018 - 4:15pm to 5:15pm
Gates 463A