From Private Simultaneous Messages to Zero-Information Arthur–Merlin Protocols and Back

Abstract

Göös, Pitassi and Watson (ITCS, 2015) have recently introduced the notion of Zero-Information Arthur-Merlin Protocols (ZAM). In this model, which can be viewed as a private version of the standard Arthur-Merlin communication complexity game, Alice and Bob are holding a pair of inputs x and y respectively, and Merlin, the prover, attempts to convince them that some public function f evaluates to 1 on (x, y). In addition to standard completeness and soundness, Göös et al., require a "zero-knowledge" property which asserts that on each yes-input, the distribution of Merlin's proof leaks no information about the inputs (x, y) to an external observer. In this paper, we relate this new notion to the well-studied model of Private Simultaneous Messages (PSM) that was originally suggested by Feige, Naor and Kilian (STOC, 1994). Roughly speaking, we show that the randomness complexity of ZAM corresponds to the communication complexity of PSM, and that the communication complexity of ZAM corresponds to the randomness complexity of PSM. This relation works in both directions where different variants of PSM are being used. As a secondary contribution, we reveal new connections between different variants of PSM protocols which we believe to be of independent interest. Our results give rise to better ZAM protocols based on existing PSM protocols, and to better protocols for conditional disclosure of secrets (a variant of PSM) from existing ZAMs.

Structure vs. Hardness Through the Obfuscation Lens

“…While most of our focus has been on showing that hardness in SZK and NP ∩ coNP does not follow from cryptography, here we ask the "inverse question", namely whether certain cryptographic primitives can be built from other cryptographic primitives together with hardness in certain structured complexity classes. Little is known in this direction with the exception of the beautiful work of Ostrovsky and Wigderson [OW93a] who construct a OWF from average-case SZK-hardness, and the recent work of Applebaum and Raykov [AR16] who showed that average-case hardness in the subclass PRE ⊆ SRE ⊆ SZK of languages with a perfect randomized encoding gives us collision-resistant hashing.…”