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

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Bibliographic Details
Title:	From Private Simultaneous Messages to Zero-Information Arthur-Merlin Protocols and Back.
Authors:	Applebaum, Benny¹ bennyap@post.tau.ac.il, Raykov, Pavel¹ pavelraykov@post.tau.ac.il
Source:	Journal of Cryptology. Oct2017, Vol. 30 Issue 4, p961-988. 28p.
Subjects:	Zero-knowledge proofs, Technological complexity, Communication complexity (Information theory), Cryptography, Mathematics
Abstract:	Göös et al. (ITCS, 2015) have recently introduced the notion of Zero-Information Arthur-Merlin Protocols ( $$\mathsf {ZAM}$$ ). 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 ( $$\mathsf {PSM}$$ ) that was originally suggested by Feige et al. (STOC, 1994). Roughly speaking, we show that the randomness complexity of $$\mathsf {ZAM}$$ corresponds to the communication complexity of $$\mathsf {PSM}$$ and that the communication complexity of $$\mathsf {ZAM}$$ corresponds to the randomness complexity of $$\mathsf {PSM}$$ . This relation works in both directions where different variants of $$\mathsf {PSM}$$ are being used. As a secondary contribution, we reveal new connections between different variants of $$\mathsf {PSM} $$ protocols which we believe to be of independent interest. Our results give rise to better $$\mathsf {ZAM}$$ protocols based on existing $$\mathsf {PSM}$$ protocols, and to better protocols for conditional disclosure of secrets (a variant of $$\mathsf {PSM}$$ ) from existing $$\mathsf {ZAM} $$ s. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	Göös et al. (ITCS, 2015) have recently introduced the notion of Zero-Information Arthur-Merlin Protocols ( $$\mathsf {ZAM}$$ ). 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 ( $$\mathsf {PSM}$$ ) that was originally suggested by Feige et al. (STOC, 1994). Roughly speaking, we show that the randomness complexity of $$\mathsf {ZAM}$$ corresponds to the communication complexity of $$\mathsf {PSM}$$ and that the communication complexity of $$\mathsf {ZAM}$$ corresponds to the randomness complexity of $$\mathsf {PSM}$$ . This relation works in both directions where different variants of $$\mathsf {PSM}$$ are being used. As a secondary contribution, we reveal new connections between different variants of $$\mathsf {PSM} $$ protocols which we believe to be of independent interest. Our results give rise to better $$\mathsf {ZAM}$$ protocols based on existing $$\mathsf {PSM}$$ protocols, and to better protocols for conditional disclosure of secrets (a variant of $$\mathsf {PSM}$$ ) from existing $$\mathsf {ZAM} $$ s. [ABSTRACT FROM AUTHOR]
ISSN:	09332790
DOI:	10.1007/s00145-016-9239-3