TY - GEN

T1 - From private simultaneous messages to zero-information Arthur-Merlin protocols and back

AU - Applebaum, Benny

AU - Raykov, Pavel

N1 - Publisher Copyright:
© International Association for Cryptologic Research 2016.

PY - 2016

Y1 - 2016

N2 - 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. Consequently, we derive better upper-bounds on the communication-complexity of ZAM for arbitrary functions. As a secondary contribution, we reveal new connections between different variants of PSM protocols which we believe to be of independent interest.

AB - 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. Consequently, we derive better upper-bounds on the communication-complexity of ZAM for arbitrary functions. As a secondary contribution, we reveal new connections between different variants of PSM protocols which we believe to be of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=84954188458&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-49099-0_3

DO - 10.1007/978-3-662-49099-0_3

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AN - SCOPUS:84954188458

SN - 9783662490983

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 65

EP - 82

BT - Theory of Cryptography - 3th International Conference, TCC 2016-A, Proceedings

A2 - Kushilevitz, Eyal

A2 - Malkin, Tal

PB - Springer Verlag

T2 - 13th International Conference on Theory of Cryptography, TCC 2016

Y2 - 10 January 2016 through 13 January 2016

ER -