### Exploring the Limits of Common Coins Using Frontier Analysis of Protocols

Hemanta K. Maji, Pichayoot Ouppaphan, Manoj Prabhakaran, and Mike Rosulek

##### Abstract

In 2-party secure computation, access to common, trusted randomness is a fundamental primitive. It is widely employed in the setting of computationally bounded players (under various complexity assumptions) to great advantage. In this work we seek to understand the power of trusted randomness, primarily in the computationally unbounded (or information theoretic) setting. We show that a source of common randomness does not add any additional power for secure evaluation of deterministic functions, even when one of the parties has arbitrary influence over the distribution of the common randomness. Further, common randomness helps only in a trivial sense for realizing randomized functions too (namely, it only allows for sampling from publicly fixed distributions), if UC security is required. To obtain these impossibility results, we employ a recently developed protocol analysis technique, which we call the {\em frontier analysis}. This involves analyzing carefully defined frontiers'' in a weighted tree induced by the protocol's execution (or executions, with various inputs), and establishing various properties regarding one or more such frontiers. We demonstrate the versatility of this technique by employing carefully chosen frontiers to derive the different results. To analyze randomized functionalities we introduce a frontier argument that involves a geometric analysis of the space of probability distributions. Finally, we relate our results to computational intractability questions. We give an equivalent formulation of the cryptomania assumption'' (that there is a semi-honest or standalone secure oblivious transfer protocol) in terms of UC-secure reduction among randomized functionalities. Also, we provide an {\em unconditional result} on the uselessness of common randomness, even in the computationally bounded setting. Our results make significant progress towards understanding the exact power of shared randomness in cryptography. To the best of our knowledge, our results are the first to comprehensively characterize the power of large classes of randomized functionalities.

Note: Full Version of the TCC-2011 Paper

Available format(s)
Category
Foundations
Publication info
Published elsewhere. TCC - 2011 (This is the full version of the paper)
Keywords
multi-party computationuniversal compositionsecure function evaluationtrusted common randomnessfrontier analysis
Contact author(s)
hemanta maji @ gmail com
History
Short URL
https://ia.cr/2011/006

CC BY

BibTeX

@misc{cryptoeprint:2011/006,
author = {Hemanta K.  Maji and Pichayoot Ouppaphan and Manoj Prabhakaran and Mike Rosulek},
title = {Exploring the Limits of Common Coins Using Frontier Analysis of Protocols},
howpublished = {Cryptology ePrint Archive, Paper 2011/006},
year = {2011},
note = {\url{https://eprint.iacr.org/2011/006}},
url = {https://eprint.iacr.org/2011/006}
}

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