Exploring the limits of common coins using frontier analysis of protocols

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 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 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.

Original languageEnglish (US)
Title of host publicationTheory of Cryptography - 8th Theory of Cryptography Conference, TCC 2011, Proceedings
Pages486-503
Number of pages18
DOIs
StatePublished - 2011
Event8th Theory of Cryptography Conference, TCC 2011 - Providence, RI, United States
Duration: Mar 28 2011Mar 30 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6597 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other8th Theory of Cryptography Conference, TCC 2011
CountryUnited States
CityProvidence, RI
Period3/28/113/30/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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