Cryptography from sunspots: How to use an imperfect reference string

Ran Canetti*, Rafael Pass, Abhi Shelat

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

44 Scopus citations

Abstract

The Common Reference String (CRS) model equips all protocol participants with a common string that is sampled from a pre-specified distribution, say the uniform distribution. This model enables otherwise-impossible cryptographic goals such as removing interaction from protocols and guaranteeing composable security. However, knowing the precise distribution of the reference string seems crucial for all known protocols in this model, in the sense that current security analyses fail when the actual distribution of the reference string is allowed to differ from the specified one even by a small amount. This fact rules out many potential implementations of the CRS model, such as measurements of physical phenomena (like sunspots), or alternatively using random sources that might be adversarially influenced. We study the possibility of obtaining universally composable (UC) security in a relaxed variant of the CRS model, where the reference string it taken from an adversarially specified distribution that's unknown to the protocol. On the positive side, we demonstrate that UC general secure computation is obtainable even when the reference string is taken from an arbitrary, adversarially chosen distribution, as long as (a) this distribution has some minimal min-entropy, (b) it has not too long a description, (c) it is efficiently samplable, and (d) the sampling algorithm is known to the adversary (and simulator). On the negative side, we show that if any one of these four conditions is removed then general UC secure computation becomes essentially impossible.

Original languageEnglish
Title of host publicationProceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007
Pages249-259
Number of pages11
DOIs
StatePublished - 2007
Externally publishedYes
Event48th Annual Symposium on Foundations of Computer Science, FOCS 2007 - Providence, RI, United States
Duration: 20 Oct 200723 Oct 2007

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference48th Annual Symposium on Foundations of Computer Science, FOCS 2007
Country/TerritoryUnited States
CityProvidence, RI
Period20/10/0723/10/07

Keywords

  • Common reference string
  • Entropy
  • Non black-box constructions
  • Setup models
  • UC security

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