License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2020.30
URN: urn:nbn:de:0030-drops-117150
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11715/
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Bitansky, Nir ; Geier, Nathan

On Oblivious Amplification of Coin-Tossing Protocols

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LIPIcs-ITCS-2020-30.pdf (0.5 MB)

Abstract

We consider the problem of amplifying two-party coin-tossing protocols: given a protocol where it is possible to bias the common output by at most ρ, we aim to obtain a new protocol where the output can be biased by at most ρ* < ρ. We rule out the existence of a natural type of amplifiers called oblivious amplifiers for every ρ* < ρ. Such amplifiers ignore the way that the underlying ρ-bias protocol works and can only invoke an oracle that provides ρ-bias bits.
We provide two proofs of this impossibility. The first is by a reduction to the impossibility of deterministic randomness extraction from Santha-Vazirani sources. The second is a direct proof that is more general and also rules outs certain types of asymmetric amplification. In addition, it gives yet another proof for the Santha-Vazirani impossibility.

BibTeX - Entry

@InProceedings{bitansky_et_al:LIPIcs:2020:11715,
  author =	{Nir Bitansky and Nathan Geier},
  title =	{{On Oblivious Amplification of Coin-Tossing Protocols}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{30:1--30:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11715},
  URN =		{urn:nbn:de:0030-drops-117150},
  doi =		{10.4230/LIPIcs.ITCS.2020.30},
  annote =	{Keywords: Coin Tossing, Amplification, Lower Bound, Santha Vazirani}
}

Keywords: Coin Tossing, Amplification, Lower Bound, Santha Vazirani
Collection: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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