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DOI: 10.4230/LIPIcs.ITCS.2020.30

On Oblivious Amplification of Coin-Tossing Protocols

Authors: Nir Bitansky and Nathan Geier

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

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.

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Nir Bitansky and Nathan Geier. On Oblivious Amplification of Coin-Tossing Protocols. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 30:1-30:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bitansky_et_al:LIPIcs.ITCS.2020.30,
  author =	{Bitansky, Nir and Geier, Nathan},
  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 =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.30},
  URN =		{urn:nbn:de:0030-drops-117150},
  doi =		{10.4230/LIPIcs.ITCS.2020.30},
  annote =	{Keywords: Coin Tossing, Amplification, Lower Bound, Santha Vazirani}
}

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On Oblivious Amplification of Coin-Tossing Protocols

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