On oblivious amplification of coin-tossing protocols

Nir Bitansky, Nathan Geier

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


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.

Original languageEnglish
Title of host publication11th Innovations in Theoretical Computer Science Conference, ITCS 2020
EditorsThomas Vidick
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771344
StatePublished - Jan 2020
Event11th Innovations in Theoretical Computer Science Conference, ITCS 2020 - Seattle, United States
Duration: 12 Jan 202014 Jan 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference11th Innovations in Theoretical Computer Science Conference, ITCS 2020
Country/TerritoryUnited States


FundersFunder number
Alon Young Faculty Fellowship
Blavatnik Family Foundation
Israel Science Foundation18/484


    • Amplification
    • Coin tossing
    • Lower bound
    • Santha vazirani


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