On Oblivious Amplification of Coin-Tossing Protocols

Authors Nir Bitansky, Nathan Geier

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Nir Bitansky
  • Tel Aviv University, Israel
Nathan Geier
  • Tel Aviv University, Israel


We thank Itay Sason for helpful discussions.

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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)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic protocols
  • Theory of computation → Oracles and decision trees
  • Coin Tossing
  • Amplification
  • Lower Bound
  • Santha Vazirani


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