A Lower Bound for Adaptively-Secure Collective Coin Flipping Protocols

Yael Tauman Kalai, Ilan Komargodski, Ran Raz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In 1985, Ben-Or and Linial (Advances in Computing Research 1989) introduced the collective coin flipping problem, where n parties communicate via a single broadcast channel and wish to generate a common random bit in the presence of adaptive Byzantine corruptions. In this model, the adversary can decide to corrupt a party in the course of the protocol as a function of the messages seen so far. They showed that the majority protocol, in which each player sends a random bit and the output is the majority value, tolerates O(√n) adaptive corruptions. They conjectured that this is optimal for such adversaries. We prove that the majority protocol is optimal (up to a poly-logarithmic factor) among all protocols in which each party sends a single, possibly long, message. Previously, such a lower bound was known for protocols in which parties are allowed to send only a single bit (Lichtenstein, Linial, and Saks, Combinatorica 1989), or for symmetric protocols (Goldwasser, Kalai, and Park, ICALP 2015).

Original languageEnglish (US)
Pages (from-to)75-98
Number of pages24
Issue number1
StatePublished - Feb 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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