A Lower Bound for Adaptively-Secure Collective Coin-Flipping Protocols

Authors Yael Tauman Kalai, Ilan Komargodski, Ran Raz

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Yael Tauman Kalai
  • Microsoft Research, 1 Memorial Dr, Cambridge, MA 02142, USA
Ilan Komargodski
  • Cornell Tech, 2 W Loop Rd, New York, NY 10044, USA
Ran Raz
  • Department of Computer Science, Princeton University, Princeton, NJ 08544, USA

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Yael Tauman Kalai, Ilan Komargodski, and Ran Raz. A Lower Bound for Adaptively-Secure Collective Coin-Flipping Protocols. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


In 1985, Ben-Or and Linial (Advances in Computing Research '89) 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(sqrt 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 '89), or for symmetric protocols (Goldwasser, Kalai, and Park, ICALP '15).

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • Coin flipping
  • adaptive corruptions
  • byzantine faults
  • lower bound


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