2020
DOI: 10.1007/s00493-020-4147-4
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A Lower Bound for Adaptively-Secure Collective Coin Flipping Protocols

Abstract: 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, t… Show more

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Cited by 3 publications
(7 citation statements)
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“…Their result extends to strongly adaptive attacks (the attacker can decide to corrupt a party after seeing the message it is about to send) on single-turn protocols. Tauman Kalai, Komargodski, and Raz [24] fully answered the single-turn case by proving that no singleturn protocol is resilient to Ω( √ n) adaptive corruptions. Lastly, Etesami, Mahloujifar, and Mahmoody [13] presented an efficient and optimal strongly adaptive attack on protocols of certain properties (e.g., public coins).…”
Section: Full-information Coin Flipmentioning
confidence: 99%
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“…Their result extends to strongly adaptive attacks (the attacker can decide to corrupt a party after seeing the message it is about to send) on single-turn protocols. Tauman Kalai, Komargodski, and Raz [24] fully answered the single-turn case by proving that no singleturn protocol is resilient to Ω( √ n) adaptive corruptions. Lastly, Etesami, Mahloujifar, and Mahmoody [13] presented an efficient and optimal strongly adaptive attack on protocols of certain properties (e.g., public coins).…”
Section: Full-information Coin Flipmentioning
confidence: 99%
“…However, the above o(1) stands for 1/ loglog(ℓ), and it remains an intriguing question whether it can be pushed to 2 −polylog(ℓ) as can be achieved, for instance, when attacking the ℓ-party majority protocol. Such attacks are known for uniform single-bit single-turn protocols (a secondary result of [24]) and for strongly adaptive attackers against single-turn protocols [13].…”
Section: Open Questionsmentioning
confidence: 99%
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“…The authors in [ 42 ] proved that a Byzantine adversary can adaptively corrupt processors in any n -processor single-turn protocol, where every processor broadcasts one-bit messages, to change the expected output of the protocol by a constant. Subsequently, [ 33 , 43 ] generalized this result to the case where the processors broadcast arbitrary-length messages. Recently, in a breakthrough result, Haitner and Karidi-Heller [ 44 ] extended this result to multi-turn coin-tossing protocols, i.e., a processor may send messages in multiple rounds.…”
Section: Optimal Coin-tossing Protocols: a Geometric Approachmentioning
confidence: 99%