Adaptively Secure Coin-Flipping, Revisited
Shafi Goldwasser, Yael Tauman Kalai, Sunoo Park

TL;DR
This paper investigates the limits of coin-flipping protocols under adaptive adversaries, showing that longer messages do not increase security against strong adaptive corruptions and establishing bounds for standard adaptive models.
Contribution
It introduces a strong adaptive corruption model, proves message length does not improve security in one-round protocols, and connects adaptive and strongly adaptive adversaries with new theoretical techniques.
Findings
One-round protocols are secure against at most ~O(√n) strong adaptive corruptions.
Increased message length does not improve security against strong adaptive corruptions.
Any symmetric one-round protocol with long messages can tolerate at most ~O(√n) adaptive corruptions.
Abstract
The full-information model was introduced by Ben-Or and Linial in 1985 to study collective coin-flipping: the problem of generating a common bounded-bias bit in a network of players with faults. They showed that the majority protocol can tolerate adaptive corruptions, and conjectured that this is optimal in the adaptive setting. Lichtenstein, Linial, and Saks proved that the conjecture holds for protocols in which each player sends a single bit. Their result has been the main progress on the conjecture in the last 30 years. In this work we revisit this question and ask: what about protocols involving longer messages? Can increased communication allow for a larger fraction of faulty players? We introduce a model of strong adaptive corruptions, where in each round, the adversary sees all messages sent by honest parties and, based on the message content,…
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Taxonomy
TopicsCryptography and Data Security · Game Theory and Applications · Distributed systems and fault tolerance
