Coin Flipping of
            <i>Any</i>
            Constant Bias Implies One-Way Functions

Berman, Itay; Haitner, Iftach; Tentes, Aris

doi:10.1145/2979676

Cited by 11 publications

(4 citation statements)

References 17 publications

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“…However, one can emulate this attack relying on a significantly weaker assumption. For instance, if one-way functions do not exist [ 47 ] then Berman, Haitner, Omri, and Tentes [ 65 , 66 ] rely on rejection sampling techniques to construct a Byzantine adversary that forces an output with (near) certainty. (Intuitively, the assumption that “one-way functions do not exist” is slightly weaker than the assumption that “ ⊆ ,” because the latter implies the former.…”

Section: Hardness Of Computation Relative To Oraclesmentioning

confidence: 99%

Computational Hardness of Collective Coin-Tossing Protocols

Maji

2020

Entropy

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Ben-Or and Linial, in a seminal work, introduced the full information model to study collective coin-tossing protocols. Collective coin-tossing is an elegant functionality providing uncluttered access to the primary bottlenecks to achieve security in a specific adversarial model. Additionally, the research outcomes for this versatile functionality has direct consequences on diverse topics in mathematics and computer science. This survey summarizes the current state-of-the-art of coin-tossing protocols in the full information model and recent advances in this field. In particular, it elaborates on a new proof technique that identifies the minimum insecurity incurred by any coin-tossing protocol and, simultaneously, constructs the coin-tossing protocol achieving that insecurity bound. The combinatorial perspective into this new proof-technique yields new coin-tossing protocols that are more secure than well-known existing coin-tossing protocols, leading to new isoperimetric inequalities over product spaces. Furthermore, this proof-technique’s algebraic reimagination resolves several long-standing fundamental hardness-of-computation problems in cryptography. This survey presents one representative application of each of these two perspectives.

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Section: Hardness Of Computation Relative To Oraclesmentioning

confidence: 99%

Computational Hardness of Collective Coin-Tossing Protocols

Maji

2020

Entropy

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“…This form of security is meaningful in many settings, and it is typically much easier to achieve; assuming one-way functions exist, secure-with-abort protocols of negligible bias are known to exist against any number of corrupted parties [15,33,41]. To a large extent, one-way functions are also necessary for such coin-flipping protocols [14,31,35,38].…”

Section: Additional Related Workmentioning

confidence: 99%

An Almost-Optimally Fair Three-Party Coin-Flipping Protocol

Haitner¹,

Tsfadia²

2017

SIAM J. Comput.

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In a multiparty fair coin-flipping protocol, the parties output a common (close to) unbiased bit, even when some corrupted parties try to bias the output. Cleve [STOC 1986] has shown that in the case of dishonest majority (i.e., at least half of the parties can be corrupted), in any m-round coin-flipping protocol the corrupted parties can bias the honest parties' common output bit by Ω(1 m). For more than two decades the best known coin-flipping protocols against dishonest majority had bias Θ(√ m), where is the number of corrupted parties. This was changed by a recent breakthrough result of Moran et al. [TCC 2009], who constructed an mround, two-party coin-flipping protocol with optimal bias Θ(1 m). In a subsequent work, Beimel et al. [Crypto 2010] extended this result to the multiparty case in which less than 2 3 of the parties can be corrupted. Still for the case of 2 3 (or more) corrupted parties, the best known protocol had bias Θ(√ m). In particular, this was the state of affairs for the natural three-party case. We make a step towards eliminating the above gap, presenting an m-round, three-party coin-flipping protocol, with bias O(log 3 m) m. Our approach (which we also apply for the two-party case) does not follow the "threshold round" paradigm used in the work of Moran et al. and Beimel et al., but rather is a variation of the majority protocol of Cleve, used to obtain the aforementioned Θ(√ m)-bias protocol.

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“…This form of security is meaningful in many settings, and it is typically much easier to achieve; assuming one-way functions exist, secure-with-abort protocols of negligi-ble bias are known to exist against any number of corrupted parties [16,33,44]. To a large extent, one-way functions are also necessary for such coin-flipping protocols [15,30,37,40].…”

Section: Additional Related Workmentioning

confidence: 99%

Fair Coin Flipping: Tighter Analysis and the Many-Party Case

Buchbinder¹,

Haitner²,

Levi³

et al. 2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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In a multi-party fair coin-flipping protocol, the parties output a common (close to) unbiased bit, even when some corrupted parties try to bias the output. In this work we focus on the case of dishonest majority, ie at least half of the parties can be corrupted. [19] [STOC 1986] has shown that in any m-round coin-flipping protocol the corrupted parties can bias the honest parties' common output bit by Θ(1/m). For more than two decades the best known coin-flipping protocols against majority was the protocol of We make a step towards eliminating the above gap, presenting a t-party, m-round coin-flipping protocol, with bias O(). This improves upon the Θ(t/ √ m)-bias protocol of [9] for any t ≤ 1/2 · log log m, and in particular for t ∈ O(1), this yields an 1/m We analyze our new protocols by presenting a new paradigm for analyzing fairness of coin-flipping protocols. We map the set of adversarial strategies that try to bias the honest parties outcome in the protocol to the set of the feasible solutions of a linear program. The gain each strategy achieves is the value of the corresponding solution. We then bound the the optimal value of the linear program by constructing a feasible solution to its dual.

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Coin Flipping of Any Constant Bias Implies One-Way Functions

Cited by 11 publications

References 17 publications

Computational Hardness of Collective Coin-Tossing Protocols

Computational Hardness of Collective Coin-Tossing Protocols

An Almost-Optimally Fair Three-Party Coin-Flipping Protocol

Fair Coin Flipping: Tighter Analysis and the Many-Party Case

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