## Abstract

A two-party coin-flipping protocol is ε -fair if no efficient adversary can bias the output of the honest party (who always outputs a bit, even if the other party aborts) by more than ε. Cleve [STOC ’86] showed that r-round o(1 / r)-fair coin-flipping protocols do not exist. Awerbuch et al. [Manuscript ’85] constructed a Θ(1/r) -fair coin-flipping protocol, assuming the existence of one-way functions. Moran et al. [Journal of Cryptology ’16] constructed an r-round coin-flipping protocol that is Θ(1 / r) -fair (thus matching the aforementioned lower bound of Cleve [STOC ’86]), assuming the existence of oblivious transfer. The above gives rise to the intriguing question of whether oblivious transfer, or more generally “public-key primitives”, is required for an o(1/r) -fair coin flipping. This question was partially answered by Dachman-Soled et al. [TCC ’11] and Dachman-Soled et al. [TCC ’14], who showed that restricted types of fully black-box reductions cannot establish o(1/r) -fair coin-flipping protocols from one-way functions. In particular, for constant-round coin-flipping protocols, [10] yields that black-box techniques from one-way functions can only guarantee fairness of order 1/r. We make progress towards answering the above question by showing that, for any constant, the existence of an 1/(c·r) -fair, r-round coin-flipping protocol implies the existence of an infinitely-often key-agreement protocol, where c denotes some universal constant (independent of r). Our reduction is non black-box and makes a novel use of the recent dichotomy for two-party protocols of Haitner et al. [FOCS ’18] to facilitate a two-party variant of the attack of Beimel et al. [FOCS ’18] on multi-party coin-flipping protocols.

Original language | English |
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Title of host publication | Theory of Cryptography - 16th International Conference, TCC 2018, Proceedings |

Editors | Amos Beimel, Stefan Dziembowski |

Publisher | Springer Verlag |

Pages | 539-562 |

Number of pages | 24 |

ISBN (Print) | 9783030038069 |

DOIs | |

State | Published - 2018 |

Event | 16th Theory of Cryptography Conference, TCC 2018 - Panaji, India Duration: 11 Nov 2018 → 14 Nov 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11239 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 16th Theory of Cryptography Conference, TCC 2018 |
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Country/Territory | India |

City | Panaji |

Period | 11/11/18 → 14/11/18 |

### Funding

Funders | Funder number |
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European Research Council | 638121 |

Israel Science Foundation | 152/17 |

## Keywords

- Coin-flipping
- Fairness
- Key-agreement