### Abstract

The design of rational cryptographic protocols is a recently created research area at the intersection of cryptography and game theory. At TCC'10, Fuchsbauer et al. introduced two equilibrium notions (computational version of strict Nash equilibrium and stability with respect to trembles) offering a computational relaxation of traditional game theory equilibria. Using trapdoor permutations, they constructed a rational t-out-of n sharing technique satisfying these new security models. Their construction only requires standard communication networks but the share bitsize is 2 n |s|∈+∈O(k) for security against a single deviation and raises to (n∈- ∈t∈+∈1)•(2n|s|∈+∈O(k)) to achieve (t∈-∈1)-resilience where k is a security parameter. In this paper, we propose a new protocol for rational t-out-of n secret sharing scheme based on the Chinese reminder theorem. Under some computational assumptions related to the discrete logarithm problem and RSA, this construction leads to a (t∈-∈1)-resilient computational strict Nash equilibrium that is stable with respect to trembles with share bitsize O(k). Our protocol does not rely on simultaneous channel. Instead, it only requires synchronous broadcast channel and synchronous pairwise private channels.

Original language | English |
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Title of host publication | Information Security and Privacy |

Subtitle of host publication | 16th Australasian Conference, ACISP 2011, Melbourne, Australia, July 11-13, 2011. Proceedings |

Editors | Udaya Parampalli, Philip Hawkes |

Place of Publication | Heidelberg |

Publisher | Springer, Springer Nature |

Pages | 259-275 |

Number of pages | 17 |

ISBN (Electronic) | 9783642224973 |

ISBN (Print) | 9783642224966 |

DOIs | |

Publication status | Published - 2011 |

Event | 16th Australasian Conference on Information Security and Privacy, ACISP 2011 - Melbourne, VIC, Australia Duration: 11 Jul 2011 → 13 Jul 2011 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer Berlin Heidelberg |

Volume | 6812 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 16th Australasian Conference on Information Security and Privacy, ACISP 2011 |
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Country | Australia |

City | Melbourne, VIC |

Period | 11/07/11 → 13/07/11 |

### Fingerprint

### Keywords

- Asmuth-Bloom sharing scheme
- computational strict Nash equilibrium
- rational cryptography
- stability with respect to trembles

### Cite this

*Information Security and Privacy: 16th Australasian Conference, ACISP 2011, Melbourne, Australia, July 11-13, 2011. Proceedings*(pp. 259-275). (Lecture Notes in Computer Science; Vol. 6812). Heidelberg: Springer, Springer Nature. https://doi.org/10.1007/978-3-642-22497-3_17