### Abstract

In this paper, we consider two very important issues namely detection and identification of k-out-of-n secret sharing schemes against rushing cheaters who are allowed to submit (possibly forged) shares after observing shares of the honest users in the reconstruction phase. Towards this, we present four different schemes. Among these, first we present two k-out-of-n secret sharing schemes, the first one being capable of detecting (k − 1)/3 cheaters such that |V_{i}| = |S|/∊^{3} and the second one being capable of detecting n − 1 cheaters such that |V_{i}| = |S|/∊^{k+1}, where S denotes the set of all possible secrets, ∊ denotes the successful cheating probability of cheaters and V_{i} denotes set all possible shares. Next we present two k-out-of-n secret sharing schemes, the first one being capable of identifying (k−1)/3 rushing cheaters with share size |V_{i}| that satisfies |V_{i}| = |S|/∊^{k}. This is the first scheme, whose size of shares does not grow linearly with n but only with k, where n is the number of participants. For the second one, in the setting of public cheater identification, we present an efficient optimal cheater resilient k-out-of-n secret sharing scheme against rushing cheaters having the share size |V_{i}| = (n−t)^{n+2t}|S|/∊^{n+2t}. The proposed scheme achieves flexibility in the sense that the security level (i.e., the cheater(s) success probability) is independent of the secret size. Each of the four proposed schemes has the smallest share size among the existing schemes having the mentioned properties in the respective models.

Original language | English |
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Title of host publication | Information Theoretic Security - 9th International Conference, ICITS 2016, Revised Selected Papers |

Editors | Paulo Barreto, Anderson C.A. Nascimento |

Publisher | Springer Verlag |

Pages | 3-23 |

Number of pages | 21 |

ISBN (Print) | 9783319491745 |

DOIs | |

Publication status | Published - Jan 1 2016 |

Event | 9th International Conference on Information-Theoretic Security, ICITS 2016 - Tacoma, United States Duration: Aug 9 2016 → Aug 12 2016 |

### 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 | 10015 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 9th International Conference on Information-Theoretic Security, ICITS 2016 |
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Country | United States |

City | Tacoma |

Period | 8/9/16 → 8/12/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Information Theoretic Security - 9th International Conference, ICITS 2016, Revised Selected Papers*(pp. 3-23). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10015 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-49175-2_1