### Abstract

We introduce two publicly cheater identifiable secret sharing (CISS) schemes with efficient reconstruction, tolerating t<k/2 cheaters. Our constructions are based on (k,n) threshold Shamir scheme, and they feature a novel application of multi-receiver authentication codes to ensure integrity of shares. The first scheme, which tolerates rushing cheaters, has the share size |S|(n-t) ^{n+t+2}/ε^{n+t+2} in the general case, that can be ultimately reduced to |S|(k-t)^{k+t+2}/ε ^{k+t+2} assuming that all the t cheaters are among the k reconstructing players. The second scheme, which tolerates non-rushing cheaters, has the share size |S|(n-t)^{2t+2}/ε^{2t+2}. These two constructions have the smallest share size among the existing CISS schemes of the same category, when the secret is a single field element. In addition, we point out that an improvement in the share size to can be achieved for a CISS tolerating t<k/3 rushing cheaters presented by Xu et al. at IWSEC 2013.

Original language | English |
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Pages (from-to) | 72-87 |

Number of pages | 16 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 8639 LNCS |

DOIs | |

Publication status | Published - Jan 1 2014 |

Event | 9th International Workshop on Security, IWSEC 2014 - Hirosaki, Japan Duration: Aug 27 2014 → Aug 29 2014 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*8639 LNCS*, 72-87. https://doi.org/10.1007/978-3-319-09843-2_6

**Cheater identifiable secret sharing schemes via multi-receiver authentication.** / Xu, Rui; Morozov, Kirill; Takagi, Tsuyoshi.

Research output: Contribution to journal › Conference article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 8639 LNCS, pp. 72-87. https://doi.org/10.1007/978-3-319-09843-2_6

}

TY - JOUR

T1 - Cheater identifiable secret sharing schemes via multi-receiver authentication

AU - Xu, Rui

AU - Morozov, Kirill

AU - Takagi, Tsuyoshi

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We introduce two publicly cheater identifiable secret sharing (CISS) schemes with efficient reconstruction, tolerating tn+t+2/εn+t+2 in the general case, that can be ultimately reduced to |S|(k-t)k+t+2/ε k+t+2 assuming that all the t cheaters are among the k reconstructing players. The second scheme, which tolerates non-rushing cheaters, has the share size |S|(n-t)2t+2/ε2t+2. These two constructions have the smallest share size among the existing CISS schemes of the same category, when the secret is a single field element. In addition, we point out that an improvement in the share size to can be achieved for a CISS tolerating t

AB - We introduce two publicly cheater identifiable secret sharing (CISS) schemes with efficient reconstruction, tolerating tn+t+2/εn+t+2 in the general case, that can be ultimately reduced to |S|(k-t)k+t+2/ε k+t+2 assuming that all the t cheaters are among the k reconstructing players. The second scheme, which tolerates non-rushing cheaters, has the share size |S|(n-t)2t+2/ε2t+2. These two constructions have the smallest share size among the existing CISS schemes of the same category, when the secret is a single field element. In addition, we point out that an improvement in the share size to can be achieved for a CISS tolerating t

UR - http://www.scopus.com/inward/record.url?scp=84907365883&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907365883&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-09843-2_6

DO - 10.1007/978-3-319-09843-2_6

M3 - Conference article

AN - SCOPUS:84907365883

VL - 8639 LNCS

SP - 72

EP - 87

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -