### Abstrakt

In this paper, we consider linear secret sharing schemes over a finite field \mathbb {F}-{q} , where the secret is a vector in \mathbb {F}-{q}^\ell and each of the n shares is a single element of \mathbb {F}-{q}. We obtain lower bounds on the so-called threshold gap g of such schemes, defined as the quantity r-T where r is the smallest number such that any subset of r shares uniquely determines the secret and t is the largest number such that any subset of t shares provides no information about the secret. Our main result establishes a family of bounds which are tighter than previously known bounds for \ell \geq 2. Furthermore, we also provide bounds, in terms of n and q , on the partial reconstruction and privacy thresholds, a more fine-grained notion that considers the amount of information about the secret that can be contained in a set of shares of a given size. Finally, we compare our lower bounds with known upper bounds in the asymptotic setting.

Originalsprog | Engelsk |
---|---|

Artikelnummer | 8654006 |

Tidsskrift | I E E E Transactions on Information Theory |

Vol/bind | 65 |

Udgave nummer | 7 |

Sider (fra-til) | 4620-4633 |

Antal sider | 14 |

ISSN | 0018-9448 |

DOI | |

Status | Udgivet - 1 jul. 2019 |

## Fingeraftryk Dyk ned i forskningsemnerne om 'Improved Bounds on the Threshold Gap in Ramp Secret Sharing'. Sammen danner de et unikt fingeraftryk.

## Citationsformater

*I E E E Transactions on Information Theory*,

*65*(7), 4620-4633. [8654006]. https://doi.org/10.1109/TIT.2019.2902151