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Improved Bounds on the Threshold Gap in Ramp Secret Sharing.
- Source :
-
IEEE Transactions on Information Theory . Jul2019, Vol. 65 Issue 7, p4620-4633. 14p. - Publication Year :
- 2019
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *QUANTUM information science
*RAMSEY numbers
*FINITE fields
*SHARING
*LINEAR codes
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 137099111
- Full Text :
- https://doi.org/10.1109/TIT.2019.2902151