2024-03-28T12:21:29Zhttp://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/401362021-06-24T07:41:13Zcom_10324_32197com_10324_952com_10324_894com_10324_1129com_10324_931col_10324_32199col_10324_1193
Cascudo, Ignacio
Gundersen, Jaron Skovsted
Ruano Benito, Diego
2020-01-13T15:34:41Z
2020-01-13T15:34:41Z
2019
I. Cascudo, J.S. Gundersen, D. Ruano: Improved Bounds on the Threshold Gap in Ramp Secret Sharing. IEEE Transactions on Information Theory. Volume 65, Issue 7, pages 4620-4633 (2019)
0018-9448
http://uvadoc.uva.es/handle/10324/40136
10.1109/TIT.2019.2902151
4620
7
4633
IEEE Transactions on Information Theory
65
1557-9654
In this paper, we consider linear secret sharing schemes over a finite field F q , where the secret is a vector in Fℓ q and each of the n shares is a single element of 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 ℓ ≳ 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.
This work is supported by the Danish Council for Independent Research, grant DFF-4002- 00367, the Spanish Ministry of Economy/FEDER: grants MTM2015-65764-C3-2-P, MTM2015-69138- REDT, and RYC-2016-20208 (AEI/FSE/UE), and Junta de CyL (Spain): grant VA166G18
application/pdf
eng
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
Improved Bounds on the Threshold Gap in Ramp Secret Sharing
info:eu-repo/semantics/article
info:eu-repo/semantics/draft
https://ieeexplore.ieee.org/document/8654006
SI