RT info:eu-repo/semantics/article
T1 Improved Bounds on the Threshold Gap in Ramp Secret Sharing
A1 Cascudo, Ignacio
A1 Gundersen, Jaron Skovsted
A1 Ruano Benito, Diego
AB 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.
SN 0018-9448
YR 2019
FD 2019
LK http://uvadoc.uva.es/handle/10324/40136
UL http://uvadoc.uva.es/handle/10324/40136
LA eng
NO 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)
DS UVaDOC
RD 17-nov-2024