RT info:eu-repo/semantics/article
T1 Improved Bounds on the Threshold Gap in Ramp Secret Sharing
A1 Cascudo, Ignacio
A1 Skovsted Gundersen, Jaron
A1 Ruano Benito, Diego
K1 Secret sharing system
K1 Sistema de compartición de secretos
K1 Cryptology
K1 Criptología
AB Abstract: In this paper we consider linear secret sharing schemes over a finite field Fq, where the secret is a vector in Fℓq and each of the n shares is a single element of Fq. 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.
PB IEEE
SN 1557-9654
YR 2019
FD 2019
LK http://uvadoc.uva.es/handle/10324/35988
UL http://uvadoc.uva.es/handle/10324/35988
LA eng
NO IEEE Transactions on Information Theory ( Early Access )
NO Producción Científica
DS UVaDOC
RD 16-nov-2024