2024-03-29T06:59:54Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/359882021-06-24T07:40:59Zcom_10324_1129com_10324_931com_10324_894com_10324_32197com_10324_952col_10324_1193col_10324_32199
Improved Bounds on the Threshold Gap in Ramp Secret Sharing
Cascudo, Ignacio
Skovsted Gundersen, Jaron
Ruano Benito, Diego
Producción Científica
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.
2019-05-09
2019-05-09
2019
info:eu-repo/semantics/article
IEEE Transactions on Information Theory ( Early Access )
1557-9654
http://uvadoc.uva.es/handle/10324/35988
https://doi.org/10.1109/TIT.2019.2902151
eng
https://ieeexplore.ieee.org/document/8654006
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
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