2024-03-29T02:25:48Zhttps://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
Secret sharing system
Sistema de compartición de secretos
Cryptology
Criptología
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.
Danish Council for Independent Research (grant DFF-4002- 00367)
Ministerio de Economía, Industria y Competitividad (grants MTM2015-65764-C3-2-P / MTM2015-69138- REDT)
RYC-2016-20208 (AEI/FSE/UE)
Junta de Castilla y León (grant VA166G18)
2019-05-09T09:01:08Z
2019-05-09T09:01:08Z
2019
info:eu-repo/semantics/article
https://doi.org/10.1109/TIT.2019.2902151
IEEE Transactions on Information Theory ( Early Access )
1557-9654
http://uvadoc.uva.es/handle/10324/35988
eng
https://ieeexplore.ieee.org/document/8654006
Attribution-NonCommercial-NoDerivatives 4.0 International
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
© 2019 IEEE
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