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Título
Improved Bounds on the Threshold Gap in Ramp Secret Sharing
Año del Documento
2019
Editorial
IEEE
Descripción
Producción Científica
Documento Fuente
IEEE Transactions on Information Theory ( Early Access )
Abstract
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.
Palabras Clave
Secret sharing system
Sistema de compartición de secretos
Cryptology
Criptología
ISSN
1557-9654
Revisión por pares
SI
Patrocinador
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)
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)
Version del Editor
Propietario de los Derechos
© 2019 IEEE
Idioma
eng
Derechos
openAccess
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