Improved Bounds on the Threshold Gap in Ramp Secret Sharing
| Autor: | Diego Ruano, Ignacio Cascudo, Jaron Skovsted Gundersen |
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| Rok vydání: | 2019 |
| Předmět: |
Cryptography
Single element Cryptology 02 engineering and technology Library and Information Sciences Secret sharing Upper and lower bounds linear codes Set (abstract data type) 0202 electrical engineering electronic engineering information engineering Secret sharing system Computer Science::Cryptography and Security Mathematics Discrete mathematics Criptología business.industry 020206 networking & telecommunications Computer Science Applications Finite field secret sharing Resilience (materials science) threshold gap business Sistema de compartición de secretos Information Systems |
| Zdroj: | UVaDOC. Repositorio Documental de la Universidad de Valladolid instname Cascudo, I, Gundersen, J S & Ruano, D 2019, ' Improved Bounds on the Threshold Gap in Ramp Secret Sharing ', I E E E Transactions on Information Theory, vol. 65, no. 7, 8654006, pp. 4620-4633 . https://doi.org/10.1109/TIT.2019.2902151 |
| DOI: | 10.1109/TIT.2019.2902151 |
| Popis: | Producción Científica 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) |
| Databáze: | OpenAIRE |
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