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Linear threshold multisecret sharing schemes

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Farras Ventura, Oriol
Gràcia Rivas, IgnacioMés informació
Martín Mollevi, SebastiàMés informacióMés informacióMés informació
Padró Laimon, CarlesMés informacióMés informacióMés informació
Document typeConference report
Defense date2009
PublisherSpringer Verlag
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
In a multisecret sharing scheme, several secret values are distributed among a set of n users, and each secret may have a differ- ent associated access structure. We consider here unconditionally secure schemes with multithreshold access structures. Namely, for every subset P of k users there is a secret key that can only be computed when at least t of them put together their secret information. Coalitions with at most w users with less than t of them in P cannot obtain any information about the secret associated to P. The main parameters to optimize are the length of the shares and the amount of random bits that are needed to set up the distribution of shares, both in relation to the length of the secret. In this paper, we provide lower bounds on this parameters. Moreover, we present an optimal construction for t = 2 and k = 3, and a construction that is valid for all w, t, k and n. The models presented use linear algebraic techniques.
CitationFarras, O. [et al.]. Linear threshold multisecret sharing schemes. A: International Conference on Information Theoretical Security. "4th. International Conference on Information Theoretical Security". Shizuoka: Springer Verlag, 2009, p. 110-126. 
URIhttp://hdl.handle.net/2117/8986
ISBN978-3-642-14496-7_9
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  • MAK - Matemàtica Aplicada a la Criptografia - Ponències/Comunicacions de congressos [23]
  • Departament de Matemàtiques - Ponències/Comunicacions de congressos [1.015]
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