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Linear threshold multisecret sharing schemes
Farras Ventura, Oriol; Gràcia Rivas, Ignacio; Martín Mollevi, Sebastià; Padró Laimon, Carles
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
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.
Peer Reviewed
Àrees temàtiques de la UPC::Informàtica::Seguretat informàtica::Criptografia
Cryptography -- Mathematical models
Threshold cryptosystem
Criptografia -- Mètodes estadístics
Springer Verlag

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