O. Farràs, I. Gracia, S. Martín, C. Padró
Linear Threshold Multisecret Sharing Schemes
Information Processing Letters 112 (2012) 667-673. A previous version of this paper appeared in Fourth International Conference on Information Theoretic Security ICITS 2009, Lecture Notes in Computer Science 5973 (2010) 110-126. Shizuoka, Japan, 2009.
In a multisecret sharing scheme, several secret values are distributed among a set of n users, and each secret may have a different associated access structure. We consider here information-theoretic 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.