Linear threshold multisecret sharing schemes

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=2t=2 and k=3k=3.

► We present new results on threshold multisecret sharing schemes. ► A lower bound for the randomness of threshold multisecret sharing schemes. ► A new proof for the lower bound on the information ratio given by Jackson et al. ► A linear construction of optimal threshold multisecret schemes for t=2t=2, k=3k=3, w