Computationally secure multiple secret sharing: models, schemes, and formal security analysis

A multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants. in such a way a multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants, such that any authorized subset of participants can reconstruct the secrets. Up to now, existing MSSs either require too long shares for participants to be perfect secure, or do not have a formal security analysis/proof. In 2013, Herranz et al. provided the first formal definition of computational security for multi-stage secret sharing scheme (MSSS) in the standard model and proposed a practical and secure scheme. As far as we know, their scheme is the only computationally secure MSS in the standard model, and there is no formal definition of the computational security for other categories of MSSs. Based on this motivation, in this paper, we define the first formal model of indistinguishability against the chosen secret attacks (CSA) for other types of MSSs in the standard model. Furthermore, we present two practical CSA-secure MSSs, belonging to different types of MSSs and enjoying the advantage of short shares. They are also provably secure in the standard model. Based on the semantic security of the underlying encryption schemes, we prove the security of our schemes.