Two Verifiable Multi-Secret Sharing Schemes: A Linear Scheme with Standard Security and A Lattice-Based Scheme

In this paper, we present two verifiable multi-secret sharing schemes, including a linear multi-secret sharing scheme with public access structure and a threshold (t, n) scheme based on the learning with errors (LWE) problem. The first scheme is a linear multi-secret sharing scheme in which a number of secrets is distributed by a dealer among a set of participants according to the access structure corresponding to each secret. This scheme has the advantages of the earlier ones and it also has many practical applications    compared to previous schemes including a multi-use verifiable multi-secret sharing scheme in which the secret reconstruction is according to the dealer’s preassigned order. In addition, the security of the scheme has been proven in the standard model. This scheme is based on the hard problems in number theory and therefore is not secure against quantum attacks. The second scheme presented in this paper is a lattice-based secret sharing scheme. In this scheme, which is a threshold (t, n) multi-secret sharing scheme, the presence of at least t participants is required for the reconstruction of the secret. The security of this scheme is based on the difficulty of the LWE problem and so it is resistant against quantum attacks.