A non-interactive (t, n)-publicly verifiable multi-secret sharing scheme

A non-interactive publicly verifiable multi secret sharing (PVMSS) scheme is a secret sharing scheme that the dealer shares multiple secrets among the participants and anyone can verify the validity of the shares by using the public information. For the first time, we propose a new PVMSS scheme based on the homogeneous linear recursions (HLR) and discrete logarithms equality (DLEQ) protocol. Compared with the previous PVMSS schemes, it has better performance and various methods for the recovery phase. Moreover, we prove its security with a formal method.