A fast non-interactive publicly verifiable secret sharing scheme

A non-interactive (t, n)-publicly verifiable secret sharing scheme (non-interactive (t, n)-PVSS scheme) is a method to share a secret among n participants so that only subsets of the participants with at least t elements can compute the secret and anyone, not only the participants of the scheme, can verify the correctness of the shares of participants without interacting with the dealer and participants of the scheme. In this paper, we propose a non-interactive (t, n)-PVSS scheme using the homogeneous linear recursions (HLRs) and prove its security in a standard model. For n ≥ t ≥ 2, our non-interactive (t, n)-PVSS scheme runs faster than Schoenmakers’s.