Publicly Verifiable Secret Sharing Scheme with Provable Security against Chosen Secret Attacks

Abstract

Secret sharing is an important aspect of key management in wireless ad hoc and sensor networks. In this paper, we define a new secure model of secret sharing, use the Lagrange interpolation and the bilinear cyclic groups to construct an efficient publicly verifiable secret sharing scheme on the basis of this model, and show that this scheme is provably secure against adaptively chosen secret attacks (CSAs) based on the decisional bilinear Diffie-Hellman (DBDH) problem. We find that this scheme has the following properties: (a) point-to-point secure channels are not required in both the secret distribution phase and the secret reconstruction phase; (b) it is a noninteractive secret sharing system in that the participants need not communicate with each other during subshadow verification; and (c) each participant is able to share many secrets with other participants despite holding only one shadow.