Efficient verifiable secret sharing scheme over bilinear groups

A verifiable secret sharing (VSS) scheme is a secret sharing scheme with the special property that every player is able to verify whether the share distributed to him by a dealer is correct. VSS is a fundamental tool of cryptography and distributed computing. VSS schemes for sharing an element in a finite field have been well established for many years. In this paper, we focus on verifiably sharing of a secret that is an element of a bilinear group. Such VSS schemes are necessary for sharing the secret keys of many bilinear pairing-based cryptosystems which have been a hot topic in cryptographic research in recent years. We introduce strict security definitions for such a noninteractive VSS scheme. Then we come up with an efficient VSS scheme for sharing a secret in a bilinear group. Compared with similar protocols available, the newly proposed scheme is more efficient while enjoys the same level of security.