Computationally Secure Verifiable Secret Sharing Scheme for Distributing Many Secrets

Many researchers studied computationally-secure (verifiable) secret sharing schemes which distribute multiple secrets with a bulletin board. However, the security definition is ambiguous in many of the past articles. In this paper, we first review existing schemes based on formal definitions of indistinguishability of secrets, verifiability of consistency, and cheater-detectability. And then, we propose a new secret sharing scheme which is the first scheme with indistinguishability of secrets, verifiability, and cheater-detectability, and allows to share secrets with arbitrary access structures. Further, our scheme is provably secure under well known computational assumptions.