Cheating Detectable Secret Sharing Scheme from Multiplicative Homomorphic Authentication Function

Abstract

Cheating Detectable Secret Sharing (CDSS for short) is a secret sharing scheme that adds the property of detecting the presence of cheaters submitting invalid shares when reconstructing a secret. A major topic of research in CDSS has been the attempt to improve efficiency with suitable authentication functions. In this paper, we construct CDSS based on an authentication function with multiplicative homomorphism, which has not been employed so far. It possesses some interesting properties and possesses the advantage that security can be proven simply by showing possession of such properties. Furthermore, we construct a secure CDSS with multiplicative homomorphic under some parameter constraints and show that this scheme is sufficient for practical use. The scheme achieves a bit length that is one bit longer than the theoretical lower bound.