On the Composability of Statistically Secure Bit Commitments

Abstract

We show that for bit commitment schemes based on two-party stateless primitives, the stand-alone statistical security implies the statistical universally composable security. I.e., all such schemes are secure with an unlimited adversary, an unlimited simulator and an unlimited environment machine in the universal composability framework. Especially, these protocols can be used in arbitrary statistically secure applications without lowering the security.