From Input Private to Universally Composable Secure Multi-party Computation Primitives

Secure multi-party computation systems are commonly built from a small set of primitive components. The composability of security notions has a central role in the analysis of such systems, as it allows us to deduce security properties of complex protocols from the properties of its components. We show that the standard notions of universally composable security are overly restrictive in this context and can lead to protocols with sub-optimal performance. As a remedy, we introduce a weaker notion of privacy that is satisfied by simpler protocols and is preserved by composition. After that we fix a passive security model and show how to convert a private protocol into a universally composable protocol. As a result, we obtain modular security proofs without performance penalties.