Synchronous Constructive Cryptography.

This paper proposes a simple synchronous composable security framework as an instantiation of the Constructive Cryptography framework, aiming to capture minimally, without unnecessary artefacts, exactly what is needed to state synchronous security guarantees. The objects of study are specifications (i.e., sets) of systems, and traditional security properties like consistency and validity can naturally be understood as specifications, thus unifying composable and property-based definitions. The framework's simplicity is in contrast to current composable frameworks for synchronous computation which are built on top of an asynchronous framework (e.g. the UC framework), thus not only inheriting artefacts and complex features used to handle asynchronous communication, but adding additional overhead to capture synchronous communication. As a second, independent contribution we demonstrate how secure (synchronous) multi-party computation protocols can be understood as constructing a computer that allows a set of parties to perform an arbitrary, on-going computation. An interesting aspect is that the instructions of the computation need not be fixed before the protocol starts but can also be determined during an on-going computation, possibly depending on previous outputs.