A Simpler Variant of Universally Composable Security for Standard Multiparty Computation

In this paper, we present a simpler and more restricted variant of the universally composable security (UC) framework that is suitable for “standard” two-party and multiparty computation tasks. Many of the complications of the UC framework exist in order to enable more general tasks than classic secure computation. This generality may be a barrier to entry for those who are used to the stand-alone model of secure computation and wish to work with universally composable security but are overwhelmed by the differences. The variant presented here (called simplified universally composable security, or just SUC) is closer to the definition of security for multiparty computation in the stand-alone setting. The main difference is that a protocol in the SUC framework runs with a fixed set of parties, and machines cannot be added dynamically to the execution. As a result, the definitions of polynomial time and protocol composition are much simpler. In addition, the SUC framework has authenticated channels built in, as is standard in previous definitions of security, and all communication is done via the adversary in order to enable arbitrary scheduling of messages. Due to these differences, not all cryptographic tasks can be expressed in the SUC framework. Nevertheless, standard secure computation tasks (like secure function evaluation) can be expressed. Importantly, we show that for every protocol that can be represented in the SUC framework, the protocol is secure in SUC if and only if it is secure in UC. Therefore, the UC composition theorem holds and any protocol that is proven secure under SUC is secure under the general framework (with some technical changes to the functionality definition). As a result, protocols that are secure in the SUC framework are secure when an a priori unbounded number of concurrent executions of the protocols take place (relative to the same fixed set of parties).