Simulatable security and polynomially bounded concurrent composability

Simulatable security is a security notion for multi-party protocols that implies strong composability features. The main definitional flavours of simulatable security are standard simulatability, universal simulatability, and black-box simulatability. All three come in "computational," "statistical" and "perfect" subflavours indicating the considered adversarial power. Universal and black-box simulatability, in all of their subflavours, are already known to guarantee that the concurrent composition even of a polynomial number of secure protocols stays secure. We show that computational standard simulatability does not allow for secure concurrent composition of polynomially many protocols, but we also show that statistical standard simulatability does. The first result assumes the existence of an interesting cryptographic tool (namely time-lock puzzles), and its proof employs a cryptographic multi-party computation in an interesting and unconventional way