Local Sequentiality Does Not Help for Concurrent Composition

Broad impossibility results have been proven regarding the feasibility of obtaining protocols that remain secure under concurrent composition when there is no honest majority. These results hold both for the case of general composition (where a secure protocol is run many times concurrently with arbitrary other protocols) and self composition (where a single secure protocol is run many times concurrently). One approach for bypassing these impossibility results is to consider more limited settings of concurrency. In this paper, we investigate a restriction that we call local sequentiality. In this setting, every honest party in the multi-party network runs its protocol executions strictly sequentially (thus, sequentiality is preserved locally, but not globally). Since security is preserved under global sequential composition, one may conjecture that it also preserved under local sequentiality. However, we show that local sequentiality does not help. That is, any protocol that is secure under local sequentiality is also secure under concurrent self composition (when the scheduling is fixed). Thus, known impossibility results apply.