Server-Aided Two-Party Computation with Minimal Connectivity in the Simultaneous Corruption Model

We consider secure two-party computation in the client-server model. In our scenario, two adversaries operate separately but simultaneously, each of them corrupting one of the parties and a restricted subset of servers that they interact with. We model security in this setting via the local universal composability framework introduced by Canetti and Vald and show that informationtheoretically secure two-party computation is possible if and only if there is always at least one server which remains uncorrupted. Moreover, in our protocols each of the servers only needs to communicate with the two clients, i.e. no messages are exchanged directly between servers. This communication pattern is minimal.