Ad Hoc PSM Protocols: Secure Computation Without Coordination

We study the notion of ad hoc secure computation, recently introduced by Beimel et al. (ITCS 2016), in the context of the Private Simultaneous Messages (PSM) model of Feige et al. (STOC 2004). In ad hoc secure computation we have n parties that may potentially participate in a protocol but, at the actual time of execution, only k of them, whose identity is not known in advance, actually participate. This situation is particularly challenging in the PSM setting, where protocols are non-interactive (a single message from each participating party to a special output party) and where the parties rely on pre-distributed, correlated randomness (that in the ad-hoc setting will have to take into account all possible sets of participants).

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