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Bounded Simultaneous Messages

30 September 2023
Andrej Bogdanov
K. Dinesh
Yuval Filmus
Yuval Ishai
Avi Kaplan
Sruthi Sekar
ArXiv (abs)PDFHTML
Abstract

We consider the following question of bounded simultaneous messages (BSM) protocols: Can computationally unbounded Alice and Bob evaluate a function f(x,y)f(x,y)f(x,y) of their inputs by sending polynomial-size messages to a computationally bounded Carol? The special case where fff is the mod-2 inner-product function and Carol is bounded to AC0^00 has been studied in previous works. The general question can be broadly motivated by applications in which distributed computation is more costly than local computation, including secure two-party computation. In this work, we initiate a more systematic study of the BSM model, with different functions fff and computational bounds on Carol. In particular, we give evidence against the existence of BSM protocols with polynomial-size Carol for naturally distributed variants of NP-complete languages.

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