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Computer Science > Computational Complexity

arXiv:2310.00334 (cs)
[Submitted on 30 Sep 2023 (v1), last revised 21 Dec 2023 (this version, v4)]

Title:Bounded Simultaneous Messages

Authors:Andrej Bogdanov, Krishnamoorthy Dinesh, Yuval Filmus, Yuval Ishai, Avi Kaplan, Sruthi Sekar
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Abstract:We consider the following question of bounded simultaneous messages (BSM) protocols: Can computationally unbounded Alice and Bob evaluate a function $f(x,y)$ of their inputs by sending polynomial-size messages to a computationally bounded Carol? The special case where $f$ is the mod-2 inner-product function and Carol is bounded to AC$^0$ 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 $f$ 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.
Comments: This version has a modified variant of the succinct subset sum candidate from the original version of this paper
Subjects: Computational Complexity (cs.CC); Cryptography and Security (cs.CR)
Cite as: arXiv:2310.00334 [cs.CC]
  (or arXiv:2310.00334v4 [cs.CC] for this version)
  https://doi.org/10.48550/arXiv.2310.00334

Submission history

From: Avi Kaplan [view email]
[v1] Sat, 30 Sep 2023 10:42:03 UTC (39 KB)
[v2] Thu, 5 Oct 2023 08:13:45 UTC (39 KB)
[v3] Sun, 26 Nov 2023 11:09:30 UTC (39 KB)
[v4] Thu, 21 Dec 2023 15:30:41 UTC (40 KB)
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