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Communication Complexity vs Randomness Complexity in Interactive Proofs

Authors Benny Applebaum, Kaartik Bhushan, Manoj Prabhakaran

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Subject Classification

ACM Subject Classification
  • Theory of computation → Interactive proof systems
Keywords
  • Interactive Proof Systems
  • Communication Complexity
  • Hash Functions
  • Pseudo-Random Generators
  • Compression

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Abstract

In this work, we study the interplay between the communication from a verifier in a general private-coin interactive protocol and the number of random bits it uses in the protocol. Under worst-case derandomization assumptions, we show that it is possible to transform any I-round interactive protocol that uses ρ random bits into another one for the same problem with the additional property that the verifier’s communication is bounded by O(I⋅ ρ). Importantly, this is done with a minor, logarithmic, increase in the communication from the prover to the verifier and while preserving the randomness complexity. Along the way, we introduce a new compression game between computationally-bounded compressor and computationally-unbounded decompressor and a new notion of conditioned efficient distributions that may be of independent interest. Our solutions are based on a combination of perfect hashing and pseudorandom generators.

Cite As Get BibTex

Benny Applebaum, Kaartik Bhushan, and Manoj Prabhakaran. Communication Complexity vs Randomness Complexity in Interactive Proofs. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITC.2024.2

Author Details

Benny Applebaum
  • Tel-Aviv University, Israel
Kaartik Bhushan
  • IIT Bombay, India
Manoj Prabhakaran
  • IIT Bombay, India

Funding

The first and second authors are supported by ISF grant no. 2805/21 and by the European Union (ERC, NFITSC, 101097959). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. The second and third authors are also supported by IIT Bombay Trust Lab. The third author is also supported by an Algorand Centre of Excellence grant by the Algorand Foundation.
  • Applebaum, Benny: Supported by ISF grant no. 2805/21 and by the European Union (ERC-2022-ADG) under grant agreement no.101097959 NFITSC.
  • Bhushan, Kaartik: Supported in part by IITB Trust Lab. Part of the research was done while visiting Tel Aviv Univerisity and was supported by ISF grant no. 2805/21 and by the European Union (ERC-2022-ADG) under grant agreement no.101097959 NFITSC. Also supported by the Prime Minister’s Research Fellowship (PMRF), Government of India.
  • Prabhakaran, Manoj: Supported in part by IITB Trust Lab and by an Algorand Centre of Excellence at IIT Bombay funded by the Algorand Foundation.

Acknowledgements

We thank Gil Segev for valuable discussions about perfect hashing. Part of the research was done while the second author visited Tel Aviv University.

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