TY - GEN
T1 - Communication Complexity vs Randomness Complexity in Interactive Proofs
AU - Applebaum, Benny
AU - Bhushan, Kaartik
AU - Prabhakaran, Manoj
N1 - Publisher Copyright:
© Benny Applebaum, Kaartik Bhushan, and Manoj Prabhakaran.
PY - 2024/8
Y1 - 2024/8
N2 - 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.
AB - 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.
KW - Communication Complexity
KW - Compression
KW - Hash Functions
KW - Interactive Proof Systems
KW - Pseudo-Random Generators
UR - http://www.scopus.com/inward/record.url?scp=85202438798&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ITC.2024.2
DO - 10.4230/LIPIcs.ITC.2024.2
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AN - SCOPUS:85202438798
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 5th Conference on Information-Theoretic Cryptography, ITC 2024
A2 - Aggarwal, Divesh
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 5th Conference on Information-Theoretic Cryptography, ITC 2024
Y2 - 14 August 2024 through 16 August 2024
ER -