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Tight Parallel Repetition Theorems for Public-Coin Arguments Using KL-Divergence
[chapter]
2015
Lecture Notes in Computer Science
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We then use this new proof to present the first tight "Chernoff-type" parallel repetition theorem for arbitrary public-coin arguments, demonstrating that parallel-repetition can be used to simultaneously ...
We present a new and conceptually simpler proof of a tight parallel-repetition theorem for public-coin arguments [Pass-Venkitasubramaniam, STOC'07], [Håstad et al, TCC'10], TCC'10]. ...
Proof of the Parallel Repetition Theorem In this section, we present the formal of our tight Chernoff-type parallel repetition theorem for public-coin protocols.
Theorem 2. ...
doi:10.1007/978-3-662-46497-7_9
fatcat:ayi7kmsq7zdrzeztja6ftoqadu
Parallel Repetition Theorems for Interactive Arguments
[chapter]
2010
Lecture Notes in Computer Science
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We show a tight parallel repetition theorem for public-coin interactive arguments by giving a tight analysis for a reduction algorithm of Håstad et al. [HPPW08] . ...
We study efficient parallel repetition theorems for several classes of interactive arguments and obtain the following results: 1. ...
We also thank Salil Vadhan for very helpful discussions throughout this work. ...
doi:10.1007/978-3-642-11799-2_2
fatcat:gehmqryjcbc5xbwgiuklvmir24
The Randomness Complexity of Parallel Repetition
2011
2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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. • We establish the first derandomized parallel repetition theorem for public-coin interactive protocols with computational soundness (a.k.a. arguments). ...
These results are tight in the sense that parallel repetition theorems in the computational setting can trivially be derandomized using pseudorandom generators, which are implied by the existence of one-way ...
We also thank Feng-Hao Liu for the collaboration in the early stage of this research, and anonymous reviewers for useful suggestions. ...
doi:10.1109/focs.2011.93
dblp:conf/focs/ChungP11
fatcat:c66rwhdzvjb3nctvhxuejeprwu
Parallel Repetition of Computationally Sound Protocols Revisited
2010
Journal of Cryptology
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Parallel Repetition for Arguments Bellare, Impagliazzo and Naor [2] show that, somewhat surprisingly, parallel repetition does not in general reduce the soundness of interactive arguments. ...
We prove a negative result concerning error reduction by parallel repetition for computationally sound protocols, e.g., interactive arguments. ...
Acknowledgements We thank Thomas Holenstein for fruitful discussions. ...
doi:10.1007/s00145-010-9090-x
fatcat:kfbapegbzbghzlvcs4ysv6qeze
Is it Easier to Prove Theorems that are Guaranteed to be True?
[article]
2020
arXiv
pre-print
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As another consequence of this treatment, we show that the existence of O(1)-round public-coin non-trivial arguments (i.e., argument systems that are not proofs) imply the existence of a hard-on-average ...
, analogous to Babai-Moran's celebrated round-collapse theorem for information-theoretically sound protocols. ...
Acknowledgements We are grateful to Johan Håstad and Salil Vadhan for discussions about non-trivial arguments back in 2005. We are also very grateful to Eylon Yogev for helpful discussions. ...
arXiv:1906.10837v2
fatcat:wb5ctjek2rd6rab4pdoscatuqq
Lower Bounds in the Quantum Cell Probe Model
[chapter]
2001
Lecture Notes in Computer Science
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We prove a lower bound for the static predecessor problem in the address-only version of this model where, essentially, we allow quantum parallelism only over the 'address lines' of the queries. ...
We also consider the one-round quantum communication complexity of set membership and show tight bounds. ...
Acknowledgements We thank Ashwin Nayak, Jaikumar Radhakrishnan and Rahul Jain for useful discussions, and Peter Bro Miltersen for telling us the "state-of-the-art" about the classical complexity of the ...
doi:10.1007/3-540-48224-5_30
fatcat:mml7vxtysjandpfghl44mwneae
Why "Fiat-Shamir for Proofs" Lacks a Proof
[chapter]
2013
Lecture Notes in Computer Science
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The Fiat-Shamir heuristic [CRYPTO '86] is used to convert any 3-message public-coin proof or argument system into a noninteractive argument, by hashing the prover's first message to select the verifier's ...
for some computationally sound arguments. ...
Note that many public-coin proof (or argument) systems (such as those discussed in Section 4.2) consist of parallel repetitions of a basic protocol where the length of the verifier's message is a constant ...
doi:10.1007/978-3-642-36594-2_11
fatcat:wa6argayqramfnwwbo2zutmcqu
A Direct Product Theorem for the Two-Party Bounded-Round Public-Coin Communication Complexity
2012
2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
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Another important tool that we use is a correlated sampling protocol, which for example, has been used in Holenstein [9] for proving a parallel repetition theorem for two-prover games. ...
Direct sum theorems have been shown in the public-coin one-way model [15], public-coin simultaneous message passing model [15], entanglement-assisted quantum oneway communication model [17], private-coin ...
It plays a critical role in his proof of a parallel repetition theorem for two-prover games. Definition II.9 ([9]). ...
doi:10.1109/focs.2012.42
dblp:conf/focs/JainPY12
fatcat:wj7ljiusl5a4pdghvaecxrthn4
Arguments of Proximity
[chapter]
2015
Lecture Notes in Computer Science
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Assuming the existence of a sub-exponentially secure FHE scheme, we construct a one-round argument of proximity for every language computable in time t, where the running time of the verifier is o(n)+polylog ...
In a recent work, Rothblum et. al (STOC, 2013) constructed an IPP for every language computable by a low depth circuit. ...
We thank Guy Rothblum for pointing out to us the question about arguments of proximity for P -the question that initiated this work. ...
doi:10.1007/978-3-662-48000-7_21
fatcat:5kuidvuiibcmjlmtv75r6oztsa
Lower bounds for non-black-box zero knowledge
2006
Journal of computer and system sciences (Print)
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There does not exist a constant-round public-coin proof system for a nontrivial language that is resettable zero knowledge. ...
The previous impossibility result for two-round zero knowledge, by Goldreich and Oren (J. Cryptology, 1994) was only for the case of auxiliary-input zero-knowledge proofs and arguments. 2. ...
Acknowledgements We thank Oded Goldreich, Silvio Micali and Luca Trevisan for helpful discussions, and the anonymous FOCS and JCSS referees for useful comments. ...
doi:10.1016/j.jcss.2005.06.010
fatcat:hllc2tom6zgrrapoftgdz5hdqy
Succinct Arguments from Multi-prover Interactive Proofs and Their Efficiency Benefits
[chapter]
2012
Lecture Notes in Computer Science
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Succinct arguments of knowledge are computationally-sound proofs of knowledge for NP where the verifier's running time is independent of the time complexity of the NP nondeterministic machine for the considered ...
The scheme is based on fully-homomorphic encryption (and no additional assumptions are needed for our succinct argument). (3) In addition, we revisit the problem of non-interactive succinct arguments of ...
We thank Eli Ben-Sasson for discussions about MIP constructions. We also thank Ran Canetti, Omer Paneth, and Ben Riva for valuable discussions on MIP-based SNARKs. ...
doi:10.1007/978-3-642-32009-5_16
fatcat:je4zuvn23bcfvb5xwzgv3t3zjm
Soundness in the Public-Key Model
[chapter]
2001
Lecture Notes in Computer Science
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The public-key model for interactive proofs has proved to be quite effective in improving protocol efficiency [CGGM00]. ...
Specifically, for the public-key model, we -identify four meaningful notions of soundness; -prove that, under minimal complexity assumptions, these four notions are distinct; -identify the exact soundness ...
Generate and send to V the second message of the n parallel repetitions of the proof of knowledge of EncSK .
V Step Two: 1. Send σ V and the coins ρ E used to encrypt it to P. 2. ...
doi:10.1007/3-540-44647-8_32
fatcat:rdd7rxhz6fb2rg66ojtnamnmry
An Exponential Separation Between MA and AM Proofs of Proximity
2021
Computational Complexity
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As an application of this result, we show an exponential separation between the power of public and private coin for oblivious interactive proofs of proximity. ...
Our lower bound also yields an alternate proof, which is more general and arguably much simpler, for a recent result of Fischer et al. (ITCS, 2014). ...
Acknowledgements We thank Oded Goldreich and Justin Thaler for very helpful discussions. We also thank the anonymous reviewers of Computational Complexity for useful comments. ...
doi:10.1007/s00037-021-00212-3
fatcat:bhjncpg5lfg5pbb4zq223nzjpm
From Laconic Zero-Knowledge to Public-Key Cryptography
[chapter]
2018
Lecture Notes in Computer Science
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Since its inception, public-key encryption (PKE) has been one of the main cornerstones of cryptography. ...
An intriguing candidate for such an assumption is the existence of a cryptographically hard language L ∈ NP ∩ SZK. ...
Acknowledgments We thank Vinod Vaikuntanathan for his encouragement and for helpful discussions. ...
doi:10.1007/978-3-319-96878-0_23
fatcat:leuv3kr2ibf7pbjn2x4ck6iiei
Information Complexity and the Quest for Interactive Compression (A Survey)
[article]
2015
arXiv
pre-print
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In recent years this field has emerged as a powerful tool for proving strong communication lower bounds, and for addressing some of the major open problems in communication complexity and circuit complexity ...
A notable achievement of information complexity is the breakthrough in understanding of the fundamental direct sum and direct product conjectures, which aim to quantify the power of parallel computation ...
Acknowledgements I would like to thank Mark Braverman and Oded Regev for helpful discussions and insightful comments on an earlier draft of this survey. ...
arXiv:1504.06830v1
fatcat:la2qwdcv2zcnvg7yblh6qovcla
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