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Tight Parallel Repetition Theorems for Public-Coin Arguments Using KL-Divergence [chapter]

Kai-Min Chung, Rafael Pass
2015 Lecture Notes in Computer Science  
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]

Kai-Min Chung, Feng-Hao Liu
2010 Lecture Notes in Computer Science  
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

Kai-Min Chung, Rafael Pass
2011 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science  
. • 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

Krzysztof Pietrzak, Douglas Wikström
2010 Journal of Cryptology  
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]

Rafael Pass, Muthuramakrishnan Venkitasubramaniam
2020 arXiv   pre-print
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]

Pranab Sen, S. Venkatesh
2001 Lecture Notes in Computer Science  
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]

Nir Bitansky, Dana Dachman-Soled, Sanjam Garg, Abhishek Jain, Yael Tauman Kalai, Adriana López-Alt, Daniel Wichs
2013 Lecture Notes in Computer Science  
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

Rahul Jain, Attila Pereszlenyi, Penghui Yao
2012 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science  
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]

Yael Tauman Kalai, Ron D. Rothblum
2015 Lecture Notes in Computer Science  
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

Boaz Barak, Yehuda Lindell, Salil Vadhan
2006 Journal of computer and system sciences (Print)  
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]

Nir Bitansky, Alessandro Chiesa
2012 Lecture Notes in Computer Science  
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]

Silvio Micali, Leonid Reyzin
2001 Lecture Notes in Computer Science  
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

Tom Gur, Yang P. Liu, Ron D. Rothblum
2021 Computational Complexity  
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]

Itay Berman, Akshay Degwekar, Ron D. Rothblum, Prashant Nalini Vasudevan
2018 Lecture Notes in Computer Science  
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]

Omri Weinstein
2015 arXiv   pre-print
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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