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

2015
*
Lecture Notes in Computer Science
*

We then use this new proof to present the first

doi:10.1007/978-3-662-46497-7_9
fatcat:ayi7kmsq7zdrzeztja6ftoqadu
*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. ...##
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Parallel Repetition Theorems for Interactive Arguments
[chapter]

2010
*
Lecture Notes in Computer Science
*

We show a

doi:10.1007/978-3-642-11799-2_2
fatcat:gehmqryjcbc5xbwgiuklvmir24
*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. ...##
###
The Randomness Complexity of Parallel Repetition

2011
*
2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
*

. • We establish the first derandomized

doi:10.1109/focs.2011.93
dblp:conf/focs/ChungP11
fatcat:c66rwhdzvjb3nctvhxuejeprwu
*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. ...##
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Parallel Repetition of Computationally Sound Protocols Revisited

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. ...

##
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Is it Easier to Prove Theorems that are Guaranteed to be True?
[article]

2020
*
arXiv
*
pre-print

As another consequence of this treatment, we show that the existence of O(1)-round

arXiv:1906.10837v2
fatcat:wb5ctjek2rd6rab4pdoscatuqq
*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. ...##
###
Lower Bounds in the Quantum Cell Probe Model
[chapter]

2001
*
Lecture Notes in Computer Science
*

We prove a lower bound

doi:10.1007/3-540-48224-5_30
fatcat:mml7vxtysjandpfghl44mwneae
*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 ...##
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Why "Fiat-Shamir for Proofs" Lacks a Proof
[chapter]

2013
*
Lecture Notes in Computer Science
*

The Fiat-Shamir heuristic [CRYPTO '86] is used to convert any 3-message

doi:10.1007/978-3-642-36594-2_11
fatcat:wa6argayqramfnwwbo2zutmcqu
*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 ...##
###
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
*

Another important tool that we use is a correlated sampling protocol, which

doi:10.1109/focs.2012.42
dblp:conf/focs/JainPY12
fatcat:wj7ljiusl5a4pdghvaecxrthn4
*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]). ...##
###
Arguments of Proximity
[chapter]

2015
*
Lecture Notes in Computer Science
*

Assuming the existence of a sub-exponentially secure FHE scheme, we construct a one-round

doi:10.1007/978-3-662-48000-7_21
fatcat:5kuidvuiibcmjlmtv75r6oztsa
*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. ...##
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Lower bounds for non-black-box zero knowledge

2006
*
Journal of computer and system sciences (Print)
*

There does not exist a constant-round

doi:10.1016/j.jcss.2005.06.010
fatcat:hllc2tom6zgrrapoftgdz5hdqy
*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. ...##
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Succinct Arguments from Multi-prover Interactive Proofs and Their Efficiency Benefits
[chapter]

2012
*
Lecture Notes in Computer Science
*

Succinct

doi:10.1007/978-3-642-32009-5_16
fatcat:je4zuvn23bcfvb5xwzgv3t3zjm
*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. ...##
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Soundness in the Public-Key Model
[chapter]

2001
*
Lecture Notes in Computer Science
*

The

doi:10.1007/3-540-44647-8_32
fatcat:rdd7rxhz6fb2rg66ojtnamnmry
*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. ...##
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An Exponential Separation Between MA and AM Proofs of Proximity

2021
*
Computational Complexity
*

As an application of this result, we show an exponential separation between the power of

doi:10.1007/s00037-021-00212-3
fatcat:bhjncpg5lfg5pbb4zq223nzjpm
*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. ...##
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From Laconic Zero-Knowledge to Public-Key Cryptography
[chapter]

2018
*
Lecture Notes in Computer Science
*

Since its inception,

doi:10.1007/978-3-319-96878-0_23
fatcat:leuv3kr2ibf7pbjn2x4ck6iiei
*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. ...##
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Information Complexity and the Quest for Interactive Compression (A Survey)
[article]

2015
*
arXiv
*
pre-print

In recent years this field has emerged as a powerful tool

arXiv:1504.06830v1
fatcat:la2qwdcv2zcnvg7yblh6qovcla
*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. ...
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