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On transformation of interactive proofs that preserve the prover's complexity

2000
*
Proceedings of the thirty-second annual ACM symposium on Theory of computing - STOC '00
*

*On*

*transformations*

*of*

*interactive*

*proofs*

*that*

*preserve*

*the*

*prover's*

*complexity*. ... Their

*transformation*has

*the*drawback

*that*

*the*computational

*complexity*

*of*

*the*

*prover's*strategy is not

*preserved*. ... Acknowledgments This work would not have been possible without

*the*help

*of*Sanjeev Arora, who suggested looking for

*a*result about black-box

*transformations*. ...

##
###
Round Complexity Versus Randomness Complexity in Interactive Proofs

2018
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

Furthermore,

doi:10.4230/lipics.approx-random.2018.49
dblp:conf/approx/Leshkowitz18
fatcat:jm5owep2ivfzdowm6cvpwnknqi
*the*randomness*complexity*is*preserved*up to*a*constant factor, and*the*resulting*interactive**proof*system has perfect completeness. ... We show*a*public-coin*interactive**proof*system for S*of*round*complexity*O(r(n)/ log n). ...*On**the**proof**of*Theorem 1 We start by giving an overview*of**a**proof**of**a*weaker result, in which we show how to*transform*any*interactive**proof*,*of*randomness*complexity*r(n), to*a*private-coin*interactive*...##
###
Cryptographic Reverse Firewalls for Interactive Proof Systems

2020
*
International Colloquium on Automata, Languages and Programming
*

We study

doi:10.4230/lipics.icalp.2020.55
dblp:conf/icalp/GaneshM020
fatcat:jngjosguf5bo7cgk7vilt2mobi
*interactive**proof*systems (IPSes) in*a*strong adversarial setting where*the*machines*of*honest parties might be corrupted and under control*of**the*adversary. ...*A*nice feature*of*our design is*that*it is completely transparent, in*the*sense*that*our RFs can be directly applied to already deployed IPSes, without*the*need to re-implement them. ... However, we would like to*note**that**the**prover's*firewall still works for*the*standard*transformation**of**a*Sigma protocol into*a*zero-knowledge*proof**of*knowledge. ...##
###
On Round-Efficient Argument Systems
[chapter]

2005
*
Lecture Notes in Computer Science
*

We consider

doi:10.1007/11523468_12
fatcat:x3k2vjcelzct5oggyjy2kujd3y
*the*problem*of*constructing round-efficient public-coin argument systems,*that*is,*interactive**proof*systems*that*are only computationally sound with*a*constant number*of*rounds. ... Next, we relate*the*existence*of*non-trivial 2-round argument systems to*that**of*hard-*on*-average search problems in NP and*that**of*efficient public-coin zero-knowledge arguments for NP. ... We also observe*that**the*Fiat-Shamir*transformation*fails to*preserve**the*weak*proof*-*of*-knowledge property.*The**proof*goes via*a*case analysis similar to*that*in [GK03] (except*a*lot simpler). ...##
###
On quantum interactive proofs with short messages
[article]

2011
*
arXiv
*
pre-print

We consider quantum

arXiv:1109.0964v1
fatcat:kuaj4bkpkfacjirwj34qkwbikq
*interactive**proof*systems where in*the*beginning*the*verifier and prover send messages to each other with*the*combined length*of*all messages being at most logarithmic (in*the*input ... This paper proves*one**of**the*open problem posed by Beigi et al. in arXiv:1004.0411v2. ... Since we are in*the*last round, we don't have to keep track*of**the**prover's*private space, so we can just describe it's strategy as*a*quantum channel*that**transforms*registers P m Q m+1 to*A*m+1 . ...##
###
Probabilistic proof systems — A survey
[chapter]

1997
*
Lecture Notes in Computer Science
*

In this exposition, we concentrate

doi:10.1007/bfb0023492
fatcat:dmjknckobrghtkdnqu67gd4pw4
*on*three such*proof*systems -*interactive**proofs*, zero-knowledge*proofs*, and probabilistic checkable*proofs*-stressing*the*essential role*of*randomness in each*of*them ... Various types*of*probabilistic*proof*systems have played*a*central role in*the*development*of*computer science in*the*last decade. ... Thanks also to Leonid Levin, Dana Ron, Madhu Sudan and Uri Zwick for commenting*on*earlier versions*of*this survey. ...##
###
Succinct Non-interactive Arguments via Linear Interactive Proofs
[chapter]

2013
*
Lecture Notes in Computer Science
*

Our contribution is three-fold: (1) We introduce and study

doi:10.1007/978-3-642-36594-2_18
fatcat:jdnygt3cszazpaubzom77wdyku
*a*natural extension*of**the**interactive**proof*model*that*considers algebraically-bounded provers; this new setting is analogous to*the*common study ...*A*common relaxation is*a*preprocessing SNARG, which allows*the*verifier to conduct an expensive offline phase*that*is independent*of**the*statement to be proven later. ...*The**transformation**preserves**the*key properties*of**the*LPCP, including*the*algebraic*complexity**of**the*verifier. ...##
###
Probabilistic Proof Systems

1994
*
BRICS Report Series
*

In this exposition, we concentrate

doi:10.7146/brics.v1i28.21643
fatcat:g7noy5g7p5fu5kvgcsodz2v3ty
*on*three such*proof*systems --*interactive**proofs*, zero-knowledge*proofs*, and probabilistic checkable*proofs*-- stressing*the*essential role*of*randomness in each*of*... Various types*of*probabilistic*proof*systems have played*a*central role in*the*development*of*computer science in*the*last decade. ... Acknowledgement I am grateful to Sha Goldwasser for suggesting*the*essential role*of*randomness as*the*unifying theme for this exposition. ...##
###
Interactive Oracle Proofs
[chapter]

2016
*
Lecture Notes in Computer Science
*

We initiate

doi:10.1007/978-3-662-53644-5_2
fatcat:4sx3qgwcuvcgflfmvjjusjdhpq
*the*study*of**a**proof*system model*that*naturally combines*interactive**proofs*(IPs) and probabilistically-checkable*proofs*(PCPs), and generalizes*interactive*PCPs (which consist*of**a*PCP followed ... We prove*that**the*soundness*of**the*resulting*proof*is tightly characterized by*the*soundness*of**the*IOP against state restoration attacks,*a*class*of*rewinding attacks*on**the*IOP verifier*that*is reminiscent ... For any oracle algorithm*A*, integers , i , i max > 0 with i ∈ {1, . . . , i max }, and ρ sampled from U(λ),*the*procedure VE, given input (*A*, , i , i max ) and with oracle access to ρ, works as follows ...##
###
PSPACE has 2-round quantum interactive proof systems
[article]

1999
*
arXiv
*
pre-print

It is proved

arXiv:cs/9901015v1
fatcat:qeh3mmyvbzdbniuwmyompwrjku
*that*every language in PSPACE has*a*quantum*interactive**proof*system*that*requires only two rounds*of*communication between*the*prover and verifier, while having exponentially small (*one*-sided ... It follows*that*quantum*interactive**proof*systems are strictly more powerful than classical*interactive**proof*systems in*the*constant-round case unless*the*polynomial time hierarchy collapses to*the*second ... We have defined in this paper*a*natural quantum analogue*of**the*notion*of*an*interactive**proof*system, and proved*that*there exist 2-round quantum*interactive**proof*systems with exponentially small error ...##
###
Improved Straight-Line Extraction in the Random Oracle Model With Applications to Signature Aggregation
[article]

2022
*
IACR Cryptology ePrint Archive
*

Our collision based

dblp:journals/iacr/KondiS22
fatcat:4isl6ls345cwzjmco67mtakp3u
*proof*-*of*-work more generally improves*the**Prover's*random oracle query*complexity*when applied in*the*NIZK setting as well. ... This is due to*a*uniquely suited polynomial evaluation algorithm, and*the*insight*that**a**proof*-*of*-work*that*relies*on*multicollisions and*the*birthday paradox is faster to solve than inverting*a*fixed ... We*note**that*Pass'*transform*(and equivalently Unruh's*transform*5 [Unr15]) has*a*(strict) query*complexity**that*is twice*that**of**the*expected prover*complexity**of*Fischlin in any non-trivial parameter ...##
###
Parallelization, amplification, and exponential time simulation of quantum interactive proof systems

2000
*
Proceedings of the thirty-second annual ACM symposium on Theory of computing - STOC '00
*

We prove

doi:10.1145/335305.335387
dblp:conf/stoc/KitaevW00
fatcat:uzf5bxj6obhandry6cnmamq2r4
*that*any polynomial-round quantum*interactive**proof*system with two-sided bounded error can be parallelized to*a*quantum*interactive**proof*system with exponentially small*one*-sided error in which ... This yields*a*simplified*proof**that*PSPACE has 3-message quantum*interactive**proof*systems. ... We thank Ashwin Nayak for constructive comments*on*an earlier version*of*this paper. ...##
###
Quantum Interactive Proofs with Competing Provers
[chapter]

2005
*
Lecture Notes in Computer Science
*

We prove

doi:10.1007/978-3-540-31856-9_50
fatcat:mnf7icnx7ffqhmixjzhwdtdtsm
*that*every language having an ordinary quantum*interactive**proof*system also has*a*quantum refereed game in which*the*verifier exchanges just*one*round*of*messages with each prover. ... This paper studies quantum refereed games, which are quantum*interactive**proof*systems with two competing provers:*one**that*tries to convince*the*verifier to accept and*the*other*that*tries to convince ...*of*Alberta. ...##
###
Replicated state machines without replicated execution

2020
*
2020 IEEE Symposium on Security and Privacy (SP)
*

To realize our approach, we build Piperine,

doi:10.1109/sp40000.2020.00068
dblp:conf/sp/Lee0S20
fatcat:k5bgipvf7jftpdcziwizcthirm
*a*system*that*makes*the**proof*machinery profitable in*the*context*of*RSMs. ...*proofs**of*correct state transitions along with state changes, which nodes in*the**transformed*RSM verify and apply respectively. ... We thank Sebastian Angel, Riad Wahby, and*the*anonymous S&P reviewers for helpful comments*that*significantly improved*the*presentation*of*this work. ...##
###
Delegating Computation

2015
*
Journal of the ACM
*

This result uses

doi:10.1145/2699436
fatcat:loxaz5ha4zfu3euozgvdw6xmim
*a*recent*transformation**of*Kalai and Raz from public-coin*interactive**proofs*to*one*-round arguments. ... This settles an open question regarding*the*expressive power*of**proof*systems with such verifiers. • Zero-knowledge*interactive**proofs*with communication*complexity**that*is quasi-linear in*the*witness ... We*note**that**the*efficiency*of**the*prover is derived from*a*special property*of*our*proof*system. ...
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