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

Salil Vadhan
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.  ... 
doi:10.1145/335305.335330 dblp:conf/stoc/Vadhan00 fatcat:37wn3ym4zrdbnddwgv6lb5cmey

Round Complexity Versus Randomness Complexity in Interactive Proofs

Maya Leshkowitz, Michael Wagner
2018 International Workshop on Approximation Algorithms for Combinatorial Optimization  
Furthermore, 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  ... 
doi:10.4230/lipics.approx-random.2018.49 dblp:conf/approx/Leshkowitz18 fatcat:jm5owep2ivfzdowm6cvpwnknqi

Cryptographic Reverse Firewalls for Interactive Proof Systems

Chaya Ganesh, Bernardo Magri, Daniele Venturi, Emanuela Merelli, Anuj Dawar, Artur Czumaj
2020 International Colloquium on Automata, Languages and Programming  
We study 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.  ... 
doi:10.4230/lipics.icalp.2020.55 dblp:conf/icalp/GaneshM020 fatcat:jngjosguf5bo7cgk7vilt2mobi

On Round-Efficient Argument Systems [chapter]

Hoeteck Wee
2005 Lecture Notes in Computer Science  
We consider 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).  ... 
doi:10.1007/11523468_12 fatcat:x3k2vjcelzct5oggyjy2kujd3y

On quantum interactive proofs with short messages [article]

Attila Pereszlényi
2011 arXiv   pre-print
We consider quantum 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 .  ... 
arXiv:1109.0964v1 fatcat:kuaj4bkpkfacjirwj34qkwbikq

Probabilistic proof systems — A survey [chapter]

Oded Goldreich
1997 Lecture Notes in Computer Science  
In this exposition, we concentrate 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.  ... 
doi:10.1007/bfb0023492 fatcat:dmjknckobrghtkdnqu67gd4pw4

Succinct Non-interactive Arguments via Linear Interactive Proofs [chapter]

Nir Bitansky, Alessandro Chiesa, Yuval Ishai, Omer Paneth, Rafail Ostrovsky
2013 Lecture Notes in Computer Science  
Our contribution is three-fold: (1) We introduce and study 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.  ... 
doi:10.1007/978-3-642-36594-2_18 fatcat:jdnygt3cszazpaubzom77wdyku

Probabilistic Proof Systems

Oded Goldreich
1994 BRICS Report Series  
In this exposition, we concentrate 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.  ... 
doi:10.7146/brics.v1i28.21643 fatcat:g7noy5g7p5fu5kvgcsodz2v3ty

Interactive Oracle Proofs [chapter]

Eli Ben-Sasson, Alessandro Chiesa, Nicholas Spooner
2016 Lecture Notes in Computer Science  
We initiate 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  ... 
doi:10.1007/978-3-662-53644-5_2 fatcat:4sx3qgwcuvcgflfmvjjusjdhpq

PSPACE has 2-round quantum interactive proof systems [article]

John Watrous
1999 arXiv   pre-print
It is proved 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  ... 
arXiv:cs/9901015v1 fatcat:qeh3mmyvbzdbniuwmyompwrjku

Improved Straight-Line Extraction in the Random Oracle Model With Applications to Signature Aggregation [article]

Yashvanth Kondi, Abhi Shelat
2022 IACR Cryptology ePrint Archive  
Our collision based 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  ... 
dblp:journals/iacr/KondiS22 fatcat:4isl6ls345cwzjmco67mtakp3u

Parallelization, amplification, and exponential time simulation of quantum interactive proof systems

Alexei Kitaev, John Watrous
2000 Proceedings of the thirty-second annual ACM symposium on Theory of computing - STOC '00  
We prove 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.  ... 
doi:10.1145/335305.335387 dblp:conf/stoc/KitaevW00 fatcat:uzf5bxj6obhandry6cnmamq2r4

Quantum Interactive Proofs with Competing Provers [chapter]

Gus Gutoski, John Watrous
2005 Lecture Notes in Computer Science  
We prove 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.  ... 
doi:10.1007/978-3-540-31856-9_50 fatcat:mnf7icnx7ffqhmixjzhwdtdtsm

Replicated state machines without replicated execution

Jonathan Lee, Kirill Nikitin, Srinath Setty
2020 2020 IEEE Symposium on Security and Privacy (SP)  
To realize our approach, we build Piperine, 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.  ... 
doi:10.1109/sp40000.2020.00068 dblp:conf/sp/Lee0S20 fatcat:k5bgipvf7jftpdcziwizcthirm

Delegating Computation

Shafi Goldwasser, Yael Tauman Kalai, Guy N. Rothblum
2015 Journal of the ACM  
This result uses 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.  ... 
doi:10.1145/2699436 fatcat:loxaz5ha4zfu3euozgvdw6xmim
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