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Rational Proofs with Multiple Provers [article]

Jing Chen, Samuel McCauley, Shikha Singh
2017 arXiv   pre-print
They leave the question of whether multiple provers are more powerful than a single prover for rational and classical proofs as an open problem.  ...  Rational interactive proofs (RIP), introduced by Azar and Micali (2012), are an interactive-proof system with payments, in which the prover is rational rather than untrustworthy---he may lie, but only  ...  While these applications differ from interactive proofs in many ways, they motivate the study of a proof system with multiple cooperative rational provers.  ... 
arXiv:1504.08361v5 fatcat:h2c46fhv2vhojbpzgium6lvwtu

Rational Proofs with Multiple Provers

Jing Chen, Samuel McCauley, Shikha Singh
2016 Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16  
Previous Discussions of Multiple Provers in Rational Proofs. The notion of rational proofs with multiple provers has appeared several times in previous work [5, 6, 29] .  ...  We further show that the full power of rational proofs with multiple provers can be achieved using only two provers and five rounds of interaction.  ...  They also mentioned that a rational proof model with multiple provers may have interesting implications in computation delegation schemes, but did not define such a model.  ... 
doi:10.1145/2840728.2840744 dblp:conf/innovations/ChenM016 fatcat:jvej5achnvfrtmgwl6ebexex5a

Efficient Rational Proofs with Strong Utility-Gap Guarantees [article]

Jing Chen, Samuel McCauley, Shikha Singh
2018 arXiv   pre-print
Interactive proofs are a widely-used model to design efficient protocols for verifiable computation delegation. Rational proofs are payment-based interactive proofs.  ...  Finally, we show when and how rational protocols can be converted to give the completeness and soundness guarantees of classical interactive proofs.  ...  We show that any rational proof with polynomial communication can be simulated by a rational proof with logarithmic communication that uses an additional prover.  ... 
arXiv:1807.01389v2 fatcat:b4avw5p2nvcarpkdsxlhgbjmsq

Efficient Rational Proofs with Strong Utility-Gap Guarantees [chapter]

Jing Chen, Samuel McCauley, Shikha Singh
2018 Lecture Notes in Computer Science  
Thus, protocols with small utility gap are sound even against provers with bounded rationality; that is, provers who are only sensitive to large losses.  ...  In rational proofs, the provers act rationally in the game-theoretic sense, that is, they want to maximize their payment.  ...  We show that any rational proof with polynomial communication can be simulated by a rational proof with logarithmic communication that uses an additional prover.  ... 
doi:10.1007/978-3-319-99660-8_14 fatcat:547nfe7mbjdznc4qb5tmqshaty

Rational Proofs against Rational Verifiers

Keita INASAWA, Kenji YASUNAGA
2017 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
Rational proofs, introduced by Azar and Micali (STOC 2012), are a variant of interactive proofs in which the prover is rational, and may deviate from the protocol for increasing his reward.  ...  By restricting the prover to be computationally bounded, they presented a one-round delegation scheme with sublinear verification for functions computable by log-space uniform circuits with logarithmic  ...  Chen, McCauley, and Singh [5] studied rational proofs that allows multiple provers, and showed that multiple rational provers are strictly more powerful than one.  ... 
doi:10.1587/transfun.e100.a.2392 fatcat:bkn43hdgpja7tesqaou7emvbli

Rational Sumchecks [chapter]

Siyao Guo, Pavel Hubáček, Alon Rosen, Margarita Vald
2015 Lecture Notes in Computer Science  
Rational proofs, introduced by Azar and Micali (STOC 2012) are a variant of interactive proofs in which the prover is neither honest nor malicious, but rather rational.  ...  As an additional contribution we study the possibility of using rational proofs as efficient blocks within classical interactive proofs.  ...  This is done by first transforming the rational interactive proof for NC to RMIP (with only negligible loss in the reward gap) and then applying Theorem 8 on the resulted RMIP.  ... 
doi:10.1007/978-3-662-49099-0_12 fatcat:t3tvm7tumneybjjt5srz2wwoa4

Rational arguments

Siyao Guo, Pavel Hubáček, Alon Rosen, Margarita Vald
2014 Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS '14  
Rational proofs, recently introduced by Azar and Micali (STOC 2012), are a variant of interactive proofs in which the prover is neither honest nor malicious, but rather rational.  ...  circuits with threshold gates.  ...  One other interesting approach is to consider a model with multiple provers. Based on Goldwasser et al.  ... 
doi:10.1145/2554797.2554845 dblp:conf/innovations/GuoHRV14 fatcat:gle7jmcp3jhtznvw4dyfqjfocm

Zero Knowledge Proofs of Elliptic Curve Inner Products from Principal Divisors and Weil Reciprocity [article]

Liam Eagen
2022 IACR Cryptology ePrint Archive  
This technique also works, with small modification, for proving multiexponentiations in the multiplicative group of the field.  ...  Since the multiplicities are field elements, this system can prove ECIP relations in zero knowledge with respect to the linear combination, the curve points, or both.  ...  with scalar multiplication by 1.  ... 
dblp:journals/iacr/Eagen22a fatcat:raswczs6dnb6njzs7p77e7f2rm

Integrating Simplex with Tableaux [chapter]

Guillaume Bury, David Delahaye
2015 Lecture Notes in Computer Science  
We also describe our implementation in the framework of Zenon, an automated theorem prover that is able to deal with first order logic with equality.  ...  This implementation has been provided with a backend verifier that relies on the Coq proof assistant, and which can verify the validity of the generated arithmetic proofs.  ...  sugar for addition with multiplication by a negative constant.  ... 
doi:10.1007/978-3-319-24312-2_7 fatcat:r24bduebg5euxfyy44tiwxn2du

Arguments of Knowledge via hidden order groups [article]

Steve Thakur
2020 IACR Cryptology ePrint Archive  
We provide protocols whereby a Prover can demonstrate certain properties of and relations between committed sets/multisets, with succinct proofs that are publicly verifiable against the constant-sized  ...  We say an argument system (PGen, P, V) is sound if P cannot forge a fake proof except with negligible probability. Definition 2.3.  ...  In section 4, we provide protocols whereby a Prover holding the data can demonstrate the pairwise disjointness of multiple data sets/multisets with proofs publicly verifiable against the commitments.  ... 
dblp:journals/iacr/Thakur20b fatcat:sk3lvlky2nbgzgjos762wg2hnq

Non-Cooperative Rational Interactive Proofs

Jing Chen, Samuel McCauley, Shikha Singh, Michael Wagner
2019 European Symposium on Algorithms  
Existing interactive-proof games largely fall into two categories: either as games of cooperation such as multi-prover interactive proofs and cooperative rational proofs, where the provers work together  ...  We show, for example, that the power of non-cooperative rational interactive proofs with a polynomial utility gap is exactly equal to the complexity class P NEXP .  ...  Existing interactive-proof games Interactive-proof systems with multiple provers have largely been studied as games that fall into two categories: either as games of cooperation such as MIP [6] , cooperative  ... 
doi:10.4230/lipics.esa.2019.29 dblp:conf/esa/0017M019 fatcat:qzysidq7izgi7lxro3rpe2rrke

Proof-of-work certificates that can be efficiently computed in the cloud [article]

Jean-Guillaume Dumas
2018 arXiv   pre-print
The idea of verifiable computing is to associate a data structure, a proof-of-work certificate, to the result of the outsourced computation.  ...  We talk about a Prover (the server performing the computations) and a Verifier.  ...  Reductions to matrix multiplication With a certificate for matrix expressions, then one can certify any algorithm that reduces to matrix multiplication: the Prover records all the intermediate matrix products  ... 
arXiv:1806.11293v2 fatcat:nhkhxiojmzfl3a63fmmk32dthi

Proof-of-Work Certificates that Can Be Efficiently Computed in the Cloud (Invited Talk) [chapter]

Jean-Guillaume Dumas
2018 Lecture Notes in Computer Science  
We talk about a Prover (the server performing the computations) and a Verifier.  ...  The idea of verifiable computing is to associate a data structure, a proof-of-work certificate, to the result of the outsourced computation.  ...  Reductions to matrix multiplication With a certificate for matrix expressions, then one can certify any algorithm that reduces to matrix multiplication: the Prover records all the intermediate matrix products  ... 
doi:10.1007/978-3-319-99639-4_1 fatcat:7usrmrmjizg45g2tyfyye3rqwe

multiPRover: Generating Multiple Proofs for Improved Interpretability in Rule Reasoning [article]

Swarnadeep Saha, Prateek Yadav, Mohit Bansal
2021 arXiv   pre-print
Experiments on multiple synthetic, zero-shot, and human-paraphrased datasets reveal that both multiPRover models significantly outperform PRover on datasets containing multiple gold proofs.  ...  Each proof provides a different rationale for the answer, thereby improving the interpretability of such reasoning systems.  ...  We observe that PROVER-all has a slightly lower proof F1 than PROVER, because the model likely gets confused with multiple possible proofs for the same context and question.  ... 
arXiv:2106.01354v1 fatcat:yhpii7kdzjh2jpbwqlq2emsgtm

Bulletproofs++ [article]

Liam Eagen
2022 IACR Cryptology ePrint Archive  
multiple types of currency.  ...  Finally, I use the permutation argument to construct a zero knowledge confidential transaction protocol for multiple types of currency.  ...  e, and the prover commits to the vector r of rational functions.  ... 
dblp:journals/iacr/Eagen22 fatcat:74kavu6najgv7gbxu6vdoqf34m
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