TY - GEN

T1 - Rational arguments

T2 - 2014 5th Conference on Innovations in Theoretical Computer Science, ITCS 2014

AU - Guo, Siyao

AU - Hubáček, Pavel

AU - Rosen, Alon

AU - Vald, Margarita

PY - 2014

Y1 - 2014

N2 - 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. The advantage of rational proofs over their classical counterparts is that they allow for extremely low communication and verification time. Azar and Micali demonstrated their potential by giving a one message rational proof for #SAT, in which the verifier runs in time O(n), where n denotes the instance size. In a follow-up work (EC 2013), Azar and Micali proposed "super-efficient" and interactive versions of rational proofs and argued that they capture precisely the class TC0 of constant-depth, polynomial-size circuits with threshold gates. In this paper, we show that by considering rational arguments, in which the prover is additionally restricted to be computationally bounded, the class NC1, of search problems computable by log-space uniform circuits of O(log n)-depth, admits rational protocols that are simultaneously one-round and polylog(n) time verifiable. This demonstrates the po-tential of rational arguments as a way to extend the notion of "super-efficient" rational proofs beyond the class TC0. The low interaction nature of our protocols, along with their sub-linear verification time, make them well suited for delegation of computation. While they provide a weaker (yet arguably meaningful) guarantee of soundness, they compare favorably with each of the known delegation schemes in at least one aspect. They are simple, rely on standard complexity hardness assumptions, provide a correctness guarantee for all instances, and do not require preprocessing.

AB - 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. The advantage of rational proofs over their classical counterparts is that they allow for extremely low communication and verification time. Azar and Micali demonstrated their potential by giving a one message rational proof for #SAT, in which the verifier runs in time O(n), where n denotes the instance size. In a follow-up work (EC 2013), Azar and Micali proposed "super-efficient" and interactive versions of rational proofs and argued that they capture precisely the class TC0 of constant-depth, polynomial-size circuits with threshold gates. In this paper, we show that by considering rational arguments, in which the prover is additionally restricted to be computationally bounded, the class NC1, of search problems computable by log-space uniform circuits of O(log n)-depth, admits rational protocols that are simultaneously one-round and polylog(n) time verifiable. This demonstrates the po-tential of rational arguments as a way to extend the notion of "super-efficient" rational proofs beyond the class TC0. The low interaction nature of our protocols, along with their sub-linear verification time, make them well suited for delegation of computation. While they provide a weaker (yet arguably meaningful) guarantee of soundness, they compare favorably with each of the known delegation schemes in at least one aspect. They are simple, rely on standard complexity hardness assumptions, provide a correctness guarantee for all instances, and do not require preprocessing.

KW - Delegation of Computation

KW - Rational Cryptography

KW - Succinct Arguments

KW - Threshold Circuits

UR - http://www.scopus.com/inward/record.url?scp=84893284656&partnerID=8YFLogxK

U2 - 10.1145/2554797.2554845

DO - 10.1145/2554797.2554845

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AN - SCOPUS:84893284656

SN - 9781450322430

T3 - ITCS 2014 - Proceedings of the 2014 Conference on Innovations in Theoretical Computer Science

SP - 523

EP - 539

BT - ITCS 2014 - Proceedings of the 2014 Conference on Innovations in Theoretical Computer Science

PB - Association for Computing Machinery

Y2 - 12 January 2014 through 14 January 2014

ER -