Interactive Oracle Proofs

Ben–Sasson, Eli; Chiesa, Alessandro; Spooner, Nicholas

doi:10.1007/978-3-662-53644-5_2

Cited by 153 publications

(49 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Zero knowledge. Zero knowledge, while not a goal of this work, is a desirable property, because zero knowledge PCP/IOPs lead to zero knowledge succinct arguments [IMSX15;BCS16]. Straightforward modifications to the protocol, similar to [BCRSVW19], achieve a notion of zero knowledge wherein the simulator runs in time polynomial in the size of the computation being checked, which is meaningful for nondeterministic problems since it does not have access to the witness.…”

Section: Open Questionsmentioning

confidence: 99%

“…In light of these apparent barriers, Ben-Sasson et al [BCS16] have demonstrated how to obtain computationally-sound delegation schemes from interactive oracle proofs (IOPs). This is a natural generalization of PCPs independently introduced by [BCS16;RRR16] (also generalizing the "interactive PCP" model studied in [KR08]). An IOP is an interactive protocol consisting of multiple rounds, where in each round the verifier sends a challenge and the prover responds with a PCP oracle to which the verifier can make a small number of queries.…”

Section: Introductionmentioning

confidence: 99%

“…The work of [BCS16] justifies why exploiting the tradeoff between round complexity and other efficiency measures is potentially advantageous for constructing computationally-sound delegation schemes. In particular, if we could obtain IOPs with constant round complexity that otherwise match the parameters of an ideal PCP (constant query complexity, polylogarithmic verifier time, linear prover time), then we would obtain delegation schemes that have the same asymptotic efficiency as those derived from an ideal PCP.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Linear-Size Constant-Query IOPs for Delegating Computation

Ben–Sasson

Chiesa

Goldberg

et al. 2019

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Open Questionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Linear-Size Constant-Query IOPs for Delegating Computation

Ben–Sasson

Chiesa

Goldberg

et al. 2019

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…In a recent breakthrough [33], constant round protocols under this framework were described using Probabilistically Checkable Interactive Proofs (PCIPs), an interactive version of PCPs where the verifier only reads a few bits of the transcripts. Independently [5], to improve the efficiency of PCPs by adding rounds of interaction (in the random oracle model), 4). To this end, we tailored these systematic subcodes in a manner that they can be encoded and (equivalently) checked (that is, decide if a given word is a codeword) with deterministic runtime exponent 3/2.…”

Section: Linear Time Encodable Codesmentioning

confidence: 99%

Subquadratic Time Encodable Codes Beating the Gilbert–Varshamov Bound

Narayanan

Weidner

2019

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

We construct explicit algebraic geometry codes built from the Garcia-Stichtenoth function field tower beating the Gilbert-Varshamov bound for alphabet sizes at least 19 2 . Messages are identified with functions in certain Riemann-Roch spaces associated with divisors supported on multiple places. Encoding amounts to evaluating these functions at degree one places. By exploiting algebraic structures particular to the Garcia-Stichtenoth tower, we devise an intricate deterministic ω/2 < 1.19 runtime exponent encoding and 1 + ω/2 < 2.19 expected runtime exponent randomized (unique and list) decoding algorithms. Here ω < 2.373 is the matrix multiplication exponent. If ω = 2, as widely believed, the encoding and decoding runtimes are respectively nearly linear and nearly quadratic. Prior to this work, encoding (resp. decoding) time of code families beating the Gilbert-Varshamov bound were quadratic (resp. cubic) or worse.

show abstract

“…Recently, Ben-Sasson, Chiesa and Spooner [BSCS16] proposed the notion of interactive oracle proofs (IOPs), which are interactive protocols where the prover may send a probabilisticaly checkable proof (PCP) in each round. Ben-Sasson et al [BSCG + 16] construct a 3-round public-coin IOP (with soundness error 1/2) for Boolean circuit satisfiability with linear proof length and quasi-linear running times for both the prover and the verifier.…”

Section: Related Workmentioning

confidence: 99%

Linear-Time Zero-Knowledge Proofs for Arithmetic Circuit Satisfiability

Bootle

Cerulli

Ghadafi

et al. 2017

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. We give computationally efficient zero-knowledge proofs of knowledge for arithmetic circuit satisfiability over a large field. For a circuit with N addition and multiplication gates, the prover only uses O(N ) multiplications and the verifier only uses O(N ) additions in the field. If the commitments we use are statistically binding, our zero-knowledge proofs have unconditional soundness, while if the commitments are statistically hiding we get computational soundness. Our zero-knowledge proofs also have sub-linear communication if the commitment scheme is compact. Our construction proceeds in three steps. First, we give a zero-knowledge proof for arithmetic circuit satisfiability in an ideal linear commitment model where the prover may commit to secret vectors of field elements, and the verifier can receive certified linear combinations of those vectors. Second, we show that the ideal linear commitment proof can be instantiated using error-correcting codes and non-interactive commitments. Finally, by choosing efficient instantiations of the primitives we obtain linear-time zero-knowledge proofs.

show abstract

Interactive Oracle Proofs

Cited by 153 publications

References 65 publications

Linear-Size Constant-Query IOPs for Delegating Computation

Linear-Size Constant-Query IOPs for Delegating Computation

Subquadratic Time Encodable Codes Beating the Gilbert–Varshamov Bound

Linear-Time Zero-Knowledge Proofs for Arithmetic Circuit Satisfiability

Contact Info

Product

Resources

About