Publicly verifiable delegation of large polynomials and matrix computations, with applications

Fiore, Dario; Gennaro, Rosario

doi:10.1145/2382196.2382250

Cited by 209 publications

(230 citation statements)

References 18 publications

Supporting

Mentioning

225

Contrasting

Order By: Relevance

“…Signatures of correct computation are closely related to publicly verifiable computation (PVC), proposed by Parno et al [34], Canetti et al [9] and Fiore and Gennaro [13,14], in concurrent and independent works to ours. Specifically, signatures of correct computation are stronger than publicly verifiable computation: given an SCC scheme, one can directly construct a PVC scheme; while the other way around does not seem to be true.…”

Section: Introductionmentioning

confidence: 74%

“…Operations on polynomials represent a common building block in a wide range of applications, such as in statistical analysis, scientific computing, and machine learning. Fiore and Gennaro [14] point out many interesting applications of publicly verifiable computation on polynomials, including its use in proofs of retrievability, verifiable keyword search, discrete Fourier tranform, and linear transformations. Our constructions are based on bilinear groups.…”

Section: Results and Contributionsmentioning

confidence: 99%

“…Specifically, our techniques can be readily applied to yield publicly verifiable computation schemes (for the same operations) with adaptive security (without the random oracle model) and with efficient updates. In comparison, existing PVC works [9,14,34], achieve adaptive security but do not support efficient updates. We give a more detailed comparison in Section 1.2.…”

Section: Results and Contributionsmentioning

confidence: 99%

“…The most closely related works are the recent works by Fiore and Gennaro [14], who presented a PVC scheme tailored for multivariate polynomials that is based on algebraic one-way functions. An improved version [13] uses less complex assumptions such as RSA to achieve the same goal.…”

Section: Related Workmentioning

confidence: 99%

“…An improved version [13] uses less complex assumptions such as RSA to achieve the same goal. The works by Fiore and Gennaro differ from ours in the following sense.…”

Section: Related Workmentioning

confidence: 99%

See 4 more Smart Citations

Signatures of Correct Computation

Papamanthou

Shi

Tamassia

2013

Lecture Notes in Computer Science

131

View full text Add to dashboard Cite

We introduce Signatures of Correct Computation (SCC), a new model for verifying dynamic computations in cloud settings. In the SCC model, a trusted source outsources a function f to an untrusted server, along with a public key for that function (to be used during verification). The server can then produce a succinct signature σ vouching for the correctness of the computation of f , i.e., that some result v is indeed the correct outcome of the function f evaluated on some point a. There are two crucial performance properties that we want to guarantee in an SCC construction: (1) verifying the signature should take asymptotically less time than evaluating the function f ; and (2) the public key should be efficiently updated whenever the function changes.We construct SCC schemes (satisfying the above two properties) supporting expressive manipulations over multivariate polynomials, such as polynomial evaluation and differentiation. Our constructions are adaptively secure in the random oracle model and achieve optimal updates, i.e., the function's public key can be updated in time proportional to the number of updated coefficients, without performing a linear-time computation (in the size of the polynomial).We also show that signatures of correct computation imply Publicly Verifiable Computation (PVC), a model recently introduced in several concurrent and independent works. Roughly speaking, in the SCC model, any client can verify the signature σ and be convinced of some computation result, whereas in the PVC model only the client that issued a query (or anyone who trusts this client) can verify that the server returned a valid signature (proof) for the answer to the query. Our techniques can be readily adapted to construct PVC schemes with adaptive security, efficient updates and without the random oracle model.

show abstract

Section: Introductionmentioning

confidence: 74%

Section: Results and Contributionsmentioning

confidence: 99%

Section: Results and Contributionsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…An improved version [13] uses less complex assumptions such as RSA to achieve the same goal. The works by Fiore and Gennaro differ from ours in the following sense.…”

Section: Related Workmentioning

confidence: 99%

See 3 more Smart Citations

Signatures of Correct Computation

Papamanthou

Shi

Tamassia

2013

Lecture Notes in Computer Science

131

View full text Add to dashboard Cite

show abstract

Verifiable Outsourced Computation with Full Delegation

Wang

Zhou

et al. 2018

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Verifiable and Private Oblivious Polynomial Evaluation

Gajera

Giraud

Gerault

et al. 2020

Information Security Theory and Practice

View full text Add to dashboard Cite

It is a challenging problem to delegate the computation of a polynomial on encrypted data to a server in an oblivious and verifiable way. In this paper, we formally define Verifiable and Private Oblivious Polynomial Evaluation (VPOPE) scheme. We design a scheme called Verifiable IND-CFA Paillier based Private Oblivious Polynomial Evaluation (VIP-POPE). Using security properties of Private Polynomial Evaluation (PPE) schemes and Oblivious Polynomial Evaluation (OPE) schemes, we prove that our scheme is proof unforgeability, indistinguishability against chosen function attack, and client privacy-secure under the Decisional Composite Residuosity assumption in the random oracle model.

show abstract

Publicly verifiable delegation of large polynomials and matrix computations, with applications

Cited by 209 publications

References 18 publications

Signatures of Correct Computation

Signatures of Correct Computation

Verifiable Outsourced Computation with Full Delegation

Verifiable and Private Oblivious Polynomial Evaluation

Contact Info

Product

Resources

About