Verifiable Delegation of Computation over Large Datasets

Benabbas, Siavosh; Gennaro, Rosario; Vahlis, Yevgeniy

doi:10.1007/978-3-642-22792-9_7

Cited by 269 publications

(286 citation statements)

References 60 publications

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“…A substantial body of theoretical work in this area has focused on the development of protocols targeted at specific problems (e.g. [15,19,51]). Other theoretical works have focused on the development of general-purpose argument systems.…”

Section: Related Workmentioning

confidence: 99%

Practical verified computation with streaming interactive proofs

Cormode

Mitzenmacher

Thaler

2012

Proceedings of the 3rd Innovations in Theoretical Computer Science Conference

153

269

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When delegating computation to a service provider, as in the cloud computing paradigm, we seek some reassurance that the output is correct and complete. Yet recomputing the output as a check is inefficient and expensive, and it may not even be feasible to store all the data locally. We are therefore interested in what can be validated by a streaming (sublinear space) user, who cannot store the full input, or perform the full computation herself. Our aim in this work is to advance a recent line of work on "proof systems" in which the service provider proves the correctness of its output to a user. The goal is to minimize the time and space costs of both parties in generating and checking the proof. Only very recently have there been attempts to implement such proof systems, and thus far these have been quite limited in functionality.Here, our approach is two-fold. First, we describe a carefully chosen instantiation of one of the most efficient general-purpose constructions for arbitrary computations (streaming or otherwise), due to Goldwasser, Kalai, and Rothblum [19]. This requires several new insights and enhancements to move the methodology from a theoretical result to a practical possibility. Our main contribution is in achieving a prover that runs in time O(S(n) log S(n)), where S(n) is the size of an arithmetic circuit computing the function of interest; this compares favorably to the poly(S(n)) runtime for the prover promised in [19]. Our experimental results demonstrate that a practical general-purpose protocol for verifiable computation may be significantly closer to reality than previously realized.Second, we describe a set of techniques that achieve genuine scalability for protocols fine-tuned for specific important problems in streaming and database processing. Focusing in particular on noninteractive protocols for problems ranging from matrix-vector multiplication to bipartite perfect matching, we build on prior work [8,15] to achieve a prover that runs in nearly linear-time, while obtaining optimal tradeoffs between communication cost and the user's working memory. Existing techniques required (substantially) superlinear time for the prover. Finally, we develop improved interactive protocols for specific problems based on a linearization technique originally due to Shen [34]. We argue that even if general-purpose methods improve, fine-tuned protocols will remain valuable in real-world settings for key problems, and hence special attention to specific problems is warranted.

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Section: Related Workmentioning

confidence: 99%

Practical verified computation with streaming interactive proofs

Cormode

Mitzenmacher

Thaler

2012

Proceedings of the 3rd Innovations in Theoretical Computer Science Conference

153

269

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“…Verifiable computation for polynomials. Benabbas et al [3] developed methods for efficient verification of multivariate polynomial evaluation by using algebraic one-way functions-however, in the SVC model. This work does not achieve efficient updates of polynomial coefficients (specifically, in order to update a coefficient, one has to re-randomize all the existing coefficients).…”

Section: Related Workmentioning

confidence: 99%

“…Moreover several useful constructions are also enabled by verifying polynomial operations, such as accumulators [30], verifiable set operations [33], verifiable databases [3] and proofs of retrievability [3]. Although applications of polynomial evaluation are more straightforward, one might wonder what is the meaning of a derivative in Z p and why its verification can be of any use.…”

Section: F Applicationsmentioning

confidence: 99%

Signatures of Correct Computation

Papamanthou

Shi

Tamassia

2013

Lecture Notes in Computer Science

131

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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.

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“…Other related works such as verifiable computation [2,5,15,16,17,18,34,40] and authenticated data structures [13,20,21,31,35,36,37,38] are not directly applicable to the streaming setting or their application yields high complexities or interactive protocols.…”

Section: Related Workmentioning

confidence: 99%

Streaming Authenticated Data Structures

Papamanthou

Shi

Tamassia

et al. 2013

Lecture Notes in Computer Science

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Abstract. We consider the problem of streaming verifiable computation, where both a verifier and a prover observe a stream of n elements x1, x2, . . . , xn and the verifier can later delegate some computation over the stream to the prover. The prover must return the output of the computation, along with a cryptographic proof to be used for verifying the correctness of the output. Due to the nature of the streaming setting, the verifier can only keep small local state (e.g., logarithmic) which must be updatable in a streaming manner and with no interaction with the prover. Such constraints make the problem particularly challenging and rule out applying existing verifiable computation schemes.We propose streaming authenticated data structures, a model that enables efficient verification of data structure queries on a stream. Compared to previous work, we achieve an exponential improvement in the prover's running time: While previous solutions have linear prover complexity (in the size of the stream), even for queries executing in sublinear time (e.g., set membership), we propose a scheme with O(log M log n) prover complexity, where n is the size of the stream and M is the size of the universe of elements. Our schemes support a series of expressive queries, such as (non-)membership, successor, range search and frequency queries, over an ordered universe and even in higher dimensions. The central idea of our construction is a new authentication tree, called generalized hash tree. We instantiate our generalized hash tree with a hash function based on lattices assumptions, showing that it enjoys suitable algebraic properties that traditional Merkle trees lack. We exploit such properties to achieve our results.

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Verifiable Delegation of Computation over Large Datasets

Cited by 269 publications

References 60 publications

Practical verified computation with streaming interactive proofs

Practical verified computation with streaming interactive proofs

Signatures of Correct Computation

Streaming Authenticated Data Structures

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