Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

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The knowledge complexity of interactive proof-systems

In this paper, we define and explore proofs of retrievability (PORs). A POR scheme enables an archive or back-up service (prover) to produce a concise proof that a user (verifier) can retrieve a target file F, that is, that the archive retains and reliably transmits file data sufficient for the user to recover F in its entirety.A POR may be viewed as a kind of cryptographic proof of knowledge (POK), but one specially designed to handle a large file (or bitstring) F. We explore POR protocols here in which the communication costs, number of memory accesses for the prover, and storage requirements of the user (verifier) are small parameters essentially independent of the length of F. In addition to proposing new, practical POR constructions, we explore implementation considerations and optimizations that bear on previously explored, related schemes.In a POR, unlike a POK, neither the prover nor the verifier need actually have knowledge of F. PORs give rise to a new and unusual security definition whose formulation is another contribution of our work.We view PORs as an important tool for semi-trusted online archives. Existing cryptographic techniques help users ensure the privacy and integrity of files they retrieve. It is also natural, however, for users to want to verify that archives do not delete or modify files prior to retrieval. The goal of a POR is to accomplish these checks without users having to download the files themselves. A POR can also provide quality-of-service guarantees, i.e., show that a file is retrievable within a certain time bound.

PORs: Proofs of Retrievability for Large Files

Searchable symmetric encryption (SSE) allows a party to outsource the storage of its data to another party (a server) in a private manner, while maintaining the ability to selectively search over it. This problem has been the focus of active research in recent years. In this paper we show two solutions to SSE that simultaneously enjoy the following properties: Both solutions are more efficient than all previous constant-round schemes. In particular, the work performed by the server per returned document is constant as opposed to linear in the size of the data. Both solutions enjoy stronger security guarantees than previous constant-round schemes. In fact, we point out subtle but serious problems with previous notions of security for SSE, and show how to design constructions which avoid these pitfalls. Further, our second solution also achieves what we call adaptive SSE security, where queries to the server can be chosen adaptively (by the adversary) during the execution of the search; this notion is both important in practice and has not been previously considered.Surprisingly, despite being more secure and more efficient, our SSE schemes are remarkably simple. We consider the simplicity of both solutions as an important step towards the deployment of SSE technologies.As an additional contribution, we also consider multi-user SSE. All prior work on SSE studied the setting where only the owner of the data is capable of submitting search queries. We consider the natural extension where an arbitrary group of parties other than the owner can submit search queries. We formally define SSE in the multi-user setting, and present an efficient construction that achieves better performance than simply using access control mechanisms.

/pdf/searchable-symmetric-encryption-improved-definitions-and-19ss3wg07l.pdf

Searchable symmetric encryption: improved definitions and efficient constructions

We consider the problem of building a secure cloud storage service on top of a public cloud infrastructure where the service provider is not completely trusted by the customer We describe, at a high level, several architectures that combine recent and non-standard cryptographic primitives in order to achieve our goal We survey the benefits such an architecture would provide to both customers and service providers and give an overview of recent advances in cryptography motivated specifically by cloud storage

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Cryptographic cloud storage

In a proof-of-retrievability system, a data storage center convinces a verifier that he is actually storing all of a client's data. The central challenge is to build systems that are both efficient and provably secure--that is, it should be possible to extract the client's data from any prover that passes a verification check. In this paper, we give the first proof-of-retrievability schemes with full proofs of security against arbitrary adversaries in the strongest model, that of Juels and Kaliski. Our first scheme, built from BLS signatures and secure in the random oracle model, has the shortest query and response of any proof-of-retrievability with public verifiability. Our second scheme, which builds elegantly on pseudorandom functions (PRFs) and is secure in the standard model, has the shortest response of any proof-of-retrievability scheme with private verifiability (but a longer query). Both schemes rely on homomorphic properties to aggregate a proof into one small authenticator value.

/pdf/compact-proofs-of-retrievability-2cuaz82nov.pdf

Compact Proofs of Retrievability

In the problem of private outsourced computation, a client wishes to delegate the evaluation of a function f on a private input x to an untrusted worker without the latter learning anything about x and f(x). This problem occurs in many applications and, most notably, in the setting of cloud computing. In this work, we consider the problem of privately outsourcing computation to a cluster of machines, which typically happens when the computation is to be performed over massive datasets, e.g., to analyze large social networks or train machine learning algorithms on large corpora. At such scales, computation is beyond the capabilities of any single machine so it is performed by large-scale clusters of workers. We address this problem by introducing the notion of parallel homomorphic encryption (PHE) schemes, which are encryption schemes that support computation over encrypted data via evaluation algorithms that can be efficiently executed in parallel. We also consider delegated PHE schemes which, in addition, can hide the function being evaluated. More concretely, we focus on the MapReduce model of parallel computation and show how to construct PHE schemes that can support various MapReduce operations on encrypted datasets including element testing and keyword search. More generally, we construct schemes that can support the evaluation of functions in NC with locality 1 and m = polylog(k) (where k is the security parameter). Underlying our PHE schemes are two new constructions of (local) randomized reductions (Beaver and Feigenbaum, STACS ′90) for univariate and multivariate polynomials. Unlike previous constructions, our reductions are not based on secret sharing and are fully-hiding in the sense that the privacy of the input is guaranteed even if the adversary sees all the client’s queries. Our randomized reduction for univariate polynomials is information-theoretically secure and is based on permutation polynomials, whereas our reduction for multivariate polynomials is computationallysecure under the multi-dimensional noisy curve reconstruction assumption (Ishai, Kushilevitz, Ostrovsky, Sahai, FOCS ’06 ).

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Seny Kamara

Papers

Parallel Homomorphic Encryption.