Private Outsourcing of Polynomial Evaluation and Matrix Multiplication using Multilinear Maps

{\em Verifiable computation} (VC) allows a computationally weak client to outsource the evaluation of a function on many inputs to a powerful but untrusted server. The client invests a large amount of off-line computation and gives an encoding of its function to the server. The server returns both an evaluation of the function on the client's input and a proof such that the client can verify the evaluation using substantially less effort than doing the evaluation on its own. We consider how to privately outsource computations using {\em privacy preserving} VC schemes whose executions reveal no information on the client's input or function to the server. We construct VC schemes with {\em input privacy} for univariate polynomial evaluation and matrix multiplication and then extend them such that the {\em function privacy} is also achieved. Our tool is the recently developed {mutilinear maps}. The proposed VC schemes can be used in outsourcing {private information retrieval (PIR)}.Comment: 23 pages, A preliminary version appears in the 12th International Conference on Cryptology and Network Security (CANS 2013

Extended Functionality in Verifiable Searchable Encryption

Abstract. When outsourcing the storage of sensitive data to an (un-trusted) remote server, a data owner may choose to encrypt the data beforehand to preserve confidentiality. However, it is then difficult to efficiently retrieve specific portions of the data as the server is unable to identify the relevant information. Searchable encryption has been well studied as a solution to this problem, allowing data owners and other au-thorised users to generate search queries which the server may execute over the encrypted data to identify relevant data portions. However, many current schemes lack two important properties: verifia-bility of search results, and expressive queries. We introduce Extended Verifiable Searchable Encryption (eVSE) that permits a user to verify that search results are correct and complete. We also permit verifiabl

Smarter Data Availability Checks in the Cloud: Proof of Storage via Blockchain

Cloud computing offers clients flexible and cost-effective resources. Nevertheless, past incidents indicate that the cloud may misbehave by exposing or tampering with clients' data. Therefore, it is vital for clients to protect the confidentiality and integrity of their outsourced data. To address these issues, researchers proposed cryptographic protocols called “proof of storage” that let a client efficiently verify the integrity or availability of its data stored in a remote cloud server. However, in these schemes, the client either has to be online to perform the verification itself or has to delegate the verification to a fully trusted auditor. In this chapter, a new scheme is proposed that lets the client distribute its data replicas among multiple cloud servers to achieve high availability without the need for the client to be online for the verification and without a trusted auditor's involvement. The new scheme is mainly based on blockchain smart contracts. It illustrates how a combination of cloud computing and blockchain technology can resolve real-world problems

Multi-instance publicly verifiable time-lock puzzle and its applications

Time-lock puzzles are elegant protocols that enable a party to lock a message such that no one else can unlock it until a certain time elapses. Nevertheless, existing schemes are not suitable for the case where a server is given multiple instances of a puzzle scheme at once and it must unlock them at different points in time. If the schemes are naively used in this setting, then the server has to start solving all puzzles as soon as it receives them, that ultimately imposes significant computation cost and demands a high level of parallelisation. We put forth and formally define a primitive called “multi-instance time-lock puzzle” which allows composing a puzzle’s instances. We propose a candidate construction: “chained time-lock puzzle” (C-TLP). It allows the server, given instances’ composition, to solve puzzles sequentially, without having to run parallel computations on them. C-TLP makes black-box use of a standard time-lock puzzle scheme and is accompanied by a lightweight publicly verifiable algorithm. It is the first time-lock puzzle that offers a combination of the above features. We use C-TLP to build the first “outsourced proofs of retrievability” that can support real-time detection and fair payment while having lower overhead than the state of the art. As another application of C-TLP, we illustrate in certain cases, one can substitute a “verifiabledelay function” with C-TLP, to gain much better efficiency

VD-PSI : verifiable delegated private set intersection on outsourced private datasets

Private set intersection (PSI) protocols have many real world applications. With the emergence of cloud computing the need arises for PSI protocols on outsourced datasets where the computation is delegated to the cloud. However, due to the possibility of cloud misbehaviors, it is essential to verify the correctness of any delegated computation, and the integrity of any outsourced datasets. Verifiable Computation on private datasets that does not leak any information about the data is very challenging, especially when the datasets are outsourced independently by different clients. In this paper we present VD-PSI, a protocol that allows multiple clients to outsource their private datasets and delegate computation of set intersection to the cloud, while being able to verify the correctness of the result. Clients can independently prepare and upload their datasets, and with their agreement can verifiably delegate the computation of set intersection an unlimited number of times, without the need to download or maintain a local copy of their data. The protocol ensures that the cloud learns nothing about the datasets and the intersection. VD-PSI is efficient as its verification cost is linear to the intersection cardinality, and its computation and communication costs are linear to the dataset cardinality. Also, we provide a formal security analysis in the standard model