With the development of sensor network, mobile computing, and web applications, data are now collected from many distributed sources to form big datasets. Such datasets can be hosted in the cloud to achieve economical processing. However, these data might be highly sensitive requiring secure storage and processing. We envision a cloud-based data storage and processing framework that enables users to economically and securely share and handle big datasets. Under this framework, we study the matrix-based data mining algorithms with a focus on the secure top-k eigenvector algorithm. Our approach uses an iterative processing model in which the authorized user interacts with the cloud to achieve the result. In this process, both the source matrix and the intermediate results keep confidential and the client-side incurs low costs. The security of this approach is guaranteed by using Paillier Encryption and a random perturbation technique. We carefully analyze its security under a cloud-specific threat model. Our experimental results show that the proposed method is scalable to big matrices while requiring low client-side costs.
A framework for securely outsourcing general computations is given in @cite_16 . However, this framework is based on Gentry's fully homomorphic encryption scheme @cite_9 rendering it impractical due to the high computational costs and ciphertext sizes. A simple test with the Scarab FHE library (hcrypt.com scarab-library) yielded ciphertext sizes more than ten times those generated using Paillier @cite_14 . Very recent work by @cite_12 propose a secure outsourcing solution for problems which only require the encryption scheme to be somewhat'' homomorphic (SHE). They use the SHE scheme of @cite_10 which provides reasonably efficient computational performance but still suffers from large ciphertexts.
@cite_14 @cite_9 @cite_16 @cite_10 @cite_12
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We present a novel approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), without Gentry's bootstrapping procedure. Specifically, we offer a choice of FHE schemes based on the learning with error (LWE) or ring-LWE (RLWE) problems that have 2λ security against known attacks. For RLWE, we have: • A leveled FHE scheme that can evaluate L-level arithmetic circuits with O(λ · L3) per-gate computation -- i.e., computation quasi-linear in the security parameter. Security is based on RLWE for an approximation factor exponential in L. This construction does not use the bootstrapping procedure. • A leveled FHE scheme that uses bootstrapping as an optimization, where the per-gate computation (which includes the bootstrapping procedure) is O(λ2), independent of L. Security is based on the hardness of RLWE for quasi-polynomial factors (as opposed to the sub-exponential factors needed in previous schemes). We obtain similar results to the above for LWE, but with worse performance. Based on the Ring LWE assumption, we introduce a number of further optimizations to our schemes. As an example, for circuits of large width -- e.g., where a constant fraction of levels have width at least λ -- we can reduce the per-gate computation of the bootstrapped version to O(λ), independent of L, by batching the bootstrapping operation. Previous FHE schemes all required Ω(λ3.5) computation per gate. At the core of our construction is a much more effective approach for managing the noise level of lattice-based ciphertexts as homomorphic operations are performed, using some new techniques recently introduced by Brakerski and Vaikuntanathan (FOCS 2011). Cloud computing has emerged as one of the most influential paradigms in the IT industry in recent years. Since this new computing technology requires users to entrust their valuable data to cloud providers, there have been increasing security and privacy concerns on outsourced data. Several schemes employing attribute-based encryption (ABE) have been proposed for access control of outsourced data in cloud computing; however, most of them suffer from inflexibility in implementing complex access control policies. In order to realize scalable, flexible, and fine-grained access control of outsourced data in cloud computing, in this paper, we propose hierarchical attribute-set-based encryption (HASBE) by extending ciphertext-policy attribute-set-based encryption (ASBE) with a hierarchical structure of users. The proposed scheme not only achieves scalability due to its hierarchical structure, but also inherits flexibility and fine-grained access control in supporting compound attributes of ASBE. In addition, HASBE employs multiple value assignments for access expiration time to deal with user revocation more efficiently than existing schemes. We formally prove the security of HASBE based on security of the ciphertext-policy attribute-based encryption (CP-ABE) scheme by Bethencourt and analyze its performance and computational complexity. We implement our scheme and show that it is both efficient and flexible in dealing with access control for outsourced data in cloud computing with comprehensive experiments. We propose the first fully homomorphic encryption scheme, solving an old open problem. Such a scheme allows one to compute arbitrary functions over encrypted data without the decryption key—i.e., given encryptions E(m1), ..., E( mt) of m1, ..., m t, one can efficiently compute a compact ciphertext that encrypts f(m1, ..., m t) for any efficiently computable function f. Fully homomorphic encryption has numerous applications. For example, it enables encrypted search engine queries—i.e., a search engine can give you a succinct encrypted answer to your (boolean) query without even knowing what your query was. It also enables searching on encrypted data; you can store your encrypted data on a remote server, and later have the server retrieve only files that (when decrypted) satisfy some boolean constraint, even though the server cannot decrypt the files on its own. More broadly, it improves the efficiency of secure multiparty computation. In our solution, we begin by designing a somewhat homomorphic "boostrappable" encryption scheme that works when the function f is the scheme's own decryption function. We then show how, through recursive self-embedding, bootstrappable encryption gives fully homomorphic encryption. Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic encryption, which is the encryption of quantum information such that quantum computations can be performed given the ciphertext only. Our schemes allow for arbitrary Clifford group gates, but become inefficient for circuits with large complexity, measured in terms of the non-Clifford portion of the circuit (we use the “ ( 8 )” non-Clifford group gate, also known as the ( T )-gate).