text: 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.
  @cite_14: This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to public-key cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes : a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA. Our cryptosystems, based on usual modular arithmetics, are provably secure under appropriate assumptions in the standard model.
  @cite_9: We propose a fully homomorphic encryption scheme -- i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result -- that, to construct an encryption scheme that permits evaluation of arbitrary circuits, it suffices to construct an encryption scheme that can evaluate (slightly augmented versions of) its own decryption circuit; we call a scheme that can evaluate its (augmented) decryption circuit bootstrappable. Next, we describe a public key encryption scheme using ideal lattices that is almost bootstrappable. Lattice-based cryptosystems typically have decryption algorithms with low circuit complexity, often dominated by an inner product computation that is in NC1. Also, ideal lattices provide both additive and multiplicative homomorphisms (modulo a public-key ideal in a polynomial ring that is represented as a lattice), as needed to evaluate general circuits. Unfortunately, our initial scheme is not quite bootstrappable -- i.e., the depth that the scheme can correctly evaluate can be logarithmic in the lattice dimension, just like the depth of the decryption circuit, but the latter is greater than the former. In the final step, we show how to modify the scheme to reduce the depth of the decryption circuit, and thereby obtain a bootstrappable encryption scheme, without reducing the depth that the scheme can evaluate. Abstractly, we accomplish this by enabling the encrypter to start the decryption process, leaving less work for the decrypter, much like the server leaves less work for the decrypter in a server-aided cryptosystem.
  @cite_16: We introduce and formalize the notion of Verifiable Computation, which enables a computationally weak client to "outsource" the computation of a function F on various dynamically-chosen inputs x1, ...,xk to one or more workers. The workers return the result of the function evaluation, e.g., yi = F(xi), as well as a proof that the computation of F was carried out correctly on the given value xi. The primary constraint is that the verification of the proof should require substantially less computational effort than computing F(i) from scratch. We present a protocol that allows the worker to return a computationally-sound, non-interactive proof that can be verified in O(mċpoly(λ)) time, where m is the bit-length of the output of F, and λ is a security parameter. The protocol requires a one-time pre-processing stage by the client which takes O(|C|ċpoly(λ)) time, where C is the smallest known Boolean circuit computing F. Unlike previous work in this area, our scheme also provides (at no additional cost) input and output privacy for the client, meaning that the workers do not learn any information about the xi or yi values.
  @cite_10: We present a fully homomorphic encryption scheme that is based solely on the(standard) learning with errors (LWE) assumption. Applying known results on LWE, the security of our scheme is based on the worst-case hardness of short vector problems'' on arbitrary lattices. Our construction improves on previous works in two aspects: We show that somewhat homomorphic'' encryption can be based on LWE, using a new re-linearization technique. In contrast, all previous schemes relied on complexity assumptions related to ideals in various rings. We deviate from the "squashing paradigm'' used in all previous works. We introduce a new dimension-modulus reduction technique, which shortens the cipher texts and reduces the decryption complexity of our scheme, without introducing additional assumptions . Our scheme has very short cipher texts and we therefore use it to construct an asymptotically efficient LWE-based single-server private information retrieval (PIR) protocol. The communication complexity of our protocol (in the public-key model) is @math bits per single-bit query (here, @math is a security parameter).
  @cite_12: 
summary: 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.