A practical and secure multi-keyword search method over encrypted cloud data

Cloud computing technologies become more and more popular every year, as many organizations tend to outsource their data utilizing robust and fast services of clouds while lowering the cost of hardware ownership. Although its benefits are welcomed, privacy is still a remaining concern that needs to be addressed. We propose an efficient privacy-preserving search method over encrypted cloud data that utilizes minhash functions. Most of the work in literature can only support a single feature search in queries which reduces the effectiveness. One of the main advantages of our proposed method is the capability of multi-keyword search in a single query. The proposed method is proved to satisfy adaptive semantic security definition. We also combine an effective ranking capability that is based on term frequency-inverse document frequency (tf-idf) values of keyword document pairs. Our analysis demonstrates that the proposed scheme is proved to be privacy-preserving, efficient and effective

Sketching and streaming algorithms for processing massive data

The rate at which electronic information is generated in the world is exploding. In this article we explore techniques known as sketching and streaming for processing massive data both quickly and memory-efficiently.Engineering and Applied Science

Hardness Amplification of Optimization Problems

In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products. We say that an optimization problem ? is direct product feasible if it is possible to efficiently aggregate any k instances of ? and form one large instance of ? such that given an optimal feasible solution to the larger instance, we can efficiently find optimal feasible solutions to all the k smaller instances. Given a direct product feasible optimization problem ?, our hardness amplification theorem may be informally stated as follows: If there is a distribution D over instances of ? of size n such that every randomized algorithm running in time t(n) fails to solve ? on 1/?(n) fraction of inputs sampled from D, then, assuming some relationships on ?(n) and t(n), there is a distribution D\u27 over instances of ? of size O(n??(n)) such that every randomized algorithm running in time t(n)/poly(?(n)) fails to solve ? on 99/100 fraction of inputs sampled from D\u27. As a consequence of the above theorem, we show hardness amplification of problems in various classes such as NP-hard problems like Max-Clique, Knapsack, and Max-SAT, problems in P such as Longest Common Subsequence, Edit Distance, Matrix Multiplication, and even problems in TFNP such as Factoring and computing Nash equilibrium

Many Hard Examples in Exact Phase Transitions with Application to Generating Hard Satisfiable Instances

This paper first analyzes the resolution complexity of two random CSP models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, it is proved that almost all instances of Model RB/RD have no tree-like resolution proofs of less than exponential size. Thus, we not only introduce new families of CNF formulas hard for resolution, which is a central task of Proof-Complexity theory, but also propose models with both many hard instances and exact phase transitions. Then, the implications of such models are addressed. It is shown both theoretically and experimentally that an application of Model RB/RD might be in the generation of hard satisfiable instances, which is not only of practical importance but also related to some open problems in cryptography such as generating one-way functions. Subsequently, a further theoretical support for the generation method is shown by establishing exponential lower bounds on the complexity of solving random satisfiable and forced satisfiable instances of RB/RD near the threshold. Finally, conclusions are presented, as well as a detailed comparison of Model RB/RD with the Hamiltonian cycle problem and random 3-SAT, which, respectively, exhibit three different kinds of phase transition behavior in NP-complete problems.Comment: 19 pages, corrected mistakes in Theorems 5 and

Approximate Degree, Secret Sharing, and Concentration Phenomena

The epsilon-approximate degree deg~_epsilon(f) of a Boolean function f is the least degree of a real-valued polynomial that approximates f pointwise to within epsilon. A sound and complete certificate for approximate degree being at least k is a pair of probability distributions, also known as a dual polynomial, that are perfectly k-wise indistinguishable, but are distinguishable by f with advantage 1 - epsilon. Our contributions are: - We give a simple, explicit new construction of a dual polynomial for the AND function on n bits, certifying that its epsilon-approximate degree is Omega (sqrt{n log 1/epsilon}). This construction is the first to extend to the notion of weighted degree, and yields the first explicit certificate that the 1/3-approximate degree of any (possibly unbalanced) read-once DNF is Omega(sqrt{n}). It draws a novel connection between the approximate degree of AND and anti-concentration of the Binomial distribution. - We show that any pair of symmetric distributions on n-bit strings that are perfectly k-wise indistinguishable are also statistically K-wise indistinguishable with at most K^{3/2} * exp (-Omega (k^2/K)) error for all k < K <= n/64. This bound is essentially tight, and implies that any symmetric function f is a reconstruction function with constant advantage for a ramp secret sharing scheme that is secure against size-K coalitions with statistical error K^{3/2} * exp (-Omega (deg~_{1/3}(f)^2/K)) for all values of K up to n/64 simultaneously. Previous secret sharing schemes required that K be determined in advance, and only worked for f=AND. Our analysis draws another new connection between approximate degree and concentration phenomena. As a corollary of this result, we show that for any d deg~_{1/3}(f). These upper and lower bounds were also previously only known in the case f=AND