Data outsourcing allows data owners to keep their data at untrusted clouds that do not ensure the privacy of data and/or computations. One useful framework for fault-tolerant data processing in a distributed fashion is MapReduce, which was developed for trusted private clouds. This paper presents algorithms for data outsourcing based on Shamir's secret-sharing scheme and for executing privacy-preserving SQL queries such as count, selection including range selection, projection, and join while using MapReduce as an underlying programming model. Our proposed algorithms prevent an adversary from knowing the database or the query while also preventing output-size and access-pattern attacks. Interestingly, our algorithms do not involve the database owner, which only creates and distributes secret-shares once, in answering any query, and hence, the database owner also cannot learn the query. Logically and experimentally, we evaluate the efficiency of the algorithms on the following parameters: (i) the number of communication rounds (between a user and a server), (ii) the total amount of bit flow (between a user and a server), and (iii) the computational load at the user and the server.

In this paper, we propose a new type of non-recursive Mastrovito multiplier for $\text {GF}(2^{m})$ using an $n$ -term Karatsuba algorithm (KA), where $\text {GF}(2^{m})$ is defined by an irreducible trinomial, $x^{m}+x^{k}+1, m=nk$ . We show that such a type of trinomial combined with the $n$ -term KA can fully exploit the spatial correlation of entries in related Mastrovito product matrices and lead to a low-complexity architecture. The optimal parameter $n$ is further studied. As the main contribution of this paper, the lower bound of the space complexity of our proposal is about $O({m^{2}}/{2})+m^{3/2})$ . Meanwhile, the time complexity matches the best Karatsuba multiplier known to date. To the best of our knowledge, it is the first time that Karatsuba-based multiplier has reached such a space complexity bound while maintaining a relatively low time delay.

We continue the study of Mastrovito form of Karatsuba (MK) multipliers under the shifted polynomial basis (SPB). An MK multiplier utilizes Karatsuba algorithm and Mastrovito approach to optimize polynomial multiplication and modular reduction, which lead to a better space and time tradeoff for all trinomials. Based on this work, we make two types of contributions: 1) We derive a new modular reduction formulation for constructing Mastrovito matrix associated with special types of pentanomials, i.e., Types I, II, and Type C.1 pentanomial. Through related formulations, we demonstrate that Type I pentanomial is less efficient than Type II because of a more complicated modular reduction under the same SPB; conversely, Type C.1 pentanomial is as good as Type II under generalized polynomial basis (GPB). 2) We introduce a new MK multiplier for Type II pentanomial. It is shown that our proposal is only one TX slower than the fastest quadratic multipliers for Type II pentanomial, but its space complexity is roughly 3/4 of those schemes. To the best of our knowledge, it is the first time for hybrid multiplier to achieve such a time delay bound.

Searchable public key encryption scheme is a key technique for protecting data confidentiality in today’s cloud environment. Specifically, public key encryption with conjunctive and disjunctive keyword search (PECDK) can provide flexible search options without sacrificing keywords security and thus attracts a lot of attention nowadays. However, the most effective PECDK scheme is based on the inner product encryption (IPE), which needs more time and space cost. In this paper, by utilizing the bilinear pairing with a prime order group, we propose an efficient PECDK scheme needing less time and storage consumption. The proposed scheme is proven to be secure under a rigorous security definition. The theoretical analysis and experimental results demonstrate that our proposed scheme can significantly improve the time and space efficiency over the state-of-the-art scheme.

In the post-Cloud era, the proliferation of Internet of Things (IoT) has pushed the horizon of Edge computing, which is a new computing paradigm with data processed at the edge of the network. As the important systems of Edge computing, wireless sensor and actuator networks (WSANs) play an important role in collecting and processing the sensing data from the surrounding environment as well as taking actions on the events happening in the environment. In WSANs, in-network data storage and information discovery schemes with high energy efficiency, high load balance and low latency are needed because of the limited resources of the sensor nodes and the real-time requirement of some specific applications, such as putting out a big fire in a forest. In this article, the existing schemes of WSANs on data storage and information discovery are surveyed with detailed analysis on their advancements and shortcomings, and possible solutions are proposed on how to achieve high efficiency, good load balance, and perfect real-time performances at the same time, hoping that it can provide a good reference for the future research of the WSANs-based Edge computing systems.