Abstract. In this paper, we present an improvement of the Nguyen-Vidick heuristic sieve algorithm for shortest vector problem in general lattices, which time complexity is 2 0.3836n polynomial computations, and space complexity is 2 0.2557n . In the new algorithm, we introduce a new sieve technique with two-level instead of the previous one-level sieve, and complete the complexity estimation by calculating the irregular spherical cap covering.
With the recent growth and commercialization of cloud computing, outsourcing computation has become one of the most important cloud services, which allows the resource-constrained clients to efficiently perform large-scale computation in a pay-per-use manner. Meanwhile, outsourcing large scale computing problems and computationally intensive applications to the cloud has become prevalent in the science and engineering computing community. As important fundamental operations, large-scale matrix multiplication computation (MMC), matrix inversion computation (MIC), and matrix determinant computation (MDC) have been frequently used. In this paper, we present three new algorithms to enable secure, verifiable, and efficient outsourcing of MMC, MIC, and MDC operations to a cloud that may be potentially malicious. The main idea behind our algorithms is a novel matrix encryption/decryption method utilizing consecutive and sparse unimodular matrix transformations. Compared to previous works, this versatile technique can be applied to many matrix operations while achieving a good balance between security and efficiency. First, the proposed algorithms provide robust confidentiality by concealing the local information of the entries in the input matrices. Besides, they also protect the statistic information of the original matrix. Moreover, these algorithms are highly efficient. Our theoretical analysis indicates that the proposed algorithms reduce the time overhead on the client side from O(n 2.3728639 ) to O(n 2 ). Finally, the extensive experimental evaluations demonstrate the practical efficiency and effectiveness of our algorithms.INDEX TERMS Cloud computing, outsourcing computation, matrix operations, privacy, efficiency.
Mobile ad hoc networks (MANETs) are originally designed for a cooperative environment, which are vulnerable to a wide variety of attacks due to their intrinsic characteristics. Trust can be introduced to address this security issue at some level. In this paper, we focus on the concept of trust and abstract a decentralized trust inference model, where the trust an entity has for a neighbor forms the basic building block of this model. Basing on the interest entity's historical behaviors, multi-dimensional trust attributes are incorporated to reflect trust relationship's complexity in various angles. The weight vector of attributes is calculated by fuzzy AHP scheme based on entropy weight measure. The trust inference framework provides the considerable security with an additional small overhead, which can be incorporated into any routing protocol. In this paper, the standard Ad hoc On-demand Multi-path Distance Vector protocol (AOMDV) is extended as the base routing protocol to evaluate this model. The proposed lightweight trust-enhanced routing protocol (TeAOMDV) can provide a feasible approach to choose an optimal two-way trusted route without containing the untrustworthy entities instead of the shortest route, thus mitigate the impairment effects from such entities. It is lightweight in the sense that the trust framework uses only passive and local monitoring information to evaluate the behaviors of an interest entity which is translated to an estimate of the trust, consumes limited computational resource. Moreover, the new proposed data-driven route maintenance mechanism reduces routing overhead and route discovery frequency. The simulations show that the proposed routing scheme behaves better in attack resistance (i.e., grey-hole attack and black-hole attack), and makes an improvement on the packets delivery ratio, routing packets overhead, route discovery frequency and malicious node detection. Finally, as an extension of the trust model, by utilizing the trust assessment data sequence, we propose an improved SCGM(1,1)-Markov chain prediction method based on the system cloud grey model and Markov stochastic chain theory to forecast entity's trust level for future decision making.
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