Abstract. The complexity of the Shortest Vector Problem (SVP) in lattices is directly related to the security of NTRU and the provable level of security of many recently proposed lattice-based cryptosystems. We integrate several recent algorithmic improvements for solving SVP and take first place at dimension 120 in the SVP Challenge Hall of Fame. Our implementation allows us to find a short vector at dimension 114 using 8 NVIDIA video cards in less than two days.Specifically, our improvements to the recent Extreme Pruning in enumeration approach, proposed by Gama et al. in Eurocrypt 2010, include: (1) a more flexible bounding function in polynomial form; (2) code to take advantage of Clouds of commodity PCs (via the MapReduce framework); and (3) the use of NVIDIA's Graphics Processing Units (GPUs). We may now reasonably estimate the cost of a wide range of SVP instances in U.S. dollars, as rent paid to cloud-computing service providers, which is arguably a simpler and more practical measure of complexity.
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This paper presented a heterodyne speckle interferometer (HSI) for the measurement of two-dimensional in-plane displacement. A diffraction grating is used to split the light source into four beams, which are then reflected into a non-mirror measurement surface at symmetrical incident angles, before being scattered to form an interference pattern. In accordance with the Doppler Effect, in-plane displacement of the surface causes phase variations in speckle interference patterns, from which displacement information can be obtained. Several experiments were performed to evaluate the feasibility of the proposed HSI. Experiment results demonstrate that the proposed system is capable of accurately measuring in-plane displacement with a resolution of approximately 1.5 nm.
The Byzantine general problem is the core problem that consensus algorithms are trying to solve, which is at the heart of the design of blockchains. As a result, we have seen numerous proposals of consensus algorithms in recent years, trying to improve the level of decentralization, performance, and security of blockchains. In our opinion, there are two most challenging issues when we consider the design of such algorithms in the context of powering blockchains in practice. First, the outcome of a consensus algorithm usually depends on the underlying incentive model, so each participant should have an equal probability of receiving rewards for its work. Secondly, the protocol should be able to resist network failures, such as cloud services shutdown, while maintaining high performance otherwise. We address these two critical issues in this paper. First, we propose a new metric, called fair validity, for measuring the performance of Byzantine agreements. Intuitively, fair validity provides a lower bound for the probability of acceptances of honest nodes' proposals. This is a strong notion of fairness, and we argue that it is crucial for the success of a blockchain in practice. We then show that any Byzantine agreement could not achieve fair validity in an asynchronous network, so we will focus on synchronous protocols. This leads to our second contribution: we propose a fair, responsive, and partition-resilient Byzantine agreement protocol able to tolerate up to 1/3 corruptions. As we will show in the paper, our protocol achieves fair validity and is responsive in the sense that the termination time only depends on actual network delay, as opposed to arbitrary, predetermined time-bound. Furthermore, our proposal is partition-resilient. Last but not least, experimental results show that our Byzantine agreement protocol outperforms a wide variety of state-of-art synchronous protocols, combining the best from both theoretic and practical worlds.
In ISSAC 2017, van der Hoeven and Larrieu showed that evaluating a polynomial P ∈ F q [x] of degree < n at all n-th roots of unity in F q d can essentially be computed d-time faster than evaluating Q ∈ F q d [x] at all these roots, assuming F q d contains a primitive n-th root of unity [vdHL17a]. Termed the Frobenius FFT, this discovery has a profound impact on polynomial multiplication, especially for multiplying binary polynomials, which finds ample application in coding theory and cryptography. In this paper, we show that the theory of Frobenius FFT beautifully generalizes to a class of additive FFT developed by Cantor and Gao-Mateer [Can89, GM10]. Furthermore, we demonstrate the power of Frobenius additive FFT for q = 2: to multiply two binary polynomials whose product is of degree < 256, the new technique requires only 29,005 bit operations, while the best result previously reported was 33,397. To the best of our knowledge, this is the first time that FFT-based multiplication outperforms Karatsuba and the like at such a low degree in terms of bit-operation count. CCS CONCEPTS• Mathematics of computing → Computations in finite fields; KEYWORDS addtitive FFT, Frobenius FFT, polynomial multiplication
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Clustering is an useful tool in the data analysis to discover the natural structure in the data. The technique separates given smart meter data set into several representative clusters for the convenience of energy management. Each cluster may has its own attributes, such as energy usage time and magnitude. These attributes can help the electrical operators to manage their electrical grids with goals of energy and cost reduction. In this paper, we use principle component analysis and K-means as dimensional reduction and the reference clustering algorithm, respectively, and several choices must be considered: the number of cluster, the number of the leading principle components, and whether use normalized principle analysis schema or not. To answer these issues simultaneously, we use the stability scores as measured by dot similarity and confusion matrix as our evaluation decision. The advantage is that it is useful for comparing the performance under different decisions, and thus provides us to make these choices simultaneously.
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