Search Results - polynomial multi-point evaluation algorithm complexity

Faster multi-point evaluation over any field by van der Hoeven, Joris, Lecerf, Grégoire

“… For this purpose,we analyze the precomputation costs of recent amortized evaluation algorithms,and then study the complexity of the problem as a function of the number…”
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Amortized multi-point evaluation of multivariate polynomials by van der Hoeven, Joris, Lecerf, Grégoire

“… Several efficient algorithms for this kind of “amortized” multi-point evaluation have been developed recently for the special cases of bivariate polynomials or when the set of evaluation points is generic…”
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On the bit-complexity of sparse polynomial and series multiplication by van der Hoeven, Joris, Lecerf, Grégoire

“…In this paper we present various algorithms for multiplying multivariate polynomials and series…”
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Towards Scalable Threshold Cryptosystems by Tomescu, Alin, Chen, Robert, Zheng, Yiming, Abraham, Ittai, Pinkas, Benny, Gueta, Guy Golan, Devadas, Srinivas

“… First, we use efficient algorithms for evaluating polynomials at multiple points to speed up computing Lagrange coefficients when aggregating threshold signatures…”
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Efficient Multi-Point Local Decoding of Reed-Muller Codes via Interleaved Codex by Cramer, Ronald, Xing, Chaoping, Yuan, Chen

“… This decoding algorithm might be more expensive, i.e., require higher query complexity. In this paper, we focus on Reed-Muller codes with usual parameter regime, namely…”
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Multi-point evaluation in higher dimensions by van der Hoeven, Joris, Schost, Éric

“… ; one particularly important example is the algebra of truncated power series . Similarly to what is known for multi-point evaluation and interpolation in the univariate case, our algorithms have quasi-linear time complexity…”
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New data structure for univariate polynomial approximation and applications to root isolation, numerical multipoint evaluation, and other problems by Moroz, Guillaume

“… i . Its properties allow us to improve the state-of-the-art bounds on the bit complexity for the problems of root isolation and approximate multi-point evaluation…”
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Fast Operations on Linearized Polynomials and their Applications in Coding Theory by Puchinger, Sven, Wachter-Zeh, Antonia

“… \(s\). Also, we propose algorithms with sub-quadratic complexity for the \(q\)-transform, multi-point evaluation, computing minimal subspace polynomials, and interpolation, whose implementations were at least quadratic…”
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Sub-quadratic decoding of Gabidulin codes by Puchinger, Sven, Wachter-Zeh, Antonia

“… The complexity reduction is achieved by accelerating operations on linearized polynomials. In particular, we present fast algorithms for division, multi-point evaluation…”
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Fast In-place Algorithms for Polynomial Operations: Division, Evaluation, Interpolation by Giorgi, Pascal, Grenet, Bruno, Roche, Daniel S

“…We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation…”
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Efficient Multi-Point Local Decoding of Reed-Muller Codes via Interleaved Codex by Cramer, Ronald, Xing, Chaoping, Chen, Yuan

“… This decoding algorithm might be more expensive, i.e., require higher query complexity. In this paper, we focus on Reed-Muller codes with usual parameter regime, namely, the total degree of evaluation polynomials is \(d=\Theta({q})\), where \(q…”
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Sub-Quadratic Decoding of Gabidulin Codes by Puchinger, Sven, Wachter-Zeh, Antonia

“… The complexity reduction is achieved by accelerating operations on linearized polynomials. In particular, we present fast algorithms for division, multi-point evaluation…”
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Dimensionality Reduction, Modelling, and Optimization of Multivariate Problems Based on Machine Learning by Alswaitti, Mohammed, Siddique, Kamran, Jiang, Shulei, Alomoush, Waleed, Alrosan, Ayat

“… However, carrying out multi-point, multi-variable, and multi-objective optimization work is faced…”
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门限密码技术及其标准化进展 by Ji-Wu, JING, Shi-Cong, ZHANG, Ping-Jian, WANG, 荆继武, 张世聪, 王平建

“…信息技术的发展, 加剧了信息终端的多样性和复杂性, 使得单个终端的安全保障变得更加脆弱, 能抵御"单点故障"的门限密码需求就变得更加重要. 本文从门限密码的基础元素和框…”
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Optimal Communication Unbalanced Private Set Union by Dumas, Jean-Guillaume, Galan, Alexis, Grenet, Bruno, Maignan, Aude, Roche, Daniel S

“… Furthermore, the Sender's computational cost, along with the communication complexity, should be smaller when the Sender has a smaller…”
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On the Parallelization of Integer Polynomial Multiplication by Mansouri, Farnam

“…With the advent of hardware accelerator technologies, multi-core processors and GPUs, much effort for taking advantage of those architectures by designing parallel algorithms has been made…”
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