Results 111 to 120 of about 142,409 (160)
On the fundamental subdirect factorization theorems of primal algebra theory
Mathematische Zeitschrift, 1969 openaire +2 more sources
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Clever Factorization Algorithms and Primality Testing
, 2018The main theoretical way of attacking RSA, at least when it is used with best practices, is by factoring the modulus. The most obvious way of factoring a number n is to try dividing by 2, 3, 5, 7, and so on, through all the primes less than \(\sqrt{n}\), until we find a factor.
Simon Rubinstein-Salzedo
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Applications: Algorithms, Primality and Factorization, Codes
, 2011This chapter describes some industrial applications of number theory, via computer science. We succinctly describe the main algorithms as well as their theoretical complexity or computation time. We use the notation O(f(n)) to denote a function ≤Cf(n); furthermore, the unimportant—at least from a theoretical point of view—constants which appear will be
M. Hindry
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Factorization and Primality Testing
Mathematics of Computation, 1991B. Burn, D. Bressoud
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arXiv.org
This paper presents a novel primality test based on the eigenvalue structure of circulant matrices constructed from roots of unity. We prove that an integer $n>2$ is prime if and only if the minimal polynomial of the circulant matrix $C_n = W_n + W_n^2 ...
Marius-Constantin Dinu
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This paper presents a novel primality test based on the eigenvalue structure of circulant matrices constructed from roots of unity. We prove that an integer $n>2$ is prime if and only if the minimal polynomial of the circulant matrix $C_n = W_n + W_n^2 ...
Marius-Constantin Dinu
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Feasibility of Primality in Bounded Arithmetic
arXiv.orgWe prove the correctness of the AKS algorithm \cite{AKS} within the bounded arithmetic theory $T^{count}_2$ or, equivalently, the first-order consequences of the theory $VTC^0$ expanded by the smash function, which we denote by $VTC^0_2$.
Raheleh Jalali, Ondrej Jezil
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Parsimonious kernel extreme learning machine in primal via Cholesky factorization
Neural Networks, 2016Recently, extreme learning machine (ELM) has become a popular topic in machine learning community. By replacing the so-called ELM feature mappings with the nonlinear mappings induced by kernel functions, two kernel ELMs, i.e., P-KELM and D-KELM, are obtained from primal and dual perspectives, respectively.
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Sparse LSSVM in Primal Using Cholesky Factorization for Large-Scale Problems
IEEE Transactions on Neural Networks and Learning Systems, 2016For support vector machine (SVM) learning, least squares SVM (LSSVM), derived by duality LSSVM (D-LSSVM), is a widely used model, because it has an explicit solution. One obvious limitation of the model is that the solution lacks sparseness, which limits it from training large-scale problems efficiently.
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Primality tests and factorization algorithms. I
2001Schöne Übersichtsarbeit über Primzahltests; im vorliegenden Teil werden die theoretisch aufwendigeren Tests nach Adleman-Rumely-Pomerance-Cohen-Lenstra und Goldwasser-Kilian ausgespart. Für neueste Entwicklungen auf diesem Gebiet, vgl. ein Preprint von Agrawal, Kayal, Saxena (``PRIMES is in \(P\)''), wo ein deterministischer Polynomzeit-Algorithmus ...
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