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Lenstra
Results: 153

#	Item
51	Elliptic Curves in Algorithmic Number Theory and Cryptography Otto Forster §1 Applications in Algorithmic Number Theory In this section we describe briefly the use of elliptic curves over finite fields for Add to Reading List Source URL: www.mathematik.uni-muenchen.de Language: English - Date: 2003-12-07 11:29:32 Finite fields Group theory Elliptic curves Cryptography Polynomials Elliptic curve Lenstra elliptic curve factorization Division polynomials Prime number Abstract algebra Mathematics Algebra
52	Abstract Fix an integer m > 2 and let K be a number field containing the mth roots of unity with ring of integers R. Suppose that a is an element of K with a = c/d for c, d ∈ R, and that b is an ideal of R relatively Add to Reading List Source URL: douglassquirrel.com Language: English - Date: 2013-08-17 18:16:01 Lattice points Algebraic number theory Analytic geometry Lattice Lenstra–Lenstra–Lovász lattice basis reduction algorithm Algebraic number field Field extension Vector space Ideal lattice cryptography Algebra Abstract algebra Mathematics
53	THE ELLIPTIC CURVE METHOD PAUL ZIMMERMANN The Elliptic Curve Method (ECM for short) was invented in 1985 by H. W. Lenstra, Jr[removed]It is suited to find small — say 9 to 30 digits — prime factors of large numbers. Am Add to Reading List Source URL: www.loria.fr Language: English - Date: 2004-09-06 05:03:02 Cryptography Lenstra elliptic curve factorization Quadratic sieve Integer factorization Elliptic curve Primality test Prime number Prime factor Algebraic-group factorisation algorithm Integer factorization algorithms Abstract algebra Mathematics
54	Fast arithmetic and pairing evaluation on genus 2 curves David Freeman University of California, Berkeley [removed] November 6, 2005 Add to Reading List Source URL: theory.stanford.edu Language: English - Date: 2008-06-06 19:27:47 Group theory Polynomial Euclidean algorithm Finite fields Elliptic curves Integer factorization algorithms Lenstra elliptic curve factorization Factorization of polynomials over a finite field and irreducibility tests Abstract algebra Mathematics Algebra
55	International Mathematical Olympiad Preliminary Selection Contest 2007 — Hong Kong Outline of Solutions Answers: Add to Reading List Source URL: www.mathdb.org Language: English - Date: 2007-10-04 22:57:03 Coding theory Algebra Lenstra elliptic curve factorization SYmbolic LinK Finite fields Mathematics Integer factorization algorithms
56	Reverse Engineering of Strong CryptoSignatures Schemes Add to Reading List Source URL: www.reteam.org Language: English - Date: 2009-05-17 13:10:56 Elliptic curve Lenstra elliptic curve factorization Discrete logarithm XTR Elliptic Curve DSA Prime number Cyclic group Hyperelliptic curve cryptography Hessian form of an elliptic curve Abstract algebra Finite fields Elliptic curve cryptography
57	SOLILOQUY: A CAUTIONARY TALE Peter Campbell, Michael Groves and Dan Shepherd CESG, Cheltenham, UK 1. Introduction The Soliloquy primitive, first proposed by the third author in 2007, is Add to Reading List Source URL: docbox.etsi.org Language: English - Date: 2014-10-13 10:57:18 Theoretical computer science Cryptography Lattice points Quantum information science Analytic geometry Lattice Quantum algorithm Quantum computer Lenstra–Lenstra–Lovász lattice basis reduction algorithm Mathematics Applied mathematics Abstract algebra
58	Selected Applications of LLL in Number Theory Denis SIMON Abstract In this survey, I describe some applications of LLL in number theory. I show in particular how it can be used to solve many different linear problems, to Add to Reading List Source URL: www.math.unicaen.fr Language: English - Date: 2014-01-09 12:01:30 Polynomials Linear algebra Quadratic forms Elementary algebra Equations Factorization of polynomials Lenstra–Lenstra–Lovász lattice basis reduction algorithm Quadratic equation Algebraic number field Algebra Mathematics Abstract algebra
59	Lattice Reduction: a Toolbox for the Cryptanalyst Antoine Joux Jacques Stern Add to Reading List Source URL: www1.lip6.fr Language: English - Date: 2015-01-20 15:22:52 Linear algebra Computational number theory Cryptography Lattice reduction Lenstra–Lenstra–Lovász lattice basis reduction algorithm Lattice problem Lattice Integer relation algorithm Vector space Mathematics Algebra Lattice points
60	Journal de Th´eorie des Nombres de Bordeaux 00 (XXXX), 000–000 Solving conics over function fields par Mark van HOEIJ et John CREMONA ´sume Add to Reading List Source URL: homepages.warwick.ac.uk Language: English - Date: 2006-07-31 04:25:06 Algebraic curves Modular arithmetic Analytic geometry Birational geometry Conic section Chinese remainder theorem Lenstra elliptic curve factorization Euclidean algorithm Abstract algebra Mathematics Geometry

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