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Lenstra
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#	Item
91 $Integer factorization algorithms / Finite fields / Euclidean algorithm / Continued fraction / Elliptic curve / Quadratic sieve / Lenstra elliptic curve factorization / XTR / Prime number / Mathematics / Abstract algebra / Number theory$	Cryptanalysis of RSA Using the Ratio of the Primes Abderrahmane Nitaj Laboratoire de Math´ematiques Nicolas Oresme Universit´e de Caen, France [removed] Add to Reading List Source URL: www.math.unicaen.fr Language: English - Date: 2009-03-27 17:29:38 Integer factorization algorithms Finite fields Euclidean algorithm Continued fraction Elliptic curve Quadratic sieve Lenstra elliptic curve factorization XTR Prime number Mathematics Abstract algebra Number theory
92	THREE NEW FACTORS OF FERMAT NUMBERS R. P. BRENT, R. E. CRANDALL, K. DILCHER, AND C. VAN HALEWYN Abstract We report the discovery of a new factor for each of the Fermat numbers F13 , F15 , F16 . These new factors have 27, Add to Reading List Source URL: gan.anu.edu.au Language: English - Date: 2003-11-05 11:07:22 Integer sequences Integer factorization algorithms Euclidean plane geometry Fermat number Number theory Pierre de Fermat Lenstra elliptic curve factorization Integer factorization Richard P. Brent Mathematics Abstract algebra Group theory
93	pomerance.qxp[removed]:16 AM Page[removed]A Tale of Two Sieves Carl Pomerance (This paper is dedicated to the memory of my friend and Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2005-03-02 15:21:07 Numbers Quadratic sieve General number field sieve Lenstra elliptic curve factorization Prime number Integer factorization Factorization Sieve of Eratosthenes Factor base Integer factorization algorithms Mathematics Number theory
94	version[removed]Primality testing with Gaussian periods Primality testing with Gaussian periods H. W. Lenstra jr. and Carl Pomerance Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2009-10-01 13:32:09 Primality tests Finite fields Polynomials Integer factorization algorithms Field theory Prime number Root of unity Number theory Miller–Rabin primality test Abstract algebra Mathematics Algebra
95	Mathematical routines for the NIST prime elliptic curves April 05, 2010 Contents Add to Reading List Source URL: www.nsa.gov Language: English - Date: 2010-11-08 09:26:06 Analytic number theory Finite fields Modular forms Elliptic curves Modular arithmetic Prime number Lenstra elliptic curve factorization Hessian form of an elliptic curve Abstract algebra Mathematics Group theory
96	version[removed]Primality testing with Gaussian periods Primality testing with Gaussian periods H. W. Lenstra jr. and Carl Pomerance Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2009-02-25 13:32:39 Primality tests Finite fields Polynomials Integer factorization algorithms Field theory Prime number Root of unity Miller–Rabin primality test Elliptic curve primality testing Abstract algebra Mathematics Algebra
97	A HYPERELLIPTIC SMOOTHNESS TEST, II H. W. LENSTRA Jr, J. PILA and CARL POMERANCE [Received 28 June[removed]Contents 1. Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2005-03-02 15:21:08 Algebraic curves Polynomials Analytic number theory Algebraic surfaces Elliptic curve Abelian variety Lenstra elliptic curve factorization Field Intersection number Abstract algebra Algebra Niels Henrik Abel
98	Extended gcd and Hermite normal form algorithms via lattice basis reduction George Havas School of Information Technology The University of Queensland Queensland 4072, Australia Add to Reading List Source URL: www.numbertheory.org Language: English - Date: 2002-01-22 06:23:32 Algebra Abstract algebra Lie groups Euclidean algorithm Lenstra–Lenstra–Lovász lattice basis reduction algorithm Lattice reduction Lattice Hungarian algorithm Mathematics Computational number theory Lattice points
99	SIAM J. COMPUT. (C[removed]Society for Industrial and Applied Mathematics Vol. 17, No. 2, April 1988 Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2010-11-16 13:52:48 Cryptography Quadratic sieve Quadratic residue Prime number Lenstra elliptic curve factorization Factorization Integer factorization Primality certificate Euclidean algorithm Integer factorization algorithms Mathematics Number theory
100	ROOT NUMBERS AND RANKS IN POSITIVE CHARACTERISTIC B. CONRAD, K. CONRAD, AND H. HELFGOTT Abstract. For a global field K and an elliptic curve Eη over K(T ), Silverman’s specialization theorem implies rank(Eη (K(T ))) Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2005-10-02 23:07:54 Group theory Diophantine geometry Algebraic curves Abelian variety Birch and Swinnerton-Dyer conjecture Supersingular elliptic curve Finite field Separable extension Lenstra elliptic curve factorization Abstract algebra Elliptic curves Number theory

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