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Lenstra elliptic-curve factorization
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#	Item
31	Elligator Squared Uniform Points on Elliptic Curves of Prime Order as Uniform Random Strings Mehdi Tibouchi NTT Secure Platform Laboratories [removed] Add to Reading List Source URL: fc14.ifca.ai Language: English - Date: 2014-02-15 11:16:53 Finite fields Group theory Elliptic curves Analytic number theory Curve Elliptic Curve DSA Ellipse Lenstra elliptic curve factorization Homomorphic signatures for network coding Abstract algebra Geometry Mathematics
32	R. van Bommel Almost all hyperelliptic Jacobians have a bad semi-abelian prime Master’s thesis, 23 June 2014 Supervisor: dr. D. Holmes Add to Reading List Source URL: www.algant.eu Language: English - Date: 2014-07-04 05:58:52 Elliptic curves Abelian varieties Algebraic curves Number theory Semistable abelian variety Finite field Lenstra elliptic curve factorization Hyperelliptic curve cryptography Abstract algebra Algebraic geometry Diophantine geometry
33	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
34	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
35	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
36	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
37	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
38	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
39	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
40	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