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Elliptic curve primality
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#	Item
11	Faster deterministic integer factorisation David Harvey (joint work with Edgar Costa, NYU) University of New South Wales 6th January 2012, Joint Mathematics Meetings, Boston Add to Reading List Source URL: web.maths.unsw.edu.au Language: English - Date: 2012-01-11 02:12:51 Mathematics General number field sieve Time complexity Integer factorization Primality test Algorithm NP Prime number Lenstra elliptic curve factorization Theoretical computer science Integer factorization algorithms Applied mathematics
12	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
13	FINDING COMPOSITE ORDER ORDINARY ELLIPTIC CURVES USING THE COCKS-PINCH METHOD D. BONEH, K. RUBIN, AND A. SILVERBERG Abstract. We apply the Cocks-Pinch method to obtain pairing-friendly composite order groups with prescri Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2010-05-03 13:25:59 Elliptic curves Finite fields Modular arithmetic Integer factorization algorithms Elliptic curve Supersingular elliptic curve Prime number Quadratic reciprocity Primality test Abstract algebra Mathematics Number theory
14	Edwards Curves and the ECM Factorisation Method Peter Birkner Eindhoven University of Technology Fields Cryptography Retrospective Meeting Add to Reading List Source URL: www.fields.utoronto.ca Language: English - Date: 2009-05-14 13:31:42 Group theory Lenstra elliptic curve factorization Elliptic curve Elliptic curve cryptography Torsion Edwards curve Elliptic curve primality testing Algebraic-group factorisation algorithm Abstract algebra Finite fields Integer factorization algorithms
15	On the Power of Non-Adaptive Learning Graphs arXiv:1210.3279v2 [quant-ph] 16 Dec 2012 Aleksandrs Belovs∗ Add to Reading List Source URL: arxiv.org Language: English - Date: 2012-12-17 21:58:17 Complexity classes Algebra Boundedly generated group Geometric group theory Decision tree model FO NP Quantum algorithm Elliptic curve primality testing Theoretical computer science Applied mathematics Mathematics
16	Advances in the CM method for elliptic curves F. Morain Laboratoire d’Informatique de l’École polytechnique logoX Add to Reading List Source URL: www.lix.polytechnique.fr Language: English - Date: 2009-05-14 14:22:49 Elliptic curve Group theory Prime number Finite fields Primality tests Elliptic curve primality proving Abstract algebra Mathematics Analytic number theory
17	IMPLEMENTING THE ASYMPTOTICALLY FAST VERSION OF THE ELLIPTIC CURVE PRIMALITY PROVING ALGORITHM F. MORAIN Abstract. The elliptic curve primality proving (ECPP) algorithm is one of the current fastest practical algorithms Add to Reading List Source URL: www.lix.polytechnique.fr Language: English - Date: 2005-12-13 09:43:17 Number theory Finite fields Conjectures Analytic number theory Elliptic curves Elliptic curve primality proving AKS primality test Quadratic residue Prime number Abstract algebra Mathematics Primality tests
18	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
19	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
20	INFINITUDE OF ELLIPTIC CARMICHAEL NUMBERS AARON EKSTROM, CARL POMERANCE and DINESH S. THAKUR (September 25, 2011) Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2011-09-27 14:35:17 Integer sequences Modular arithmetic Group theory Analytic number theory Elliptic curve Primality test Coprime Prime number Carmichael number Mathematics Abstract algebra Number theory

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