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Tate curve
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31	Constructing Abelian Varieties for Pairing-Based Cryptography Constructing Abelian Varieties for Add to Reading List Source URL: theory.stanford.edu Language: English - Date: 2009-05-04 09:49:01 Abelian varieties Algebraic curves Cryptography Finite fields Hasse–Witt matrix Weil pairing Supersingular elliptic curve Tate pairing Complex multiplication Abstract algebra Algebra Elliptic curves
32	Abelian Varieties and Pairing-Based Cryptography Theoretical foundations Practical results Pairing-friendly Hyperelliptic Curves and Weil Restriction Add to Reading List Source URL: theory.stanford.edu Language: English - Date: 2009-09-23 22:25:58 Cryptography Algebraic curves Elliptic curves Algebraic surfaces Abelian varieties Weil pairing Pairing Tate pairing Hyperelliptic curve Abstract algebra Algebraic geometry Geometry
33	Numerical evidence for the Birch–Swinnerton-Dyer conjecture John Cremona University of Warwick Add to Reading List Source URL: homepages.warwick.ac.uk Language: English - Date: 2011-05-11 12:31:35 Diophantine geometry Conjectures Analytic number theory Elliptic curve Group theory Birch and Swinnerton-Dyer conjecture Néron–Tate height Heegner point Abstract algebra Mathematics Number theory
34	Height Difference Bounds For Elliptic Curves over Number Fields J. E. Cremona School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK. Add to Reading List Source URL: homepages.warwick.ac.uk Language: English - Date: 2006-06-26 05:45:45 Number theory Symbol Elliptic curve Néron–Tate height Algebraic number field XTR Abstract algebra Mathematics Algebra
35	Computing a Lower Bound for the Canonical Height on Elliptic Curves over Q John Cremona1 and Samir Siksek2 1 School of Mathematical Sciences, University of Nottingham, University Park, Add to Reading List Source URL: homepages.warwick.ac.uk Language: English - Date: 2006-06-26 05:45:47 Analytic number theory Elliptic curve Néron–Tate height Support Mathematics Number theory Group theory
36	CONICS - A POOR MAN’S ELLIPTIC CURVES FRANZ LEMMERMEYER Contents Introduction 1. Dramatis Personae: Conics and Elliptic Curves Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2005-05-18 04:50:24 Conic sections Curves Number theory Analytic geometry Analytic number theory Elliptic curve Birch and Swinnerton-Dyer conjecture Néron–Tate height Parabola Geometry Abstract algebra Algebraic geometry
37	MUMFORD-TATE GROUPS AND ABELIAN VARIETIES PETE L. CLARK 1. Introduction These are notes for a lecture in Elham Izadi’s 2006 VIGRE seminar on the Hodge Conjecture. Add to Reading List Source URL: math.uga.edu Language: English - Date: 2006-11-09 20:58:22 Mumford–Tate group Hodge structure Hodge conjecture Abelian variety Abelian group Representation theory Elliptic curve Algebraic group Complex multiplication Abstract algebra Algebra Hodge theory
38	SOME FAMILIES OF NON-CONGRUENT NUMBERS FRANZ LEMMERMEYER Abstract. In this article we study the Tate-Shafarevich groups corresponding to 2-isogenies of the curve Ek : y 2 = x(x2 − k2 ) and construct infinitely many exa Add to Reading List Source URL: www.fen.bilkent.edu.tr Language: English - Date: 2003-09-11 11:03:50 Analytic number theory Symbol Quadratic reciprocity Elliptic curve Spectral theory of ordinary differential equations Μ operator Abstract algebra Mathematics Number theory
39	Visibility of Ideal Classes Ren´e Schoof ∗ Lawrence C. Washington Add to Reading List Source URL: www.mat.uniroma2.it Language: English - Date: 2010-09-17 08:27:56 Field theory Algebraic structures Ideal class group Ideals Elliptic curve Tate–Shafarevich group Algebraic number field Field Discriminant of an algebraic number field Abstract algebra Algebra Algebraic number theory
40	An Introduction to Pairing-Based Cryptography Alfred Menezes Abstract. Bilinear pairings have been used to design ingenious protocols for such tasks as one-round three-party key agreement, identity-based encryption, and Add to Reading List Source URL: cacr.uwaterloo.ca Language: English - Date: 2013-10-27 06:53:30 Pairing Boneh/Franklin scheme Elliptic curve cryptography Diffie–Hellman problem Elliptic curve ID-based encryption Tate pairing BLS Supersingular elliptic curve Cryptography Abstract algebra Algebra

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