Read online Aliquot Cycles for Elliptic Curves with Complex Multiplication
Aliquot Cycles for Elliptic Curves with Complex Multiplication
Date: 24 Mar 2013
Publisher: Createspace Independent Publishing Platform
Language: English
Book Format: Paperback::60 pages
ISBN10: 1483902323
ISBN13: 9781483902326
File size: 43 Mb
Filename: aliquot-cycles-for-elliptic-curves-with-complex-multiplication.pdf
Dimension: 216x 279x 3mm::163g
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Read online Aliquot Cycles for Elliptic Curves with Complex Multiplication. With complex multiplication and special values of automorphic functions ([2]). 2 Endomorphisms of elliptic curves An elliptic curve can be defined in five different ways: 1. A connected compact Lie group of dimension 1, 2. A complex torus C/L, where L is a lattice in C, 3. A Riemann surface of genus 1, 4. A non-singular cubic in P 2(C), When the field of definition is a finite field, there are always non-trivial endomorphisms of an elliptic curve, coming from the Frobenius map, so the complex multiplication case is in a sense typical (and the terminology isn't often applied). But when the base field is a number field, complex multiplication Intel Polynomial Multiplication Instruction and its Usage for Elliptic Curve Cryptography 2 Executive Summary Elliptic Curve Cryptography (ECC) is an algorithm for public-key cryptography based on elliptic curves over finite fields and is an alternative to commonly-used methods, such an aliquot cycle of length L for E if each pi is a prime number of good Let E be an elliptic curve over Q without complex multiplication and L 2 a fixed integer. Complex Multiplication: Kronecker s Jugendtraum for Q(i) Alex Halperin April 29, 2008 Abstract We discuss Chapter 6 from Silverman & Tate s Rational Points on Elliptic Curves, in which the authors outline a means of proving Kronecker s Jugendtraum for Q and Q(i). One considers C[n], the kernel of the multiplication--n map on an elliptic Elliptic curve point multiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic curve cryptography AMICABLE PAIRS AND ALIQUOT CYCLES FOR ELLIPTIC CURVES OVER NUMBER FIELDS JIM BROWN, DAVID HERAS, KEVIN JAMES, RODNEY KEATON, AND ANDREW QIAN Abstract. The notion of amicable pairs and aliquot cycles has been generalized to elliptic curves Silverman and Stange. In their work they provide a detailed analysis in the case the elliptic curve is An amicable pair for an elliptic curve is a pair of primes (p, q) of good reduction for E and.In this paper we study elliptic amicable pairs and analogously defined 2 Iwasawa Theory of Elliptic Curves without Complex Multiplication Yoshihiro Ochi Korea Institute for Advanced Study (KIAS) 207-43 Cheongryangri-dong, Dongdaemun-gu Seoul 130-012, South Korea Email: Abstract Recently new results have been obtained in the GL 2 Iwasawa theory of elliptic curves without complex multiplication. related to the notions of amicable pairs and aliquot cycles for elliptic curves introduced Silverman and Stange. For elliptic curves with complex multiplication. We next study the reduction of elliptic curves, we describe the so called Complex Multiplication method and finally we explain Schoof s algorithm for computing point on elliptic curves over finite fields. As an application, we see how to compute square roots modulo a prime p. Ex-plicit algorithms and full-detailed examples are also given. I am trying to understand the main theorem ov CM for elliptic curves. I work with the version stated in the second chapter of Silvermans "Advanced Topics in the Arithmetics of Elliptic Curves". I would like to make an example or something what illustrates clearly the statement. I am looking forward for any ideas! Aliquot Cycles For Elliptic Curves With Complex Multiplication is most popular ebook you must read. You can download any ebooks you wanted like Aliquot a precise version of the main conjecture of Iwasawa theory for an elliptic curve E over Q, without complex multiplication, over the field F generated the coordinates of all its p-power division points; here p is a prime at least 5 where E has good ordinary reduction, and G is the Galois group of F over Q. CONTENTS 1. Aliquot Cycles for Elliptic Curves with Complex Multiplication (2013) Cached. Download Links [ ] aliquot cycle complex multiplication elliptic curve washington university open scholarship authorized administrator undergraduate thesis amicable pairs and aliquot cycles, first considered Silverman and Stange [SS]. For an elliptic Let E/Q be an elliptic curve without complex multiplication and. Silverman and Stange, Amicable Pairs and Aliquot Cycles in Elliptic Curves, Experimental Rajwade, Arithmetic on curves with complex multiplication . Now, if the number of points on the curve is smooth (that is, is composed of small factors), there are quite efficient ways to compute discrete logs; we never use an elliptic curve with a smooth group order, specifically because they're cryptographically weak. Hence, I'll ignore those methods, and talk about a method that applies to all curves. for new questions, such as the problem of amicable pairs and aliquot cycles, t is a fixed integer and E/Q is a fixed elliptic curve without complex multiplication. Cycles on modular varieties and rational points on elliptic curves Henri Darmon July 31, 2009 This is a summary of a three-part lecture series given at the meeting on Explicit methods in number theory that was held in Oberwolfach from July 12 to 18, 2009. The theme of this Download this best ebook and read the Aliquot Cycles For Elliptic Curves With Complex. Multiplication ebook. You can't find this ebook anywhere online. arxiv:0909.1661v2 [ ] 4 jun 2010 on fields of definition of torsion points of elliptic curves with complex multiplication luis dieulefait, enrique gonzalez-jim enez, and jorge jimenez urroz 6. H. Cohen, A. Miyaji and T. Ono, E cient elliptic curve exponentiation using mixedcoordinates",AdvancesinCryptology{Asiacrypt 98,1998,51-65. 7. D.Cox,Primes of the Form x2 +ny2. Fermat, Class Field Theory and Complex Multiplication,Wiley,1989. 8. G. Frey and H. Ruc k, A remark concerning m-divisibility and the discrete log- Download this great ebook and read the Aliquot Cycles For Elliptic Curves With Complex. Multiplication ebook. You can't find this ebook anywhere online. Complex Multiplication Structure of Elliptic Curves H. W. Lenstra, Jr. Department of Mathematics, 3840, University of California, Berkeley, California 94720-3840 Communicated K. Ribet Received October 23, 1990; revised February 18, 1994 Let k be a finite field and let E be an elliptic curve ALIQUOT CYCLES FOR ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION - In this site isn`t the same as a solution manual you buy in a book store. To obtain information on the group of rational points or the Tate-Safarevic group of an elliptic curve E defined over Q, Rubin K. (1987) Descents on Elliptic Curves with Complex Multiplication. In: Goldstein C. (eds) Séminaire de Théorie des Nombres, Paris 1985 86. Progress We then use the properties of elliptic pairs to prove that aliquot cycles of length greater than two exist for elliptic curves with complex multiplication, contrary to an In this article we treat the case of elliptic curve defined over the rationals with complex multiplication. For this particular case, we give a description of the possible torsion growth over cubic fields and a completely explicit description of this growth in terms of some invariants attached to a given elliptic curve. Construction of Elliptic Curves with Complex Multiplication: Applied to Primality Testing [Özkan Canbay] on *FREE* shipping on qualifying offers. An abstract model of an elliptic curve is designed as a Java-based application. In this abstract model we implement two distinct elliptic curve types: the Weierstraß curve and the Generalizing the notion of amicable pair, we define an aliquot cycle of length for to We next consider the case of elliptic curves having complex multiplication. Amicable pairs and aliquot cycles for elliptic curves over number fields Jim Formal groups of Q-curves with complex multiplication Fumio Sairaiji. Aliquot Cycles for Elliptic Curves with Complex Multiplication. Find all books from Morrell, Thomas. At you can find used, antique and new books TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX ALEX RICE) PETE L. CLARK, BRIAN COOK, AND JAMES STANKEWICZ Abstract. We present seven theorems on the structure of prime order torsion points on CM elliptic curves de ned over number elds. The rst three results
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