MODULAR POLYNOMIALS FOR GENUS 2

MODULAR POLYNOMIALS FOR GENUS 2 (2009)

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by Reinier Bröker , Kristin Lauter

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@MISC{Bröker09modularpolynomials,
    author = {Reinier Bröker and Kristin Lauter},
    title = { MODULAR POLYNOMIALS FOR GENUS 2},
    year = {2009}
}

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Abstract

Modular polynomials are an important tool in many algorithms involving elliptic curves. In this article we investigate their generalization to the genus 2 case following pioneering work by Gaudry and Dupont. We prove various properties of these genus 2 modular polynomials and give an improved way to explicitly compute them.

Citations

155	The Theory of Jacobi Forms - Eichler, Zagier - 1985
154	Elliptic curves over finite fields and the computation of square roots mod p - Schoof - 1985
96	Complex Abelian Varieties - Lange - 1992
91	Primes of the form x 2 + ny 2 - Cox - 1989
68	A.: Compactification of arithmetic quotients of bounded symmetric domains - Baily, Borel - 1966
67	Counting points on elliptic curves over finite fields - Schoof - 1995
54	Counting points on hyperelliptic curves over finite fields - Gaudry, Harley - 2000
50	Complex Abelian Varieties. Grundlehren der - Birkenhake, Lange - 2004
40	Geometric Algebra - Artin - 1957
38	Construction de courbes de genre 2 à partir de leurs modules - Mestre - 1990
33	Moyenne Arithmético-géometrique et Périodes des Courbes de genre 1 et 2 - Bost, Mestre
31	On Siegel modular forms of genus two - Igusa - 1962
21	Action of modular correspondences around CM points - Couveignes, Henocq - 2002
20	Algorithmique des courbes hyperelliptiques et applications à la cryptologie - Gaudry - 2000
15	Constructing elliptic curves with a known number of points over a prime field - Agashe, Lauter, et al.
14	A CRT algorithm for constructing genus 2 curves over finite fields - Eisenträger, Lauter
13	A 2-adic CM method for genus 2 curves with application to cryptography - Gaudry, Houtmann, et al. - 2006
13	Computing Hilbert class polynomials with the Chinese remainder theorem - Sutherland - 2011
11	Modular equations for hyperelliptic curves - GAUDRY, SCHOST
10	A p-adic algorithm to compute the Hilbert class polynomial - Bröker
10	Proving the primality of very large numbers with fastECPP, in "Algorithmic Number Theory - FRANKE, KLEINJUNG, et al. - 2004
9	Computing Hilbert class polynomials - Belding, Bröker, et al. - 2008
9	Bad reduction of the Siegel moduli scheme of genus two with Γ0(p)-level structure - Chai, Norman - 1990
8	et al., Handbook of elliptic and hyperelliptic curve cryptography - Cohen - 2006
8	Moyenne arithmético-géométrique, suites de Borchardt et applications - Dupont - 2006
8	Computing Hilbert class polynomials, Algorithmic Number Theory Symposium–ANTS VIII - Belding, Bröker, et al. - 2008
4	The subgroup structure of finite classical groups in terms of geometric configurations - King - 2005
4	Elliptic functions, Springer Graduate Texts - Lang - 1987
4	Genus 2 curves covering elliptic curves, a computational approach - Shaska - 2005
4	Genus 2 fields with degree 3 elliptic subfields - Shaska
3	The moduli space of curves of genus two covering elliptic curves - Murabayashi - 1994
2	Zur Theorie der Modulfunktionen n-ten Grades - Koecher - 1954
1	Compactification of arithemetic quotients of bounded symmetric domains - Baily, Borel - 1966
1	Genus 2 curves with degree 5 elliptic subcovers - Magaard, Shaska, et al.
1	Modular forms and Hecke operators, AMS Translations of mathematical monographs, vol 145 - Andrianov, Zhuravlev - 1995
1	Primes of the form x 2 + ny 2 , 1st edn - Cox - 1989
1	SEA in genus 1: 2500 decimal digits, Announcement sent to the Number theory mailing list, online available at http://listserv.nodak.edu/archives/nmbrthry.html - Enge, Morain - 2006
1	Genus 2 curves covering elliptic curves, a compuational approach - Shaska - 2005