Constructing all genus 2 curves with supersingular Jacobian

被引：1
|
作者：
Pieper, Andreas [1 ]
机构：
[1] Univ Ulm, Inst Algebra & Zahlentheorie, Helmholtzstr 18, D-89081 Ulm, Germany
来源：
RESEARCH IN NUMBER THEORY | 2022年 / 8卷 / 02期
关键词：
D O I：
10.1007/s40993-022-00330-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
L. Moret-Bailly constructed families C -> P-1 of genus 2 curves with supersingular Jacobian. In this paper we first classify the reducible fibers of a Moret-Bailly family using linear algebra over a quaternion algebra. The main result is an algorithm that exploits properties of two reducible fibers to compute a hyperelliptic model for any irreducible fiber of a Moret-Bailly family.
引用
收藏
页数：26
相关论文
共 50 条
  • [21] Constructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves
    Xiao, Guanju
    Luo, Lixia
    Deng, Yingpu
    JOURNAL OF MATHEMATICAL CRYPTOLOGY, 2021, 15 (01) : 454 - 464
  • [22] Constructing supersingular elliptic curves with a given endomorphism ring
    Chevyrev, Ilya
    Galbraith, Steven D.
    LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2014, 17 : 71 - 91
  • [23] Supersingular genus-2 curves over fields of characteristic 3
    Howe, Everett A.
    COMPUTATIONAL ARITHMETIC GEOMETRY, 2008, 463 : 49 - 69
  • [24] Extractors for Jacobian of hyperelliptic curves of genus 2 in odd characteristic
    Farashahi, Reza Rezaeian
    CRYPTOGRAPHY AND CODING, PROCEEDINGS, 2007, 4887 : 313 - +
  • [25] Bad reduction of genus 2 curves with CM jacobian varieties
    Habegger, Philipp
    Pazuki, Fabien
    COMPOSITIO MATHEMATICA, 2017, 153 (12) : 2534 - 2576
  • [26] Points of order l of the Jacobian of special curves of genus 2
    LeDuff, P
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 325 (03): : 243 - 246
  • [27] The existence of supersingular curves of genus 4 in arbitrary characteristic
    Momonari Kudo
    Shushi Harashita
    Hayato Senda
    Research in Number Theory, 2020, 6
  • [28] The existence of supersingular curves of genus 4 in arbitrary characteristic
    Kudo, Momonari
    Harashita, Shushi
    Senda, Hayato
    RESEARCH IN NUMBER THEORY, 2020, 6 (04)
  • [29] Optimal Eta Pairing on Supersingular Genus-2 Binary Hyperelliptic Curves
    Aranha, Diego F.
    Beuchat, Jean-Luc
    Detrey, Jeremie
    Estibals, Nicolas
    TOPICS IN CRYPTOLOGY - CT-RSA 2012, 2012, 7178 : 98 - +
  • [30] The number of rational points on hyperelliptic supersingular curves of genus 4 in characteristic 2
    McGuire, Gary
    Zaytsev, Alexey
    FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (05) : 886 - 893
12345