Fast enumeration of superspecial hyperelliptic curves of genus 4 with automorphism group V4
Fast enumeration of superspecial hyperelliptic curves of genus 4 with automorphism group V4
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具有自同构群V4的属4超特殊超椭圆曲线的快速计数
DOI：
10.1007/978-3-031-22944-2_6
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Harashita Shushi
中科院分区：
文献类型：
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作者：
Ohashi Ryo;Kudo Momonari;Harashita Shushi
在算术几何和代数几何中，超特殊曲线是一个重要的研究对象，在密码学和编码理论中有着重要的应用。这类曲线的计数是一个中心问题，但是否存在超特殊曲线的一般特征，甚至还不知道。本文提出了一个计算亏格为4的超特殊超椭圆曲线的算法，该算法具有复杂性，其自同构群为4阶非循环群。通过在Magma上执行该算法，我们将这些曲线的数量增加到200。我们还成功地找到了超特殊的超椭圆曲线亏格4的每一个特征pwith。
In arithmetic and algebraic geometry,superspecial curveshave been studied as one of the most important objects, with practical applications to cryptography and coding theory. The enumeration of those curves is a central problem, but ifit is not even known whether a superspecial curve of genusgexists in general characteristic. In this paper, we propose an algorithm with complexityto enumerate superspecial hyperelliptic curves of genus 4 with automorphism group, whereis the non-cyclic group of order 4. By executing the algorithm over Magma, we enumerate those curves overforpup to 200. We also succeeded in finding a superspecial hyperelliptic curve of genus 4 in every characteristicpwith.