构造小嵌入次数的椭圆曲线参数化族

张猛; 徐茂智; 胡志; 侯英

doi:10.11999/JEIT170261

构造小嵌入次数的椭圆曲线参数化族

doi: 10.11999/JEIT170261

1.
(北京大学数学科学学院北京 100871)
2.
(中南大学数学与统计学院长沙 410083)
3.
(清华大学计算机科学与技术系北京 100084)

基金项目:

国家自然科学基金(61272499, 61472016, 61672059, 61602526)，国家重点研发计划资助(2017YFB0802000)

计量
- 文章访问数: 1198
- HTML全文浏览量: 147
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- 被引次数: 0
出版历程
- 收稿日期: 2017-03-29
- 修回日期: 2017-10-20
- 刊出日期: 2018-01-19

On Parameterized Families of Elliptic Curves with Low Embedding Degrees

1.
(School of Mathematical Sciences, Peking University, Beijing 100871, China)
2.
(School of Mathematics and Statistics, Central South University, Changsha 410083, China)
3.
(Department of Compute Science and Technology, Tsinghua University, Beijing 100084, China)

Funds:

The National Natural Science Foundation of China (61272499, 61472016, 61672059, 61602526), The National Key RD Program of China (2017YFB0802000)

摘要

摘要: 配对友好椭圆曲线在基于配对的密码系统中起关键作用。这类曲线的构造不仅极大影响实现效率，更关系到系统安全。虽然目前已提出很多构造方法，但几乎都依赖穷尽搜索。该文提出一种构造该类曲线的系统方法，将寻找配对友好曲线问题转化到解方程，从而避免了穷尽搜索，并设计出具体算法。最后，将该算法应用到寻找嵌入次数为5,8,10和12的配对友好曲线中，发现所有类型的椭圆曲线族都可由该方法统一得到，包括完全族、可变判别式的完全族和稀疏族。特别地，还找到了新的椭圆曲线族。
- 基于配对的密码 /
- 椭圆曲线 /
- 配对友好曲线 /
- 参数化族
Abstract: Pairing-friendly elliptic curves play a vital role in pairing-based cryptography. The constructionof such curves not only influences the implementation efficiency, but concerns the security of system. Though many methods for constructing such curves are introduced, most of which rely on exhaustive search. In this paper, a new systematic method is proposed for constructing such curves which converts the problem to solving equation systems, instead of exhaustive searching. The utility of the method is demonstrated by surveying such elliptic curves with embedding degree 5, 8, 10 and 12, and all kinds of families can be explained via the proposed method including complete families, complete families with variable discriminant and sparse families. Specifically, a new family of elliptic curves is found.
- Pairing-based cryptography /
- Elliptic curves /
- Pairing-friendly curves /
- Parameterized families

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参考文献(19)

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