Fast Construction of Secure Discrete Logarithm Problems over Jacobian Varieties
Fast Construction of Secure Discrete Logarithm Problems over Jacobian Varieties
复制标题
雅可比簇上安全离散对数问题的快速构造
DOI：
10.1007/978-0-387-35515-3_25
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
S. Tsujii
中科院分区：
文献类型：
--
作者：
J. Chao;Kazuto Matsuo;S. Tsujii
超椭圆曲线的雅可比簇最近已被用于密码系统中。然而，由于缺乏有效的点计数算法在有限域上的这类品种，使得安全密码系统的设计非常困难。本文给出了计算有限域上Jacobian簇的Frobenius自同态的CM型和理想分解的有效算法。然后，我们证明了如何在大素域上构造小亏格的安全超椭圆曲线。
Jacobian varieties of hyperelliptic curves have been recently used in cryptosystems. However, lacking of efficient point-counting algorithms for such varieties over finite fields makes the design of secure cryptosystems very difficult. This paper presents efficient algorithms to calculate the CM type and ideal factorization of Frobenius endomorphisms of Jacobian varieties over finite fieldsFpin polynomial time of logp. Then we show how to construct secure hyperelliptic curves of small genera over large prime fieldsFpin polynomial time of logp.