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投稿时间：2006-11-09
投稿时间：2006-11-09
中文摘要: 为讨论环Z/nZ上圆锥曲线RSA型公钥密码体制的安全性，研究了对其的小私钥d攻击方法。给出了基于连分数方法分解n的算法，并通过两个简单的例子对该攻击方法进行了说明。由此指出Z/nZ上圆锥曲线RSA型公钥密码体制不能抵抗小私钥攻击,即在私钥d过小时，环Z/nZ上圆锥曲线RSA型公钥密码体制是不安全的。
Abstract:To discuss the security of RSA type cryptosystem over conic curves on the ring Z/nZ, two algorithms of short private exponent attack on such cryptosystems were presented. Two simple examples illuminating the algorithms were also given. The results showed that the RSA type cryptosystem over conic curves on the ring Z/nZ can not resist short private exponent attack. In other word, the parameter n can be factored in polynomial time of lnn if the private exponent is too small.
文章编号：20080217 中图分类号： 文献标志码：
基金项目:国家自然科学基金资助项目（90304014；60673065）
| Author Name | Affiliation |
| Dept. of Computer Sci. and Technol., Tsinghua Univ., Beijing 100084,China | |
| Dept. of Computer Sci. and Technol., Tsinghua Univ., Beijing 100084,China |
作者简介:
引用文本：
刘铎,戴一奇.对环Z/nZ上圆锥曲线RSA型公钥密码体系的小私钥d攻击[J].工程科学与技术,2008,40(2):86-90.
.Short Private Exponent Attacks on RSA type Cryptosystem Based on Conic Curves[J].Advanced Engineering Sciences,2008,40(2):86-90.
引用文本：
刘铎,戴一奇.对环Z/nZ上圆锥曲线RSA型公钥密码体系的小私钥d攻击[J].工程科学与技术,2008,40(2):86-90.
.Short Private Exponent Attacks on RSA type Cryptosystem Based on Conic Curves[J].Advanced Engineering Sciences,2008,40(2):86-90.