对环Z/nZ上圆锥曲线RSA型公钥密码体系的小私钥d攻击

刘铎; 戴一奇

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对环Z/nZ上圆锥曲线RSA型公钥密码体系的小私钥d攻击

信息工程 | 更新时间：2023-11-28

- 对环Z/nZ上圆锥曲线RSA型公钥密码体系的小私钥d攻击
- Short Private Exponent Attacks on RSA type Cryptosystem Based on Conic Curves
- 工程科学与技术 2008年40卷第2期页码：86-90
- 作者机构：
  
  清华大学计算机科学与技术系北京,100084
- 作者简介：
- 基金信息：
  
  国家自然科学基金资助项目（90304014;60673065）
- DOI：
  中图分类号：
- 纸质出版日期：2008，
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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.
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. DOI：

Short Private Exponent Attacks on RSA type Cryptosystem Based on Conic Curves[J]. Advanced Engineering Sciences, 2008,40(2):86-90. DOI：

摘要

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

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.

关键词

密码学圆锥曲线小私钥攻击连分数

Keywords

cryptologyconic curveshort private exponent attackscontinue fraction

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