An Attack on the Generalized RSA Public Key Scheme Using Two-dimension Lattice

Gou Yun; Zeng Guang; Han Wen Bao; Wang Zheng

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An Attack on the Generalized RSA Public Key Scheme Using Two-dimension Lattice

更新时间：2023-11-14

- An Attack on the Generalized RSA Public Key Scheme Using Two-dimension Lattice
- Advanced Engineering Sciences Vol. 47, Issue Z1, Pages: 99-104(2015)
- 作者机构：
  
  1. 信息工程大学
  2. 国家电网郑州供电公司通信分公司
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2015，
  
  Published Online：3 December 2014，
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勾云,曾光,韩文报,王峥.对广义RSA公钥密码体制的二维格攻击（研究生论坛）[J].工程科学与技术,2015,47(Z1):99-104.

Gou Yun, Zeng Guang, Han Wen Bao, et al. An Attack on the Generalized RSA Public Key Scheme Using Two-dimension Lattice. [J]. Advanced Engineering Sciences 47(Z1):99-104(2015)
勾云,曾光,韩文报,王峥.对广义RSA公钥密码体制的二维格攻击（研究生论坛）[J].工程科学与技术,2015,47(Z1):99-104. DOI：

Gou Yun, Zeng Guang, Han Wen Bao, et al. An Attack on the Generalized RSA Public Key Scheme Using Two-dimension Lattice. [J]. Advanced Engineering Sciences 47(Z1):99-104(2015) DOI：

摘要

中文摘要: 利用二维格上的拉格朗日格基约化算法和欧拉函数的下界从新的角度提出一种对广义RSA公钥密码体制的格攻击方法。同时给出了对应的攻击算法，证明了使用该方法可在多项式时间内分解RSA模数N。相比最初针对这一体制的连分式攻击手段，该方法不需要计算和重复验证连分式的渐进分数，而是直接求出素因子p，从而简化了整个求解过程，提高了RSA模数的分解效率。结果表明：该方法时间复杂度更低，实验中加速效果良好，可以有效攻击广义RSA公钥密码体制。

Abstract

Abstract:A method for breaking the generalized RSA public key scheme was proposed using Lagrange’s reduction algorithm based on the two-dimension lattice and the lower bound of Euler's totient function. Moreover

the corresponding attack algorithm was also given and it was proved that the RSA modulus N could be factorized in polynomial time. Compared with the original continued fraction attack

this method removed the steps of computing and repeatedly verifying the convergent of continued fraction

obtained the prime factor p directly

so it simplified the whole solving procedures and improved the factoring efficiency. The results show that this method has lower time complexity

works faster in the experiment

and can be efficiently used to attack the generalized RSA public key scheme.

关键词

广义RSA公钥密码体制连分式二维格拉格朗日约化

Keywords

generalized RSApublic key schemecontinued fractiontwo-dimension latticeLagrange’s reduction

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