电子学报 ›› 2013, Vol. 41 ›› Issue (5): 833-839.DOI: 10.3969/j.issn.0372-2112.2013.05.001

• 学术论文 •    下一篇

基于Grobner基的Rijndael-192代数攻击方案

崔杰1,2, 黄刘生1,3, 仲红2, 杨威1,3   

  1. 1. 中国科学技术大学计算机科学与技术学院,安徽合肥 230026;
    2. 安徽大学计算机科学与技术学院,安徽合肥 230039;
    3. 中国科学技术大学苏州研究院,江苏苏州 215123
  • 收稿日期:2012-05-16 修回日期:2012-08-10 出版日期:2013-05-25 发布日期:2013-05-25
  • 作者简介:崔 杰 男,1980年生于河南淮阳,现为中国科学技术大学计算机科学与技术学院博士生,安徽大学计算机科学与技术学院讲师.研究方向为信息安全. E-mail:cuijie@mail.ustc.edu.cn
  • 基金资助:
    国家自然科学基金(No.60903217,No.61173188,No.61173187);中央高校基本科研业务费专项资金(No.WK0110000027);国家自然科学基金数学天元基金(No.11126174);安徽省高校自然科学研究重点项目(No.KJ2013A017);江苏省自然科学基金(No.BK2011357);安徽大学博士科研启动经费项目

Algebraic Attack on Rijndael-192 Based on Grobner Basis

CUI Jie1,2, HUANG Liu-sheng1,3, ZHONG Hong2, YANG Wei1,3   

  1. 1. School of Computer Science and Technology,University of Scienc and Technology of China,Hefei,Anhui 230026,China;
    2. School of Computer Science and Technology,Anhui University,Hefei,Anhui 230039,China;
    3. Suzhou Institute for Advanced Study,University of Science and Technology of China,Suzhou,Jiangsu 215123,China
  • Received:2012-05-16 Revised:2012-08-10 Online:2013-05-25 Published:2013-05-25

摘要: 由于对Rijndael算法实施Grobner基攻击的一个关键环节是构造出其零维Grobner基,本文对Rijndael-192密码的线性变换和多变元方程系统进行了深入研究,通过选择合理的项序及变量次序,提出了Rijndael-192零维Grobner基的构造方法.文中详述了该Grobner基的构造方法,并给出了相关性质的理论证明.此外,本文提出了一种Rijndael-192的Grobner基攻击方案,攻击复杂度低于穷举攻击.

关键词: Rijndael算法, Grobner基, 代数攻击, 多变元方程系统

Abstract: Because a key step of Grobner basis attack on Rijndael is constructing its zero-dimensional Grobner basis,authors perform some particular studies on the linear transformation and the system of multivariate polynomial equations of Rijndael-192,and propose its zero-dimensional Grobner basis construction method through choosing suitable term order and variable order.After presenting the construction method of the Grobner basis,authors give the necessary theorical proves.Moreover,authors propose an algebraic attack on Rijndael-192 based on Grobner basis.Analysis suggest that the attack complexity is lower than exhaustive attack.

Key words: Rijndael algorithm, Grobner basis, Algebraic attack, Multivariate equation system

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