| S盒的二次方程及一个新的设计准则 |
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| 引用本文： | 张国基,肖皇培.S盒的二次方程及一个新的设计准则[J].华南理工大学学报(自然科学版),2008,36(8). |
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| 作者姓名： | 张国基 肖皇培 |
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| 作者单位： | 1. 华南理工大学,数学科学学院,广东,广州,510640
2. 华南理工大学,计算机科学与工程学院,广东,广州,510640 |
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| 摘 要： | S盒是许多分组密码算法中唯一的非线性部件, 因此它的密码强度决定了整个密码算法的安全强度. 本文从理论上分析S盒中二次方程的存在条件, 证明了AES(Advanced Encryption Standard)密码的S盒在有限域GF(256)上存在55个线性无关的二次方程, 并第一次给出了GF(256)上的这些二次方程. 这些方程可能被用于一些代数攻击中, 如XSL(eXtended Sparse Linearization)攻击. 为了防止利用这些二次方程进行的代数攻击, 本文提出一个新的S盒设计准则.
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| 关 键 词： | 分组密码 AES S盒 二次方程 |
| 收稿时间： | 2007-8-30 |
| 修稿时间： | 2007-10-19 |
Quadratic Equations on S-boxes and A New S-box Design Criterion |
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| Zhang Guo-ji,Xiao Huang-pei.Quadratic Equations on S-boxes and A New S-box Design Criterion[J].Journal of South China University of Technology(Natural Science Edition),2008,36(8). |
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| Authors: | Zhang Guo-ji Xiao Huang-pei |
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| Abstract: | Abstract: As the only nonlinear components in most block ciphers, S-boxes account for the block ciphers’ security. The existence of quadratic equations on S-boxes is analyzed theoretically in this paper. It is proved that there exists 55 linearly independent quadratic equations on the AES (Advanced Encryption Standard) S-box over GF(256). All these equations are given for the first time. These equations may be exploited in some algebraic attacks, such as the XSL (eXtended Sparse Linearization) attack. In order to avoid this type of attack, a new S-box design criterion is presented. |
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| Keywords: | block cipher AES S-box quadratic equation |
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