计算机工程与应用 ›› 2008, Vol. 44 ›› Issue (7): 16-18.

• 博士论坛 • 上一篇    下一篇

一类完全非线性S-盒的构造

杨 敏1,孟庆树2,张焕国2   

  1. 1.武汉大学 国际软件学院,武汉 430079
    2.武汉大学 计算机学院,武汉 430079
  • 收稿日期:2007-10-29 修回日期:2007-12-03 出版日期:2008-03-01 发布日期:2008-03-01
  • 通讯作者: 杨 敏

Construction of one kind of perfect nonlinear S-boxes

YANG Min1,MENG Qing-shu2,ZHANG Huan-guo2   

  1. 1.International School of Software,Wuhan University,Wuhan 430079,China 2.Computer School,Wuhan University,Wuhan 430079,China
  • Received:2007-10-29 Revised:2007-12-03 Online:2008-03-01 Published:2008-03-01
  • Contact: YANG Min

摘要: 完全非线性S-盒在对称密码中有着重要的运用。给出有限域上完全非线性S-盒的一种构造方法。与在向量空间上构造的方法比,有限域上置换多项式的代数次数等性质更容易研究。该方法可以构造多类完全非线性S-盒,例如,通过选择幂函数形式的置换αx,得到Satoh等人构造的S-盒;通过选取指数形式的置换xd,所得完全非线性S-盒的分量函数的任意非零线性组合的代数次数达到最高。

Abstract: S-box is important in symmetric cryptosystem.One method is proposed to constructed perfect nonlinear S-box over finite field.Compared to the construction over vector space,it is easier to study the properties of permutation polynomials,like algebraic degree.By choosing different parameters,different types of S-boxes can be constructed.For example,by choosing αx as the permutation polynomial,we obtain the S-box once constructed by Satoh et al.By selecting permutation of form xd,we obtain another type of S-boxes.The algebraic degree of any nonzero linear combination of its output functions is highest.