素域GF(p)上旋转对称函数的性质

元彦斌; 赵亚群; 郑兴; 郭威

doi:10.3724/SP.J.1146.2008.01498

素域GF(p)上旋转对称函数的性质

doi: 10.3724/SP.J.1146.2008.01498

元彦斌^{①②;赵亚群},
赵亚群,
郑兴,
郭威

基金项目:

信息安全国家重点实验室开放基金(01-02)资助课题

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出版历程
- 收稿日期: 2008-11-14
- 修回日期: 2009-09-28
- 刊出日期: 2009-12-19

The Properties of Rotation Symmetric Functions over GF(p)

Yuan Yan-bin^{①②;赵亚群},
Zhao Ya-qun,
Zheng Xing,
Guo Wei

摘要

摘要: 该文给出了素域上旋转对称函数的Chrestenson循环谱特征和自相关函数特征，根据旋转对称函数的多项式所具备的特点，通过构造相应的关联矩阵，将旋转对称函数的真值表，简化代数标准型和Chrestenson循环谱联系起来，并由此给出了旋转对称函数满足平衡性、相关免疫性、稳定性等密码学性质的充分必要条件。
- 密码学; 旋转对称函数; Chrestenson循环谱; 自相关函数; 平衡性; 相关免疫性; 广义Bent 函数
Abstract: In this paper, the Chrestenson spectrum and the autocorrelation functions of Rotation Symmetric(RotS) functions are researched. The polynomials of RotS functions have special properties, by constructing matrixes, the relationship of the truth table, short algebric normal form and the chrestenson spectrum are established. By studying the matrixes, the sufficient and necessary conditions of the RotS functions to satisfying cryptographic properties of balancedness, correlation immunity and the stability are given.

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参考文献(1)

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