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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (7): 94-102.doi: 10.6040/j.issn.1671-9352.2.2021.064

• • 上一篇    

具有抵抗DPA攻击能力的高非线性度旋转对称布尔函数的搜索

师宇1,郑东1,2,赵庆兰1*,李路阳1,王勇1   

  1. 1.西安邮电大学无线网络安全技术国家工程实验室, 陕西 西安 710121;2.卫士通摩石实验室, 北京 100070
  • 发布日期:2022-06-29
  • 作者简介:师宇(1998— ),男,硕士研究生, 主要研究方向为布尔函数. E-mail:1901200069@stu.xupt.edu.cn*通信作者简介:赵庆兰(1981— ), 女, 博士, 教授, 主要研究方向为密码函数、对称密码算法的设计和分析. E-mail:zhaoqinglan@foxmail.com
  • 基金资助:
    国家自然科学基金资助项目(61902314,62072371);陕西省自然科学基础研究计划(2019JQ867,2018JZ6001);陕西省教育厅专项科研计划(20JK0911);陕西省重点研发计划项目(2021ZDLGY06-02)

Searching for Boolean functions with DPA-resistance and high nonlinearity in the rotation symmetric class

SHI Yu1, ZHENG Dong1,2, ZHAO Qing-lan1*, LI Lu-yang1, WANG Yong1   

  1. 1. National Engineering Laboratory for Wireless Security, Xian University of Posts and Telecommunications, Xian 710121, Shaanxi, China;
    2. Westone Cryptologic Research Center, Beijing 100070, China
  • Published:2022-06-29

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摘要： 提出了一种有效的搜索算法以实现在旋转对称布尔函数类中搜索具有抵抗DPA攻击能力的高非线性度布尔函数。 利用搜索算法在9、10元旋转对称布尔函数中得到了新的透明阶和非线性度等性质良好的函数, 其中包括透明阶优于已有结果的函数。 此外, 基于多核并行技术实现了8元旋转对称布尔函数的遍历, 首次给出了所有非线性度不低于112的8元旋转对称布尔函数, 并对其非线性度、透明阶、代数次数进行了统计分析, 这些函数可以用来构造密码学性质优良的S盒。

关键词: 侧信道攻击, 差分能量分析, 旋转对称布尔函数, 透明阶, 非线性度

Abstract: An efficient search algorithm is proposed to find Boolean functions with differential power analysis(DPA)resistance and high nonlinearity in the class of rotation symmetric Boolean functions(RSBFs). Using the search algorithm designed in this paper, we get functions with better properties than the existing results in the classes of 9-variable and 10-variable RSBFs. In addition, an exhaustive algorithm of 8-variable RSBFs based on multi-core parallel technology is proposed and for the first time all 8-variable RSBFs with nonlinearity not less than 112 are found and their transparency order and algebraic degree are analyzed. These functions can be utilized to construct S-Boxes with good cryptographic properties.

Key words: side channel attack, DPA, RSBFs, transparency order, nonlinearity

中图分类号: 

  • TN915.08
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