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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (9): 51-58.doi: 10.6040/j.issn.1671-9352.0.2022.162

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广义SIMON类轮函数的密码学性质研究

卢健伟1(),任济洲2,关杰1   

  1. 1. 战略支援部队信息工程大学密码工程学院, 河南 郑州 450001
    2. 澳大利亚国立大学工程计算与控制学院, 堪培拉 2600，澳大利亚
  • 收稿日期:2022-03-16 出版日期:2023-09-20 发布日期:2023-09-08
  • 作者简介:卢健伟(1997—), 男，硕士研究生，研究方向为对称密码设计与分析. E-mail：lujianwei1997@163.com
  • 基金资助:
    国家自然科学基金资助项目(61802437)

Research on cryptographic properties of generalized SIMON-like round functions

Jianwei LU1(),Jizhou REN2,Jie GUAN1   

  1. 1. Cryptographic Engineering Academy, Strategic Support Forces Information Engineering University, Zhengzhou 450001, Henan, China
    2. College of Engineering Computing & Cybernetics, Australian National University, Canberra 2600, Australia
  • Received:2022-03-16 Online:2023-09-20 Published:2023-09-08

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摘要：

在SIMON类非线性函数的基础上进行扩展, 得到一种广义的非线性函数Fabcdn(X), 结构为(x<<<a)&(x<<<b)⊕(x<<<c)&(x<<<d), 并分析其差分和线性等密码学性质。给出差分矩阵的秩、输出差分与差分概率之间的对应关系; 给出差分概率的取值为0或1/2r, 其中r ∈ [0, n-1];证明当输出差分β=0时差分概率非0;给出特殊移位参数选取下, 差分概率取到1/2时差分对应的结构和计数公式。利用不相交化算法, 将相关优势取值问题转化为不相交二次型中二次项的个数计算问题, 给出相关优势的取值范围。本文的结论为轻量级非线性函数的构造提供一种新方法。

关键词: SIMON算法, 非线性函数, 循环移位, 差分性质, 线性性质

Abstract:

Based on the SIMON-like nonlinear function, a generalized nonlinear function Fabcdn(X) is obtained, and the structure is as follows: (x<<<a)&(x<<<b)⊕(x<<<c)&(x<<<d). The cryptographic properties of Fabcdn(X) such as difference and linearity are given. The corresponding relationship between the rank of the difference matrix, output difference and difference probability is given; the value of the difference probability is 0 or 1/2r, where r ∈ [0, n-1]; the difference probability is non-zero when β=0; under the selection of special shift parameters, the corresponding difference structure and counting formula are given when the difference probability is 1/2. By using the disjoint algorithm, the problem of the correlated advantage value can be transformed into calculating the number of quadratic terms in the disjoint quadratic form, and the value range of the correlated advantage is given. These conclusions provide a new method for the construction of lightweight nonlinear functions.

Key words: SIMON algorithm, nonlinear function, cyclic shift, differential property, linear property

中图分类号: 

  • TN918.1

表1

相关优势点为1/2的计数表"

n F051n F0512n F182n F1827n
9 72 0 72 0
10 640 0 80 0
11 88 0 88 0
12 96 0 96 0
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12 YANG G, ZHU B, SUDER V, et al. The simeck family of lightweight block ciphers[C]//International Workshop on Cryptographic Hardware and Embedded Systems, Saint-Malo: Springer, 2015: 307-329.
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14 SHI D P, SUN S W, SASAKI Y, et al. Correlation of quadratic Boolean functions: cryptanalysis of all versions of full MORUS[C]// Annual International Cryptology Conference, Santa Barbara: Springer, 2019: 180-209.
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