关杰,
卢健伟,战略支援部队信息工程大学 郑州 450001
基金项目:国家自然科学基金(61572516)
详细信息 中图分类号:TN918.1
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被引次数:0
出版历程
收稿日期:2020-11-25
修回日期:2021-03-30
网络出版日期:2021-05-06
刊出日期:2021-11-23
Research on Linear Properties of SIMON Class Nonlinear Function
Jie GUAN,
Jianwei LU,Strategic Support Forces Information Engineering University, Zhengzhou 450001, China
Funds:The National Natural Science Foundation of China (61572516)
摘要 摘要:SIMON算法是由美国国家安全局(NSA)在2013 年推出的一簇轻量级分组密码算法，具有实现代价低、安全性能好等优点，其轮函数采用了
$F(x) = (x < < < a){{\& }}(x < < < b) \oplus (x < < < c)$
类型的非线性函数。该文研究了移位参数(
a,
b,
c)一般化时SIMON类算法轮函数的线性性质，解决了这类非线性函数的Walsh谱分布规律问题，证明了其相关优势只可能取到
${{0}}$
或
${2^{ - k}}$
，其中
$k \in Z$
且
${{0}} \le k \le \left\lfloor {{2^{ - 1}}n} \right\rfloor $
，并且对于特定条件下的每一个
$k$
，都存在相应的掩码对使得相关优势等于
${2^{ - k}}$，给出了相关优势取到
${2^{ - 1}}$
时的充分必要条件及掩码对的计数，给出了特定条件下非平凡相关优势取到最小值时的充分必要条件与掩码对的计数。
关键词:SIMON算法/
线性性质/
循环移位/
S盒Abstract:SIMON algorithm is a group of lightweight block cipher algorithms introduced by the National Security Agency (NSA) in 2013. It has the advantages of low implementation cost and good security performance. Its round function adopts
$F(x) = (x < < < a){{\& }}(x < < < b) \oplus (x < < < c)$
type nonlinear function. In this paper, the linear properties of the round function of SIMON algorithm when the shift parameters (
a,
b,
c) are generalized are studied. The problem of Walsh spectrum distribution of this kind of nonlinear function is solved, it is proved that the correlation advantage can only be equal to 0 or
${2^{ - k}}$
, where
$k \in Z$
and
${{0}} \le k \le \left\lfloor {{2^{ - 1}}n} \right\rfloor $
, and for each
k under specific conditions, there are corresponding mask pairs so that the correlation advantage is equal to
${2^{ - k}}$. The necessary and sufficient conditions for the correlation advantage to be equal to 1/2 and the count of mask pairs are given. And the necessary and sufficient conditions for the nontrivial correlation advantage to be equal to the minimum value and the count of mask pairs under specific conditions are also given.
Key words:SIMON algorithm/
Linear property/
Cyclic shift/
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