Research on Linear Properties of SIMON Class Nonlinear Function

Jie GUAN; Jianwei LU

doi:10.11999/JEIT200999

Volume 43 Issue 11

Nov. 2021

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Jie GUAN, Jianwei LU. Research on Linear Properties of SIMON Class Nonlinear Function[J]. Journal of Electronics & Information Technology, 2021, 43(11): 3359-3366. doi: 10.11999/JEIT200999

Citation:

Jie GUAN, Jianwei LU. Research on Linear Properties of SIMON Class Nonlinear Function[J]. Journal of Electronics & Information Technology, 2021, 43(11): 3359-3366. doi: 10.11999/JEIT200999

Jie GUAN, Jianwei LU. Research on Linear Properties of SIMON Class Nonlinear Function[J]. Journal of Electronics & Information Technology, 2021, 43(11): 3359-3366. doi: 10.11999/JEIT200999

Citation:

Jie GUAN, Jianwei LU. Research on Linear Properties of SIMON Class Nonlinear Function[J]. Journal of Electronics & Information Technology, 2021, 43(11): 3359-3366. doi: 10.11999/JEIT200999

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Research on Linear Properties of SIMON Class Nonlinear Function

doi: 10.11999/JEIT200999

Jie GUAN,
Jianwei LU^,

Strategic Support Forces Information Engineering University, Zhengzhou 450001, China

Funds: The National Natural Science Foundation of China (61572516)

Received Date: 2020-11-25
Rev Recd Date: 2021-03-30

Available Online: 2021-05-06

Publish Date: 2021-11-23

Abstract

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.
- SIMON algorithm,
- Linear property,
- Cyclic shift,
- S-box

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References(20)

References

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