JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (9): 51-58.doi: 10.6040/j.issn.1671-9352.0.2022.162

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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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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

CLC Number: 

  • TN918.1

Table 1

Counting table with 1/2 correlation advantage points"

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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