关键词: 旋转对称布尔函数, 弹性阶, 非线性度, 代数次数, 全局雪崩特征

Abstract:

Rotational Symmetric Boolean Function(RSBF) possess the advantages of simple structure, fast operation speed and high resource utilization. Using RSBF that take into account multiple security indicators as the nonlinear component of the symmetric cryptographic algorithm, which can effectively guarantee the efficiency and security of the algorithm. The search algorithm based on two importance matrices ${}_{n}\text{A}$ and ${}_{n}B$ was an important way to obtain RSBF, which had the advantages of fast realization and setting target values. This paper designed a search method based on two importance matrices to obtain RSBF that effectively considers five security indicators, including resiliency order $m$, nonlinearity $nl$, algebraic degree $d$, absolute value indicator ${{\Delta }_{f}}$, and sum of squares indicator ${{\sigma }_{f}}$. By using this search method, the 9-variable RSBF of $\left( m,nl,d,{{\Delta }_{f}},{{\sigma }_{f}} \right)=\left( 4,224,4,192,{{2}^{21}} \right)$ and the 8-variable RSBF of $\left( m,nl,d,{{\Delta }_{f}},{{\sigma }_{f}} \right)=\left( 2,112,5,32,{{2}^{17.3}} \right)$, as well as 4, 5, 6 and 7-variable RSBF with excellent comprehensive security indicators were obtained. The results demonstrate that the proposed search method can obtain RSBF with multiple security indicators reaching the ideal bound under the condition that various security indicators mutually restrict each other.

Key words: RSBF, resiliency order, nonlinearity, algeria degree, global avalanche characteristics