CAJ | 학술논문

非线性函数在编码和密码领域中扮演着非常重要的角色,衡量函数的非线性性质很重要。非线性度和差分概率是衡量函数非线性性质的重要指标,差分概率均匀的函数称为具有完全非线性的函数。文中改进了Carlet和Ding所给出的完全非线性函数的非线性度的上界和下界,提出了更好的界的优化问题模型。
비선성함수재편마화밀마영역중분연착비상중요적각색,형량함수적비선성성질흔중요。비선성도화차분개솔시형량함수비선성성질적중요지표,차분개솔균균적함수칭위구유완전비선성적함수。문중개진료Carlet화Ding소급출적완전비선성함수적비선성도적상계화하계,제출료경호적계적우화문제모형。
Nonlinear functions play a significant role in coding and cryptography,and is critical to evaluate how nonlinear a function is. Nonlinearity and differential probability are both of importance in quantifying the nonlinear extent of a function. A function with uniform differential probability is said to have perfect nonlinearity or to be perfectly nonlinear. In this manuscript,the upper and lower bounds of nonlinearity of perfectly nonlinear functions given by Carlet and Ding are improved,and an optimum question model for better nonlinearity bounds is proposed.