最大代数免疫阶弹性函数的构造

On construction of resilient functions with maximum algebraic immunity

研究最大代数免疫阶弹性函数的构造问题,提出了一种易于编程实现的弹性化思想。将择多函数作为初始函数,利用弹性化方法将其转化为弹性函数,给出了此函数具有最大代数免疫阶的充要条件,并简要讨论了该函数的非线性度及代数次数。

The construction of resilient functions with maximum algebraic immunity was studied by a newmethod of flexibility,which can be carried out by software implementation easily. By means of flexibility,any majority function can be transformed into resilient function. A sufficient and necessary condition on which the resilient function has maximum algebraic immunity was obtained. Moreover,the cryptographic properties of the resilient function,such as nonlinearity and algebraic degree were studied.