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代数免疫度是针对代数攻击而提出来的一个新的密码学概念.要能够有效地抵抗代数攻击,密码系统中使用的布尔函数必须具有平衡性、较高的代数次数、较高的非线性度和较高的代数免疫度等.为了提高布尔函数的密码学性能,通过布尔函数仿射等价的方法,找出了所有具有最优代数免疫度的三变元布尔函数.由这些具有最优代数免疫度的三变元非线性布尔函数,递归构造了一类代数免疫度最优、代数次数较高的平衡布尔函数.给出了这类布尔函数非线性度的一个下界,偶数变元时,其下界严格大于Lobanov给出的下界.
Algebraic immunity is a new concept of cryptography proposed for algebraic attacks.In order to be able to effectively resist algebraic attacks, the Boolean functions used in cipher systems must be balanced, high algebraic times, and high nonlinearity And higher algebraic immunity, etc. In order to improve the cryptographic performance of Boolean functions, all the three-argument Boolean functions with the optimal algebraic immunity are found by the affine equivalent method of Boolean functions, Algebraic immunity of the three-argument nonlinear Boolean functions, a class of recursive construction of a class of optimal balance of algebraic immunity, the higher the number of algebraic Boolean function of the nonlinearity of such Boolean functions of a lower bound, even when the number of arguments , The lower bound is strictly greater than the lower bound given by Lobanov.