完美代数免疫( PAI)的布尔函数能够抵御代数攻击和快速代数攻击。 PAI函数的构造是目前布尔函数研究最具挑战性的问题之一。利用布尔函数的双变元表达式和有限域理论，基于Carlet-Feng函数提出一种新的偶数元布尔函数的一般性构造。证明由该构造得到的函数具有一阶弹性和至少次优代数免疫度等密码学性质，给出其代数免疫度达到最优时的充分条件，并比较该类函数、Carlet-Feng函数和由一阶级联方式构造的函数在6~16之间的所有偶数变元下抵抗快速代数攻击能力。实验结果表明，该类函数能更好地抵抗快速代数攻击，且具有几乎完美的代数免疫性能。%A Perfect Algebraic Immune( PAI) function is a Boolean function with perfect immunity against algebraic and fast algebraic attacks. Constructing perfect algebraic immune Boolean functions is a very challenging problem in study of Boolean functions at present. Use bivariate representation of Boolean function and theory of fine field to construct a generalized and new class of Boolean functions on even variables based on Carlet-Feng functions. This paper proves that the functions generated by this construction have cryptographic properties such as 1-resiliency and suboptimal algebraic immunity at least and proposes the sufficient condition of achieving optimal algebraic immunity. Compared experimentally with Carlet-Feng functions and the functions constructed by the method of first order concatenation about the capability of resisting fast algebraic attacks on all even variables between 6 and 16,these functions have better immunity against fast algebraic attacks. Experimental results show that they are almost perfect algebraic immune functions.
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