引入半环描述输入存贮有限自动机及其复合运算,对非线性有限自动机的弱可逆性理论进行了代数化处理,提出相对基本分解并引出非线性核的概念等。作为应用,对FAPKC3公钥体制(文献[1])提出称之为“非线性核攻击”的攻击方法,由此提出该体制中私钥的非线性核必须符合的三条准则,并指出是否存在以及如何构造足够多的符合这些准则的密钥是有待研究的问题。 The semi-loop description of input storage finite automaton and its composite operation is introduced. The weakly invertible theory of nonlinear finite automaton is algebraically processed, and the concept of relative basic decomposition and nonlinear kernel is proposed. As an application, an attack method called “non-linear nuclear attack” is put forward on the FAPKC3 public key system (Reference [1]), from which three criteria that the nonlinear kernel of the private key in the system must meet are pointed out, And how to construct enough keys to meet these criteria is a problem to be studied.