为了保证合法用户的隐私,基于Teranisi提出的k次认证机制(k-TAA),利用Brands提出的表示问题不可解的猜想,构造了一个具有公平的匿名性的k次认证机制k-TFAA。该机制除了拥有k-TAA机制的所有特性外,还增加了一个可信方,该可信方可以有效追踪非法使用服务的用户的身份,保证了整个机制的完备性和安全性。最后,对该机制的各个特性进行了讨论。 In order to ensure the privacy of legitimate users, based on the k-ary authentication mechanism proposed by Teranisi (k-TAA), k-TFAA, a fair anonymity k-th authentication mechanism, is constructed by using the conjecture proposed by Brands to represent the problem. In addition to all the features of the k-TAA mechanism, this mechanism adds a trusted party that can effectively track the identity of users who illegally use the service and ensure the completeness and security of the entire mechanism. Finally, the various characteristics of the mechanism are discussed.