A random fault or a malicious attack can compromise the security of decryption systems. Using a stable and monotonous feedback shift register (FSR) as the main building block in a convolutional decoder can limit some error propagation. This work foucus on the synthesis of reliable (i.e., globally stable and monotonous) FSRs using the Boolean networks (BNs) method. First, we obtain an algebraic expression of the FSRs, based on which one necessary and sufficient condition for the monotonicity of the FSRs is given. Then, we obtain the upper bound of the number of cyclic attractors for monotonous FSRs. Furthermore, we propose one method of constructing n-stage reliable FSRs, and figure out that the number of reliable FSRs is \({{{2^{{2^{n - 4}}}}} \over {\phi (n)}}\) (n > 5) times of that constructed by the existing method, where ϕ denotes the Euler’s totient function. Finally, the proposed method and the obtained results are verified by some examples.

随机故障或恶意攻击可能会损害解密系统的安全性。在卷积解码器中，使用稳定且单调的反馈移位寄存器（FSR）作为主要构件可能会限制某些错误传播。这项工作着重于使用布尔网络（BNs）方法合成可靠（即，全局稳定和单调）的FSR。首先，我们获得了FSR的代数表达式，在此基础上给出了FSR的单调性的一个充要条件。然后，我们获得单调FSR的循环吸引子数的上限。此外，我们提出了一种构造n级可靠FSR的方法，并得出可靠FSR的数量为\（{{{2 ^ {{2 ^ {n-4}}}}}} n）}} \）（n> 5）乘以现有方法构造的倍数，其中ϕ表示欧拉的totient函数。最后，通过实例验证了该方法的有效性。