A novel synthesis method for reliable feedback shift registers via Boolean networks

Abstract

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.