Construction of Boolean Functions Based on Partial Walsh Spectral

In deep learning as a service, user data flows through the client and cloud, which inevitably pose a risk of being attacked. Block cipher algorithms are widely used to encrypt large datasets and protect plaintext from attackers. Boolean functions acting as nonlinear components in block ciphers play a crucial role in ensuring security. This paper explores how to construct Boolean functions given some known partial Walsh spectrum. We propose a method for constructing all Boolean functions that satisfy the given conditions based on partial Walsh spectrum.Compared to exhaustive search, this method significantly reduces computational complexity. A construction example of a 5-variable Boolean function verifies the correctness of this method. Furthermore, this paper investigates the impact of random conditions on the number of constructed Boolean functions.