Construction of Vectorial Boolean Functions with Provable Differential-Linear Uniformity and High Nonlinearity

Block cipher is used as an important technology to protect data confidentiality and user privacy in many fields such as machine learning and cloud storage. Vectorial Boolean functions often serve as the core nonlinear components in block ciphers. When designing cryptographic algorithms, it is crucial to maximize the nonlinearity of vectorial Boolean functions and minimize their autocorrelation to resist relevant cryptographic attacks, to ensure the security of the cryptographic system. In this paper, based on modified Maiorana-McFarland bent functions, we construct a balanced vectorial Boolean functions. Furthermore, we utilize optimal single-weight linear codes to provide specific constructions, and proved that they have high nonlinearity and good differential-linear uniformity.