Construction of high nonlinearity balanced Boolean functions with good global avalanche characteristics

Block cipher is an important technology to ensure data security and privacy when processing large amounts of sensitive data. Boolean functions with excellent cryptographic characteristics play a special role in block cipher. The construction of Boolean functions satisfying various cryptographic properties is a topic worth studying. In this paper, by modifying the Maiorana-McFarland class, a class of high nonlinearity balanced Boolean functions with good global avalanche characteristic is obtained with fewer constraints. In addition, using this function as a component function of vectorial Boolean functions, we put forward a class of vectorial Boolean functions and prove that this class of functions have the same good property.