On Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity

Boolean functions and vectorial Boolean functions are the most important nonlinear components of stream ciphers. They should satisfy several criteria such as high nonlinearity, proper resiliency and so on to guarantee the security of the whole system. However, there are some constraints among the criteria, and how to achieve a trade-off between them is an important issue. In this paper, some nonlinear Boolean functions possessing simple algebraic normal form with special Walsh spectrum are proposed. By using these functions, we provide two construction methods on balanced and resilient Boolean functions with high nonlinearity. In addition, based on the disjoint linear codes and vector matrices with special properties, some resilient vectorial Boolean functions with currently best-known nonlinearity have also been given.