A New Construction of Weightwise Perfectly Balanced Functions with High Weightwise Nonlinearity

The FLIP cipher was proposed at Eurocrypt 2016 for the purpose of meliorating efficiency fully homomorphic cryptosystems. Weightwise perfectly balanced Boolean functions meet balancedness requirement filter function in ciphers, and construction them has attracted serious attention from researchers. Nevertheless, literature is still thin. Modifying supports with a low degree general technique whose key problem to find class available low-degree functions. We first seek out quadratic then, based on these functions, present new weightwise by adopting an iterative approach. It worth mentioning that we construct have good performance nonlinearity. In particular, some p-weight nonlinearities achieve highest values small number variables.