Modifications of Patterson-Wiedemann functions for cryptographic applications

Three basic properties of Boolean functions to be useful for cryptographic purposes are balancedness, high algebraic degree, and high nonlinearity. In addition, strict avalanche criteria and propagation characteristics are required for design of S-boxes. In this correspondence, we introduce methods to modify the Patterson-Wiedemann and bent functions to achieve the above cryptographic properties. In the process, we are able to answer some open questions about Boolean functions.