Boolean functions with five controllable cryptographic properties

The strict avalanche criterion (SAC) was introduced by Webster and Tavares [10] in a study of cryptographic design criteria. This is an indicator for local property. In order to improve the global analysis of cryptographically strong functions, Zhang and Zheng [ 11] introduced the global avalanche characteristics (GAC). The sum-of-squares indicator related to the GAC is defined as sigma(f) = Sigma(nu)Delta(f)(2)(nu), where Delta(f)(nu) = Sigma(x)(-1)(f(x)+ f(x + nu)). In this paper, we give a few methods to construct Boolean functions controlling five good cryptographic properties, namely balancedness, good local and GAC, high nonlinearity and high algebraic degree. We improve upon the results of Stanica [ 8] and Zhang and Zheng [11].