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 σ f =∑ v Δ f 2 ( v ), where Δ f ( v )=∑ x (−1) f ( x )⊕ f ( x ⊕ v ). 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].