Boolean Functions with Five Controllable Cryptographic Properties

The Strict Avalanche Criterion (SAC) was introduced by Webster and Tavares 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 introduced the global avalanche characteristics (GAC). The sum-of-squares indicator related to the GAC is defined as σf = ∑ v ∆ 2 f (v), where ∆f (v) = ∑ x(−1). In this paper, we give a few methods to construct Boolean functions controlling five good cryptographic properties, namely balancedness, good local and global avalanche characteristics, high nonlinearity and high algebraic degree. We improve upon the results of Stănică, and Zhang and Zheng.