On the confusion and diffusion properties of Maiorana-McFarland's and extended Maiorana-McFarland's functions

摘要

A practical problem in symmetric cryptography is finding constructions of Boolean functions leading to reasonably large sets of functions satisfying some desired cryptographic criteria. The main known construction, called Maiorana-McFarland, has been recently extended. Some other constructions exist, but lead to smaller classes of functions. Here, we study more in detail the nonlinearities and the resiliencies of the functions produced by all these constructions. Further we see how to obtain functions satisfying the propagation criterion (among which bent functions) with these methods, and we give a new construction of bent functions based on the extended Maiorana-McFarland's construction.