On Various Nonlinearity Measures for Boolean Functions
Joan Boyar, Magnus Find, René Peralta
Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences.

A necessary condition for the security of cryptographic functions is to be ``sufficiently distant'' from linear, and cryptographers have proposed several measures for this distance. In this paper, we show that six common measures, nonlinearity, algebraic degree, annihilator immunity, algebraic thickness, normality, and multiplicative complexity, are incomparable in the sense that for each pair of measures, μ12, there exist functions f1,f2 with f1 being more nonlinear than f2 according to > μ1, but less nonlinear according to μ2. We also present new connections between two of these measures. Additionally, we give a lower bound on the multiplicative complexity of collision-free functions.

Last modified: Wed Apr 5 14:05:45 CEST 2017