Resumen
The denition of the propagation criterion of Boolean functions was introduced by Bart Preneel and co-authors. This concept represent a set of vectors, for which the corresponding derivatives of a Boolean function are balanced. It characterizes the statistical properties of a family of Boolean function derivatives that play an important role in the cryptosystem analysis and synthesis. For some classes of Boolean functions, the propagation criterion determines their extreme properties. For example, the propagation criterion of bent functions determines their maximum nonlinearity. However, the main disadvantage of bent functions is the lack of balancedness, which means that such functions do not have a uniform output distribution. The construction of balanced Boolean functions having a high nonlinearity and a large number of vectors satisfying the propagation criterion is still an open problem in cryptography. In this paper we obtain exact values and estimates of the number of vectors satisfying the propagation criterion of Boolean functions from well- known cryptographic classes, such as plateaued functions, Maiorana-McFarland functions, quadratic functions, algebraic degenerate functions and multiane functions. We also show that the number of vectors satisfying the propagation criterion is an invariant for the extension of the general affine group of the first degree.