On some properties of the curvature and nondegeneracy of Boolean functions

The paper is concerned with the problem of obtaining exact formulas and bounds for the curvature (i.e., the sum of modules of Walsh coefficients) and nondegeneracy (parameter related to the resistance of a Boolean function against some method of analysis) of some classes of cryptographic Boolean functions. Moreover, for these classes we determine other relevant cryptographic parameters as nonlinearity, algebraic degree and distance to linear structures. Also, we extend the notion of curvature to S-Boxes. For several nonlinear transforms used in actual symmetric cryptographic algorithms we investigate the properties of some parameters and matrices connected with the curvature of Boolean functions.