On the nonlinearity profile of cryptographic Boolean functions

Boolean functions play a major role in the construction of symmetric key primitives such as block ciphers, stream ciphers and hash functions. The security of these primitives depends on the cryptographic properties of the Boolean functions used in its construction. Various criteria, including balance, nonlinearity, resiliency and algebraic immunity, have been proposed for measuring the cryptographic strength of Boolean functions. Let criterion C denote the cryptographic property of interest. We define the C-profile of the Boolean function as a measure that shows how this criterion degrades when we fix a subset of the input coordinates of the function. This is interesting from a cryptanalytic point of view, since fixing the coordinates of a cryptosystem is a well known cryptanalysis method. In this paper, we introduce this concept and apply it to the nonlinearity property of the cryptographic Boolean function.