Cryptographic properties of monotone Boolean functions

The article of record as published may be found at http://dx.doi.org/10.1515/jmc-2014-0030We prove various results on monotone Boolean functions. In particular, we prove a conjecture proposed recently, stating that there are no monotone bent Boolean functions. Further, we give an upper bound on the nonlinearity of monotone functions in odd dimension, we describe the Walsh–Hadamard spectrum and investigate some other cryptographic properties of monotone Boolean functions