Cryptographic properties of monotone Boolean functions

Abstract

We 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.

Keywords

• boolean functions
• bent and monotone functions
• walsh–hadamard spectrum
• algebraic immunity
• 06e30
• 94c10
• 94a60
• 11t71
• 05e99