Abstract
Studying algebraic immunity of Boolean functions is recently a very important research topic in cryptography. It is recently proved by Courtois and Meier that for any Boolean function of n-variable the maximum algebraic immunity is ⌈ n 2 ⌉ . We found a large subclass of Maiorana McFarland bent functions on n-variable with a proven low level of algebraic immunity ⩽ ⌈ n 4 ⌉ + 2 . To the best of our knowledge we provide for the first time a new upper bound for algebraic immunity for a nontrivial class of Boolean functions. We also discuss that this result has some fascinating implications.
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