A note on fast algebraic attacks and higher order nonlinearities
In this note, we deduce a bound between fast algebraic immunity and higher order nonlinearity (it is the first time that a bound between these two cryptographic criteria is given), and find that a Boolean function should have high r-order nonlinearity to resist fast algebraic attacks. As a corollary, we find that no matter how much effort we make, the Tu-Deng functions cannot be repaired in a stan