Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this note,  deduce a bound beten fast algebraic immunity and higher order nonlinearity (it is the first time that a bound beten 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,  find that no matter how much effort  make, the Tu-Deng functions cannot be repaired in a standard way to behave ll against fast algebraic attacks. Therefore,  should give up repairing this class of Boolean functions and try to find other classes of functions with good cryptographic properties or to prove that the Carlet-Feng function behaves ll.
['Qichun Wang', 'Thomas Johansson']
I am writing a research paper on a idea A note on fast algebraic attacks and higher order nonlinearities
[{"from": "human", "value": "I am writing a research paper on a idea A note on fast algebraic attacks and higher order nonlinearities"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this note,  deduce a bound beten fast algebraic immunity and higher order nonlinearity (it is the first time that a bound beten 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,  find that no matter how much effort  make, the Tu-Deng functions cannot be repaired in a standard way to behave ll against fast algebraic attacks. Therefore,  should give up repairing this class of Boolean functions and try to find other classes of functions with good cryptographic properties or to prove that the Carlet-Feng function behaves ll."}]