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A note on fast algebraic attacks and higher order nonlinearities. (English) Zbl 1295.94150
Lai, Xuejia (ed.) et al., Information security and cryptology. 6th international conference, Inscrypt 2010, Shanghai, China, October 20–24, 2010. Revised selected papers. Berlin: Springer (ISBN 978-3-642-21517-9/pbk). Lecture Notes in Computer Science 6584, 404-414 (2011).
Summary: 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 standard way to behave well against fast algebraic attacks. Therefore, we 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 well.
For the entire collection see [Zbl 1218.94005].

##### MSC:
 94A60 Cryptography
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