@inbook{039d477795a64bfe87c5ede36621c2e6,
title = "A note on fast algebraic attacks and higher order nonlinearities",
abstract = "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.",
keywords = "Boolean functions, Stream ciphers, Fast algebraic attacks, High order nonlinearities",
author = "Qichun Wang and Thomas Johansson",
year = "2011",
doi = "10.1007/978-3-642-21518-6_28",
language = "English",
isbn = "978-3-642-21517-9",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "404--414",
booktitle = "Information Security and Cryptology",
address = "Germany",
note = "INSCRYPT 2010 ; Conference date: 20-10-2010 Through 24-10-2010",
}