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A note on fast algebraic attacks and higher order nonlinearities

Wang, Qichun and Johansson, Thomas LU orcid (2011) INSCRYPT 2010 In Lecture Notes in Computer Science 6584. p.404-414
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.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Boolean functions, Stream ciphers, Fast algebraic attacks, High order nonlinearities
host publication
Information Security and Cryptology : 6th International Conference, Inscrypt 2010, Shanghai, China, October 20-24, 2010, Revised Selected Papers - 6th International Conference, Inscrypt 2010, Shanghai, China, October 20-24, 2010, Revised Selected Papers
series title
Lecture Notes in Computer Science
volume
6584
pages
404 - 414
publisher
Springer
conference name
INSCRYPT 2010
conference location
Shanghai, China
conference dates
2010-10-20 - 2010-10-24
external identifiers
  • scopus:79960806168
ISSN
1611-3349
0302-9743
ISBN
978-3-642-21518-6
978-3-642-21517-9
DOI
10.1007/978-3-642-21518-6_28
language
English
LU publication?
yes
id
039d4777-95a6-4bfe-87c5-ede36621c2e6 (old id 1789337)
date added to LUP
2016-04-04 14:07:50
date last changed
2024-02-12 10:37:06
@inbook{039d4777-95a6-4bfe-87c5-ede36621c2e6,
  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.}},
  author       = {{Wang, Qichun and Johansson, Thomas}},
  booktitle    = {{Information Security and Cryptology : 6th International Conference, Inscrypt 2010, Shanghai, China, October 20-24, 2010, Revised Selected Papers}},
  isbn         = {{978-3-642-21518-6}},
  issn         = {{1611-3349}},
  keywords     = {{Boolean functions; Stream ciphers; Fast algebraic attacks; High order nonlinearities}},
  language     = {{eng}},
  pages        = {{404--414}},
  publisher    = {{Springer}},
  series       = {{Lecture Notes in Computer Science}},
  title        = {{A note on fast algebraic attacks and higher order nonlinearities}},
  url          = {{http://dx.doi.org/10.1007/978-3-642-21518-6_28}},
  doi          = {{10.1007/978-3-642-21518-6_28}},
  volume       = {{6584}},
  year         = {{2011}},
}