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Some results on fast algebraic attacks and higher-order non-linearities

Wang, Q.; Johansson, Thomas LU and Kan, H. (2012) In IET Information Security 6(1). p.41-46
Abstract
In this study, the authors investigate the resistance of Boolean functions against fast algebraic attacks and deduce a bound between fast algebraic immunity and higher-order non-linearity (it is the first time that a bound between these two cryptographic criteria is given). The authors then show that the fast algebraic immunity of the following two classes of Boolean functions is not good: (a) The repaired functions of the Tu-Deng function proposed by Carlet. The Tu-Deng function has optimum algebraic degree, optimum algebraic immunity and a very good non-linearity. However, it is weak against fast algebraic attacks. Carlet found this weakness and also tried to repair it. (b) An infinite class of balanced functions proposed by Tang et al.,... (More)
In this study, the authors investigate the resistance of Boolean functions against fast algebraic attacks and deduce a bound between fast algebraic immunity and higher-order non-linearity (it is the first time that a bound between these two cryptographic criteria is given). The authors then show that the fast algebraic immunity of the following two classes of Boolean functions is not good: (a) The repaired functions of the Tu-Deng function proposed by Carlet. The Tu-Deng function has optimum algebraic degree, optimum algebraic immunity and a very good non-linearity. However, it is weak against fast algebraic attacks. Carlet found this weakness and also tried to repair it. (b) An infinite class of balanced functions proposed by Tang et al., having optimum algebraic degree, optimum algebraic immunity and a very high non-linearity. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
IET Information Security
volume
6
issue
1
pages
41 - 46
publisher
Institution of Engineering and Technology
external identifiers
  • wos:000312961600006
  • scopus:84863373976
ISSN
1751-8717
DOI
10.1049/iet-ifs.2011.0090
language
English
LU publication?
yes
id
95d84567-ead5-4564-a8f0-6d86a2d515c6 (old id 2432928)
date added to LUP
2012-04-03 10:37:50
date last changed
2017-03-26 04:25:49
@article{95d84567-ead5-4564-a8f0-6d86a2d515c6,
  abstract     = {In this study, the authors investigate the resistance of Boolean functions against fast algebraic attacks and deduce a bound between fast algebraic immunity and higher-order non-linearity (it is the first time that a bound between these two cryptographic criteria is given). The authors then show that the fast algebraic immunity of the following two classes of Boolean functions is not good: (a) The repaired functions of the Tu-Deng function proposed by Carlet. The Tu-Deng function has optimum algebraic degree, optimum algebraic immunity and a very good non-linearity. However, it is weak against fast algebraic attacks. Carlet found this weakness and also tried to repair it. (b) An infinite class of balanced functions proposed by Tang et al., having optimum algebraic degree, optimum algebraic immunity and a very high non-linearity.},
  author       = {Wang, Q. and Johansson, Thomas and Kan, H.},
  issn         = {1751-8717},
  language     = {eng},
  number       = {1},
  pages        = {41--46},
  publisher    = {Institution of Engineering and Technology},
  series       = {IET Information Security},
  title        = {Some results on fast algebraic attacks and higher-order non-linearities},
  url          = {http://dx.doi.org/10.1049/iet-ifs.2011.0090},
  volume       = {6},
  year         = {2012},
}