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

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

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  • Author(s): Q. Wang 1 ; T. Johansson 2 ; H. Kan 3
    • View affiliations
    • Affiliations: 1: Department of Mathematics, Hunan University of Science and Engineering, Yongzhou, People's Republic of China
      2: Department of Electrical and Information Technology, Lund University, Lund, Sweden
      3: Shanghai Key Lab of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, People's Republic of China
  • Source: Volume 6, Issue 1, March 2012, p. 41 – 46
    DOI:  10.1049/iet-ifs.2011.0090 , Print ISSN 1751-8709, Online ISSN 1751-8717
© The Institution of Engineering and Technology
Published

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.

Inspec keywords: cryptography; Boolean functions

Other keywords: Boolean functions; fast-algebraic immunity; balanced functions; optimum algebraic degree; optimum algebraic immunity; Tu-Deng function; fast-algebraic attacks; cryptographic criteria; higher-order nonlinearities

Subjects: Algebra; Cryptography theory; Algebra; Cryptography

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