Cryptography and Communications

, Volume 5, Issue 3, pp 179–199 | Cite as

Secondary constructions of Boolean functions with maximum algebraic immunity

  • Konstantinos Limniotis
  • Nicholas Kolokotronis
  • Nicholas Kalouptsidis
Article
  • 380 Downloads

Abstract

The algebraic immunity of cryptographic Boolean functions with odd number of variables is studied in this paper. Proper modifications of functions with maximum algebraic immunity are proved that yield new functions whose algebraic immunity is also maximum. Several results are provided for both the multivariate and univariate representation, and their applicability is shown on known classes of Boolean functions. Moreover, new efficient algorithms to produce functions of guaranteed maximum algebraic immunity are developed, which further extend and generalize well-known constructions in this area. It is shown that high nonlinearity as well as good behavior against fast algebraic attacks are also achievable in several cases.

Keywords

Algebraic attack Algebraic immunity Annihilators  Boolean functions Cryptography 

Mathematics Subject Classifications (2000)

94A60 06E30 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Konstantinos Limniotis
    • 1
    • 2
  • Nicholas Kolokotronis
    • 3
  • Nicholas Kalouptsidis
    • 2
  1. 1.Hellenic Data Protection AuthorityAthensGreece
  2. 2.Department of Informatics and TelecommunicationsNational and Kapodistrian University of AthensAthensGreece
  3. 3.Department of Computer Science and TechnologyUniversity of PeloponneseTripolisGreece

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