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On the Secondary Constructions of Resilient and Bent Functions

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Coding, Cryptography and Combinatorics

Part of the book series: Progress in Computer Science and Applied Logic ((PCS,volume 23))

Abstract

We first give a survey of the known secondary constructions of Boolean functions, permitting to obtain resilient functions achieving the best possible trade-offs between resiliency order, algebraic degree and nonlinearity (that is, achieving Siegenthaler’s bound and Sarkar et al.’s bound). We introduce then, and we study, a general secondary construction of Boolean functions. This construction includes as particular cases the known secondary constructions previously recalled. We apply this construction to design more numerous functions achieving optimum trade-offs between the three characteristics (and additionally having no linear structure). We conclude the paper by indicating generalizations of our construction to Boolean and vectorial functions, and by relating it to a known secondary construction of bent functions.

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Author information

Authors and Affiliations

  1. INRIA Projet CODES, BP 105, F-78153, Le Chesnay Cedex, France

    Claude Carlet

  2. GREYC (Caen) and the University of Paris 8, France

    Claude Carlet

Authors
  1. Claude Carlet
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Keqin Feng

  2. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter  & Chaoping Xing  & 

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© 2004 Springer Basel AG

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Carlet, C. (2004). On the Secondary Constructions of Resilient and Bent Functions. In: Feng, K., Niederreiter, H., Xing, C. (eds) Coding, Cryptography and Combinatorics. Progress in Computer Science and Applied Logic, vol 23. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7865-4_1

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  • DOI: https://doi.org/10.1007/978-3-0348-7865-4_1

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9602-3

  • Online ISBN: 978-3-0348-7865-4

  • eBook Packages: Springer Book Archive

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