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Boolean Functions with Maximum Algebraic Immunity Based on Properties of Punctured Reed–Muller Codes

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Cryptography and Information Security in the Balkans (BalkanCryptSec 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9540))

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Abstract

The construction of Boolean functions with an odd number of variables and maximum algebraic immunity is studied in this paper. Starting with any function f obtained by the Carlet–Feng construction, we develop an efficient method to properly modify f in order to provide new functions having maximum algebraic immunity. This new approach, which exploits properties of the punctured Reed–Muller codes, suffices to generate a large number of new functions with maximum algebraic immunity through swapping an arbitrary number of elements between the support of f and its complement.

This work is co–financed by the European Union (European Social Fund) and Greek national funds through the operational program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF). Research funding program THALES: investing in knowledge society through the European Social Fund.

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Acknowledgment

The authors would like to thank the anonymous reviewers for the helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Informatics and Telecommunications, University of Athens, 15785, Athens, Greece

    Konstantinos Limniotis

  2. Hellenic Data Protection Authority, Kifissias 1–3, 11523, Athens, Greece

    Konstantinos Limniotis

  3. Department of Informatics and Telecommunications, University of Peloponnese, 22100, Tripolis, Greece

    Nicholas Kolokotronis

Authors
  1. Konstantinos Limniotis
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  2. Nicholas Kolokotronis
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Correspondence to Konstantinos Limniotis .

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Editors and Affiliations

  1. University of Primorska, Koper, Slovenia

    Enes Pasalic

  2. Technical University of Denmark, Kgs. Lyngby, Denmark

    Lars R. Knudsen

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Limniotis, K., Kolokotronis, N. (2016). Boolean Functions with Maximum Algebraic Immunity Based on Properties of Punctured Reed–Muller Codes. In: Pasalic, E., Knudsen, L. (eds) Cryptography and Information Security in the Balkans. BalkanCryptSec 2015. Lecture Notes in Computer Science(), vol 9540. Springer, Cham. https://doi.org/10.1007/978-3-319-29172-7_1

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  • DOI: https://doi.org/10.1007/978-3-319-29172-7_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29171-0

  • Online ISBN: 978-3-319-29172-7

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