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A New Construction of Boolean Functions with Maximum Algebraic Immunity

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Information Security (ISC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5735))

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Abstract

Because of the algebraic attacks, a high algebraic immunity is now an important criteria for Boolean functions used in stream ciphers. In this paper, we study the construction of Boolean functions with maximum algebraic immunity. We first present a new method to construct Boolean functions, in any number of variables, with maximum algebraic immunity(AI), and we also improve our algorithm to construct balanced functions with optimum algebraic immunity for any even number of variables. Furthermore, the enumeration and algebraic degree of the constructed Boolean functions are investigated.

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Author information

Authors and Affiliations

  1. Department of Mathematics and System Science, National University of Defence Technology, Changsha, 410073, China

    Deshuai Dong, Shaojing Fu, Longjiang Qu & Chao Li

  2. State Key Laboratory of Mobile Communication, Southeast University, Nanjing, 210018, China

    Longjiang Qu & Chao Li

Authors
  1. Deshuai Dong
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  2. Shaojing Fu
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  3. Longjiang Qu
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  4. Chao Li
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Editor information

Editors and Affiliations

  1. Dipartimento di Tecnologie dell’ Informazione, Università degli Studi di Milano, Via Bramante 65, 26013, Crema, (CR), Italy

    Pierangela Samarati

  2. Computer Science Department, Google Inc. and Columbia University, Room 464, S.W. Mudd Building, 10027, New York, NY, USA

    Moti Yung

  3. Information Security Group, Pisa Research Area, Istituto di Informatica e Telematica - IIT Consiglio Nazionale delle Ricerche - C.N.R., Via. G. Moruzzi 1, 56125, Pisa, Italy

    Fabio Martinelli

  4. Dipartimento di Tecnologie dell’Informazione, Università degli Studi di Milano, Via Bramante, 65, 26013, Crema, (CR), Italy

    Claudio A. Ardagna

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Dong, D., Fu, S., Qu, L., Li, C. (2009). A New Construction of Boolean Functions with Maximum Algebraic Immunity. In: Samarati, P., Yung, M., Martinelli, F., Ardagna, C.A. (eds) Information Security. ISC 2009. Lecture Notes in Computer Science, vol 5735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04474-8_15

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  • DOI: https://doi.org/10.1007/978-3-642-04474-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04473-1

  • Online ISBN: 978-3-642-04474-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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