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Australasian Conference on Information Security and Privacy

ACISP 2011: Information Security and Privacy pp 34–46Cite as

Results on the Immunity of Boolean Functions against Probabilistic Algebraic Attacks

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6812))

Abstract

In this paper, we study the immunity of Boolean functions against probabilistic algebraic attacks. We first show that there are functions, using as filters in a linear feedback shift register based nonlinear filter generator, such that probabilistic algebraic attacks outperform deterministic ones. Then we introduce two notions, algebraic immunity distance and k-error algebraic immunity, to measure the ability of Boolean functions resistant to probabilistic algebraic attacks. We analyze both lower and upper bounds on algebraic immunity distance, and also present the relations among algebraic immunity distance, k-error algebraic immunity, algebraic immunity and high order nonlinearity.

This work was in part supported by the National 973 Program of China under Grant 2011CB302400, the National Natural Science Foundation of China under Grants 10971246 and 60970152, the Grand Project of Institute of Software under Grant YOCX285056 and the CAS Special Grant for Postgraduate Research, Innovation and Practice.

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Author information

Authors and Affiliations

  1. The State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Meicheng Liu & Dongdai Lin

  2. College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China

    Dingyi Pei

Authors
  1. Meicheng Liu
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  2. Dongdai Lin
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  3. Dingyi Pei
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Software Engineering, The University of Melbourne, 3010, Victoria, Australia

    Udaya Parampalli

  2. Qualcomm Incorporated, Suite 301, Level 3, 77 King Street, NSW 2000, Sydney, Australia

    Philip Hawkes

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Liu, M., Lin, D., Pei, D. (2011). Results on the Immunity of Boolean Functions against Probabilistic Algebraic Attacks. In: Parampalli, U., Hawkes, P. (eds) Information Security and Privacy. ACISP 2011. Lecture Notes in Computer Science, vol 6812. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22497-3_3

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  • DOI: https://doi.org/10.1007/978-3-642-22497-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22496-6

  • Online ISBN: 978-3-642-22497-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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