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Construction of Rotation Symmetric Boolean Functions on Odd Number of Variables with Maximum Algebraic Immunity

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4851))

Abstract

In this paper we present a theoretical construction of Rotation Symmetric Boolean Functions (RSBFs) on odd number of variables with maximum possible algebraic immunity (AI) and further these functions are not symmetric. Our RSBFs are of better nonlinearity than the existing theoretical constructions with maximum possible AI. To get very good nonlinearity, which is important for practical cryptographic design, we generalize our construction to a construction cum search technique in the RSBF class. We find 7, 9, 11 variable RSBFs with maximum possible AI having nonlinearities 56, 240, 984 respectively with very small amount of search after our basic construction.

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Authors and Affiliations

  1. Applied Statistics Unit, Indian Statistical Institute, 203 B T Road, Kolkata 700108, India

    Sumanta Sarkar & Subhamoy Maitra

Authors
  1. Sumanta Sarkar
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  2. Subhamoy Maitra
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Serdar Boztaş Hsiao-Feng (Francis) Lu

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Sarkar, S., Maitra, S. (2007). Construction of Rotation Symmetric Boolean Functions on Odd Number of Variables with Maximum Algebraic Immunity. In: Boztaş, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_32

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  • DOI: https://doi.org/10.1007/978-3-540-77224-8_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77223-1

  • Online ISBN: 978-3-540-77224-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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