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

  • Sumanta Sarkar
  • Subhamoy Maitra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4851)


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.


Algebraic Immunity Boolean Function Nonlinearity Non-singular Matrix Rotational Symmetry Walsh Spectrum 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Sumanta Sarkar
    • 1
  • Subhamoy Maitra
    • 1
  1. 1.Applied Statistics Unit, Indian Statistical Institute, 203 B T Road, Kolkata 700108India

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