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Further Results Related to Generalized Nonlinearity

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Progress in Cryptology — INDOCRYPT 2002 (INDOCRYPT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2551))

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Abstract

In this paper we consider the generalized nonlinearity of Boolean functions. First we characterize n-variable Boolean functions f : GF(2n) ? GF(2) such that f(xc) = f(x) for any c coprime to 2n-1, where c is a cyclotomic coset leader modulo 2n-1. This guarantees that the generalized nonlinearity of these functions are same as their nonlinearity itself. Boolean functions with very high generalized nonlinearity have been constructed by Youssef and Gong in 2001 which uses repetition of same binary string. Here we study the trace representation for this set of functions. Further we discuss the definition of generalized nonlinearity in terms of standard truth table realization of a Boolean function and raise important issues in this direction.

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Author information

Authors and Affiliations

  1. Mathematics Group, Birla Institute of Technology & Science, 333 031, Pilani, Rajasthan, INDIA

    Sugata Gangopadhyay

  2. Applied Statistics Unit, Indian Statistical Institute, 203, B T Road, 700 108, Calcutta, INDIA

    Subhamoy Maitra

Authors
  1. Sugata Gangopadhyay
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  2. Subhamoy Maitra
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Editor information

Editors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Alfred Menezes

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

    Palash Sarkar

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© 2002 Springer-Verlag Berlin Heidelberg

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Gangopadhyay, S., Maitra, S. (2002). Further Results Related to Generalized Nonlinearity. In: Menezes, A., Sarkar, P. (eds) Progress in Cryptology — INDOCRYPT 2002. INDOCRYPT 2002. Lecture Notes in Computer Science, vol 2551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36231-2_21

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  • DOI: https://doi.org/10.1007/3-540-36231-2_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00263-5

  • Online ISBN: 978-3-540-36231-9

  • eBook Packages: Springer Book Archive

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