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Construction of Cryptographically Important Boolean Functions

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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

Boolean functions are used as nonlinear combining functions in certain stream ciphers. A Boolean function is said to be correlation immune if its output leaks no information about its input values. Balanced correlation immune functions are called resilient functions. Finding methods for easy construction of resilient functions with additional properties is an active research area. Maitra and Pasalic[3] have constructed 8-variable 1-resilient Boolean functions with nonlinearity 116. Their technique interlinks mathematical results with classical computer search. In this paper we describe a new technique to construct 8-variable 1-resilient Boolean functions with the same nonlinearity. Using a similar technique, we directly construct 10-variable (resp. 12-variable), 1-resilient functions with nonlinearity 488 (resp. 1996). Finally, we describe some results on the construction of n-variable t-resilient functions with maximum nonlinearity.

This research was supported by ReX program of Stichting Nlnet, Netherlands.

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Author information

Authors and Affiliations

  1. Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, 700108, Calcutta, INDIA

    Soumen Maity

  2. Department of Information Technology, Lund University, P.O. Box 118, S-221 00, Lund, SWEDEN

    Thomas Johansson

Authors
  1. Soumen Maity
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  2. Thomas Johansson
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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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Maity, S., Johansson, T. (2002). Construction of Cryptographically Important Boolean Functions. 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_19

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  • DOI: https://doi.org/10.1007/3-540-36231-2_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00263-5

  • Online ISBN: 978-3-540-36231-9

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