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Construction of Perfect Nonlinear and Maximally Nonlinear Multi-output Boolean Functions Satisfying Higher Order Strict Avalanche Criteria

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Progress in Cryptology - INDOCRYPT 2003 (INDOCRYPT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2904))

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Abstract

We consider the problem of constructing perfect nonlinear multi-output Boolean functions satisfying higher order strict avalanche criteria (SAC). Our first construction is an infinite family of 2-ouput perfect nonlinear functions satisfying higher order SAC. This construction is achieved using the theory of bilinear forms and symplectic matrices. Next we build on a known connection between 1-factorization of a complete graph and SAC to construct more examples of 2 and 3-output perfect nonlinear functions. In certain cases, the constructed S-boxes have optimal trade-off between the following parameters: numbers of input and output variables, nonlinearity and order of SAC. In case the number of input variables is odd, we modify the construction for perfect nonlinear S-boxes to obtain a construction for maximally nonlinear S-boxes satisfying higher order SAC. Our constructions present the first examples of perfect nonlinear and maximally nonlinear multioutput S-boxes satisfying higher order SAC. Lastly, we present a simple method for improving the degree of the constructed functions with a small trade-off in nonlinearity and the SAC property. This yields functions which have possible applications in the design of block ciphers.

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Authors and Affiliations

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

    Kishan Chand Gupta & Palash Sarkar

Authors
  1. Kishan Chand Gupta
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  2. Palash Sarkar
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Editors and Affiliations

  1. Dept. of Electrical and Information Technology, Lund University, P.O. Box 118, 221 00, Lund, Sweden

    Thomas Johansson

  2. Indian Statistical Institute, 203 B T Road, 700 108, Kolkata, India

    Subhamoy Maitra

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Gupta, K.C., Sarkar, P. (2003). Construction of Perfect Nonlinear and Maximally Nonlinear Multi-output Boolean Functions Satisfying Higher Order Strict Avalanche Criteria. In: Johansson, T., Maitra, S. (eds) Progress in Cryptology - INDOCRYPT 2003. INDOCRYPT 2003. Lecture Notes in Computer Science, vol 2904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24582-7_8

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  • DOI: https://doi.org/10.1007/978-3-540-24582-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20609-5

  • Online ISBN: 978-3-540-24582-7

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