International Association for Cryptologic Research

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

Authors:
Kishan Chand Gupta
Palash Sarkar
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URL: http://eprint.iacr.org/2003/198
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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.
BibTeX
@misc{eprint-2003-11911,
  title={Construction of Perfect Nonlinear and Maximally Nonlinear Multi-Output Boolean Functions Satisfying Higher Order Strict Avalanche Criteria},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / boolean functions , block ciphers},
  url={http://eprint.iacr.org/2003/198},
  note={ kishan_t@isical.ac.in 12320 received 24 Sep 2003, last revised 25 Sep 2003},
  author={Kishan Chand Gupta and Palash Sarkar},
  year=2003
}