Abstract
We present an infinite family of quadrinomial APN functions on GF(2n) where n is divisible by 3 but not 9. The family contains inequivalent functions, obtained by setting some coefficients equal to 0. We also discuss the inequivalence proof (by computation) which shows that these functions are new.
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Acknowledgements
We thank John Cannon, Gabriele Nebe, and Allan Steel for their work on APN functions and Magma. We are very grateful to Thomas Feulner for his computations, and for putting the results online. We thank the anonymous referees whose comments led to some improvements to this paper.
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Research of Carl Bracken was supported by Irish Research Council for Science, Engineering and Technology Postdoctoral Fellowship.
Research of Eimear Byrne, Nadya Markin and Gary McGuire was supported by the Claude Shannon Institute, Science Foundation Ireland Grant 06/MI/006.
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Bracken, C., Byrne, E., Markin, N. et al. A few more quadratic APN functions. Cryptogr. Commun. 3, 43–53 (2011). https://doi.org/10.1007/s12095-010-0038-7
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DOI: https://doi.org/10.1007/s12095-010-0038-7