Paper 2018/769

Constructing APN functions through isotopic shifts

Lilya Budaghyan, Marco Calderini, Claude Carlet, Robert S. Coulter, and Irene Villa


Almost perfect nonlinear (APN) functions over fields of characteristic 2 play an important role in cryptography, coding theory and, more generally, information theory as well as mathematics. Building new APN families is a challenge which has not been successfully addressed for more than seven years now. The most general known equivalence relation preserving APN property in characteristic 2 is CCZ-equivalence. Extended to general characteristic, it also preserves planarity. In the case of quadratic planar functions, it is a particular case of isotopic equivalence. We apply the idea of isotopic equivalence to transform APN functions in characteristic 2 into other functions, some of which can be APN. We deduce new quadratic APN functions and a new quadratic APN family.

Available format(s)
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Boolean functionAPNisotopic equivalence
Contact author(s)
Irene Villa @ uib no
2018-09-10: revised
2018-08-27: received
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Short URL
Creative Commons Attribution


      author = {Lilya Budaghyan and Marco Calderini and Claude Carlet and Robert S.  Coulter and Irene Villa},
      title = {Constructing APN functions through isotopic shifts},
      howpublished = {Cryptology ePrint Archive, Paper 2018/769},
      year = {2018},
      note = {\url{}},
      url = {}
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