Paper 2021/405

Revisiting some results on APN and algebraic immune functions

Claude Carlet


We push a little further the study of two characterizations of almost perfect nonlinear (APN) functions introduced in our recent monograph. We state open problems about them, and we revisit in their perspective a well-known result from Dobbertin on APN exponents. This leads us to new results about APN power functions and more general APN polynomials with coefficients in a subfield F_{2^k} , which ease the research of such functions and of differentially uniform functions, and simplifies the related proofs by avoiding tedious calculations. In a second part, we give slightly simpler proofs than in the same monograph, of two known results on Boolean functions, one of which deserves to be better known but needed clarification, and the other needed correction.

Available format(s)
Secret-key cryptography
Publication info
Preprint. Minor revision.
Boolean functionAlmost perfect nonlinearcorrelation immune
Contact author(s)
claude carlet @ gmail com
2021-12-18: last of 4 revisions
2021-03-27: received
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      author = {Claude Carlet},
      title = {Revisiting some results on APN and algebraic immune functions},
      howpublished = {Cryptology ePrint Archive, Paper 2021/405},
      year = {2021},
      note = {\url{}},
      url = {}
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