On APN functions L1(x3) + L2(x9) with linear L1 and L2


In a recent paper by L. Budaghyan, C. Carlet, and G. Leander (2009) it is shown that functions of the form L1(x3) + L2(x9), where L1 and L2 are linear, are a good source for construction of new infinite families of APN functions. In the present work we study necessary and sufficient conditions for such functions to be APN.

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Correspondence to Irene Villa.

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This article is part of the Topical Collection on Special Issue on Boolean Functions and Their Applications

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Villa, I. On APN functions L1(x3) + L2(x9) with linear L1 and L2. Cryptogr. Commun. 11, 3–20 (2019). https://doi.org/10.1007/s12095-018-0283-8

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  • Boolean function
  • Almost perfect nonlinear
  • CCZ-equivalence
  • Nonlinearity

Mathematics Subject Classification (2010)

  • 94A60
  • 06E30
  • 20B40