On weakly APN functions and 4-bit S-Boxes
  S-Boxes are important security components of block ciphers. We provide theoretical results on necessary or sufficient criteria for an (invertible) 4-bit S-Box to be weakly APN. Thanks to a classification of 4-bit invertible S-Boxes achieved independently by De Canni\'ere and Leander-Poschmann, we can strengthen our results with a computer-aided proof. 
Claudio Fontanari, Valentina Pulice, Anna Rimoldi, Massimiliano Sala
cs.CR math.CO