Links Between Theoretical and Effective Differential Probabilities: Experiments on PRESENT

Recent iterated ciphers have been designed to be resistant to differential cryptanalysis. This implies that cryptanalysts have to deal with differentials having so small probabilities that, for a fixed key, the whole codebook may not be sufficient to detect it. The question is then, do these theoretically computed small probabilities have any sense? We propose here a deep study of differential and differential trail probabilities supported by experimental results obtained on a reduced version of PRESENT.