In this paper, we study how exploiting multiple differential characteristics with a common initial difference and different output differences improves the complexity of differential cryptanalysis attack. We call such an approach Multiple Differential Cryptanalysis. We describe such an attack rigorously by studying the probability distribution of multiple differential characteristics and giving an attack algorithm based on LLR statistic. We also present a statistical analysis on the attack complexity based on LLR probabilistic technique. Our analysis shows that the data complexity of the proposed attack decreases as the number of characteristics increases. We do an experiment with the described method to show its improvements through cryptanalyzing a reduced round PRESENT block cipher with 5 rounds.

The security of permutation-based hash functions in the ideal permutation model has been studied when the input-length of compression function is larger than the input-length of the permutation function. In this paper, we consider permutation based compression functions that have input lengths shorter than that of the permutation. Under this assumption, we propose a permutation based compression function and prove its security with respect to collision and (second) preimage attacks in the ideal permutation model. The proposed compression function can be seen as a generalization of the compression function of MD6 hash function.