This letter discusses with cryptanalysis with impossible differentials. After Biham et al. presented an attack on Skipjack, the applications to many ciphers were done, and we think that the attack is one of the most effective tool to cryptanalyze a block cipher. However, unfortunately, there is no construction method that provably resists the attack. This letter first introduces the measure that can evaluate the resistance against cryptanalysis with impossible differentials. Then, we propose a construction that resists cryptanalysis with impossible differentials. Moreover, a cipher that is based on the construction also provably resists differential cryptanalysis and linear cryptanalysis.