Abstract We have developed a model to represent the differential operation of block ciphers in order to help finding differential characteristics. Through this model, the whole space of differential characteristics for a block cipher is represented by a multi-level weighted directed graph. In this way, the problem of finding the best differential characteristic for a block cipher reduces to the problem of finding the minimum-weight multi-branch path between two known nodes in the proposed graph. In this paper, we use recurrent neural networks to find such a path in the differential operation graph of a block cipher. The path is found through minimization of the network cost function. We use the Hopfield network and the Boltzmann machine with and without chaos to minimize the cost function. Chaos is introduced to assist the network to escape from the local minima of the cost function. Experimental results indicate the usefulness of the approach and comparison of the performance of the used techniques shows that the Boltzmann machine algorithm incorporating simulated annealing produces the best result.