In this thesis, we are interested in the use of constraint programming (CP) for solving differential cryptanalysis problems. In particular, we are interested in differential (related or single key) characteristic search problems for the symmetric encryption algorithms Rijndael, AES and Midori. We have also modelled boomerang attacks for Rijndael and generalized this method to Feistel schemes. This new modelling has been tested on WARP, Twine and LBlock-s encryption. To solve these different problems, we have proposed new techniques combining SAT and CP solvers. We have also introduced a new global constraint to more efficiently propagate a set of XOR constraints when searching for truncated differential characteristics. These new models have allowed us to improve the performance of existing solutions and to discover new distinguishers for WARP (23 rounds), Twine (15 and 16 rounds) and LBlock-s (16 rounds). We also found new attacks on Rijndael (9 rounds with the 128-160 version, 12 rounds with the 128-224 and 160-256 versions) and on WARP (26 rounds).