In this paper, we introduce Constraint Programming (CP) models to solve a cryptanalytic problem: the chosen key differential attack against the standard block cipher AES. The problem is solved in two steps: In Step 1, bytes are abstracted by binary values; In Step 2, byte values are searched. We introduce two CP models for Step 1: Model 1 is derived from AES rules in a straightforward way; Model 2 contains new constraints that remove invalid solutions filtered out in Step 2. We also introduce a CP model for Step 2. We evaluate scale-up properties of two classical CP solvers (Gecode and Choco) and a hybrid SAT/CP solver (Chuffed). We show that Model 2 is much more efficient than Model 1, and that Chuffed is faster than Choco which is faster than Gecode on the hardest instances of this problem. Furthermore, we prove that a solution claimed to be optimal in two recent cryptanalysis papers is not optimal by providing a better solution.