Differential cryptanalysis is a powerful algorithmic-level attack, playing a central role in evaluating the security of symmetric cryptographic primitives. In general, the resistance against differential cryptanalysis can be characterized by the maximum differential characteristic probability. In this paper, we present generic and extensible approaches based on mixed integer linear programming (MILP) to bound such probability. We design a high-level cryptography-specific language EasyBC tailored for block ciphers and provide various rigorous procedures, formulated as differential denotational semantics, to automate the generation of MILP from block ciphers written in EasyBC. We implement an open-sourced tool that provides support for fully automated resistance evaluation of block ciphers against differential cryptanalysis. The tool is extensively evaluated on 22 real-life cryptographic primitives including all the 10 finalists of the NIST lightweight cryptography standardization process. The experiments confirm the expressivity of EasyBC and show that the tool can effectively prove the resistance against differential cryptanalysis for all cryptographic primitives under consideration. EasyBC makes resistance evaluation against differential cryptanalysis easily accessible to cryptographers.