Extract or Figure out the encryption/encoding algorithm and build this API

Hi, I have some sample data inputs and encoded/encrypted outputs. I want to know the exact algorithm used for obtaining the output and convert into PHP or C++ code that can do the same encryption/encoding. We have this thirdparty API, Example : [login to view URL] We need the same API to be build. So we need to figure out the encrpytion method used here. Please only bid if you are familiar with complex encryption methods.