Api data info

There is a software that sends authentication information to a WEB API, that server returns some authentication values depending on the data sent by the authentication software, I need to know exactly how the data that the server returns to the software is generated, I have 2 examples real data sent to the server and received from the server I have been doing cryptographic tests but I have not been able to replicate exactly the same data. I need to find the exact algorithm or hash or jump or encryption that replicates the values that the web api sends to the software. You should not develop any software or project, just analyze the data that I will send you and tell me how it is generated so that I can generate new data with other new information. Any question Send me SMS