it uses a cracked private key from Microsoft to sign some stuff encoded in the 25-digit product key. It also does this process in reverse to check for the validation of the keys.
*telephone activation* method, then, fire up [this website](https://msdev.gointeract.io/interact/index?interaction=1461173234028-3884f8602eccbe259104553afa8415434b4581-05d1&accountId=microsoft&appkey=196de13c-e946-4531-98f6-2719ec8405ce) and enter the installation ID that the activation wizard gave you.