Comparing if two List of strings are equal using hashcode

I am writing a Java/J2EE client server application. I have a requirement were the files present in the server should match with the files present in the client. I am only trying to validating if there is an exact match to the file names and number of files in a specific directory.

Example of what is required:

Server DirectoryA FileA FileB FileC

Client DirectoryA FileA FileB FileC

What would be the most efficient way for the server to make sure that all clients have the same files, assuming I can have over 100 clients and that I do not want my client/server communication to be too chatty.