Perhaps the following might work:
After login with userName,
For listing files in anyFolder in Briefcase
http://server/home/userName/Briefcas...older?fmt=json
for searching a particular file with name anyFileName in anyFolder in Briefcase
http://server/home/userName/Briefcas...eName&fmt=json
Replace username and anyfolder and anyFileName with appropriate values in above REST calls.
If you need to login using basic authentication and get the list of files from within a Java application with the above REST API, try with Apache HttpClient. You would need to URL encode anyFileName. Ruby also has its own way of performing basic authentication on REST calls.