The database security requirements in any environment will be same because an OS may change but the application, database, and security requirements will not change. Probably you want to ask how to attain database security in a Linux environment. You can use Symantec Enterprise Security Manager for Databases Application Modules for this purpose.

There is a very good blog article in backyardgeek explaining different security issues and their solution, see: backyardgeek.blogspot.com/2007/10/linux-database-security-explained.html