BuddyPress.org

Yuo have to define “secure” on a technical level. SSL only secures the transport of bytes, that should work right out of the box with buddypress, you just need to upgrade you existing webserver configuration and get a SSL certificate. YOu can get free certs at cert.org.
However, this does not mean that the messages are encrypted – so content in your database will still be readable to anybody who has access to the database.