What is the right way of storing database connection strings from the security point of view?
Best option: Don't use a password for the database, but instead employ (Windows) Integrated Authentication if it's possible, and of course isolate the application's identity that is authorized for the database. That way you have the OS/Webserver/SCM manage your identity, in a very secured manner.
If it's not possible to go the way of Integrated Windows Authentication (IWA), you'll need to securely encrypt the connstring, preferably using something like DPAPI (so you dont have to manage the encryption key), and store the encrypted value in a protected Registry key with strong ACLs.
If you are on ASP.NET (from your comments, but not OP), there are built-in tools to do this automatically (aspnet_setreg, aspnet_regiis, etc depending on version...)
As an option, try to use application role to access sql server
- Regular network administrators can manage data access without needing to consult the database administrator (DBA), simply by controlling who has access to an application.
- You don’t need to worry about keeping track of changing users with SQL Server itself. Set up an application role and you can delegate that back to the network level.
- You can limit data availability to a single application. For example, a user might be able to modify accounting information only when using the general ledger application, and not when he connects directly to SQL Server.
things you should never do
- putting connection string in a text file.
- have configuration file in public accessible folder/directory.
things you should do.