Mono to SQL Server with Windows Auth
This is not as easy to accomplish as it sounds. As I'm sure you know, Mono SqlClient has support for NT authentication:
Has a connection string format for NT Authentication: Server=hostname;Database=databaseName;User ID=windowsDomain\windowsUserid;Password=windowsPassword;Integrated Security=SSPI
But of course, you want the simpler form of Integrated Security=SSPI and let the NT authentication handshake use the current process credentials. And here lies the problem. While trivial to retrieve the current process user name (identity), is impossible for a process to discover it's own credentials password. When doing NT authentication an Windows process does not actually do the authentication, but instead is asking the Locas Security Authority (aka. LSASS.EXE, trivia: don't attach a debugger to it ;) ) to authenticate this process. Which means that any library that wants to achieve the same must use the same protocol, ie. ask LSA to authenticate it. The actual details, for the curious, are in the sequence of AcquireCredentialHandle, InitializeSecurityContext, AcceptSecurityContext as described in Using SSPI. I did not study the mono source for SqlClient, but I'm pretty sure they use some GSS-API library for the authentication, not SSPI. therefore, by definition, they require to know the password since they are going to do the Kerberos exchange themselves, not ask LSA to do it on their behalf.
This is, as you can tell, speculation and more of a guess on my side, but I would be surprised to hear a different story. While it is certainly possible to fork or patch Mono.Data.Tds and modify the authentication implementation to use SSPI instead of GSS, this would, by definition, be a non-portable Windows specific implementation. I would guess there is little incentive for it given that the #1 attraction point of Mono is that is not Windows specific. I'm afraid you are going to have to implement it on your own.