Which user account is using trusted_connection in sql2008?
It uses the user who is running in your application pool, the default is "NT AUTHORITY \ NETWORK SERVICE"
The title of the question should be "What user account will ASP.NET use when connecting to SQL Server using trusted___connection". Trusted_connection uses the current (or issued) credentials of the current process.
Your .NET code runs inside an application pool. You can set up a user account in the application pool as part of the IIS configuration. The best practice is to run the application pool under a restricted account and grant access to this database to the user.
Do not confuse this with the default IIS Anonymous user account, the IIS service account, or the IIS Security tab in the website settings. You can configure your web application to impersonate (run as) a user that IIS authenticates as (see Impersonation in the ASP.NET doco).
Rob
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