I'm not sure which version of JIRA you are using so I'll provide documentation on both self hosted and OnDemand.
OnDemand Zendesk integration: http://www.jusuchyne.com/codingforme/2012/11/jira-ondemand-integration-with-zendesk/
Behind the Firewall Zendesk Integration: https://support.zendesk.com/entries/20560907-zendesk-for-jira-2-0-getting-started#jira_setup_connection
Please confirm that you've followed all of the steps and are still getting an Auth error as it could be password mismatch or something along those lines. If you encounter errors please note which instructions you are using, which step you are at when you see the error, and the actual error message you're getting.
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