Configuring your firewall for Trello
You can configure your firewall to allow Trello as a trusted source by following these guidelines. Because Trello’s IP addresses can change frequently and without notice, we’d suggest that you use our site’s domain names instead of a particular site IP address.

First, please configure host names to recognize any sub-domain of:

*.trello.com
*.trello.services
*.trellostatus.com
*.braintreegateway.com (paid accounts only)

In addition, these are the domains for the external resources for Trello:

https://trello-backgrounds.s3.amazonaws.com/
https://trello-avatars.s3.amazonaws.com/
https://trello-attachments.s3.amazonaws.com/
https://trello-logos.s3.amazonaws.com/
https://trello-emoji.s3.amazonaws.com
https://trello-stickers.s3.amazonaws.com
https://apis.google.com/ + https://accounts.google.com/o/oauth2 (for SSO (paid accounts only))
dropbox.com (for dropbox attachments)
app.box.com (for box.com attachments)
js.live.net (for one drive attachments)

via Configuring your firewall for Trello – Trello Help

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