What internet addresses are used in OTA iOS updates?

Hi all,

We have a large number of new iPad Air's for our School, which are all failing to install their iOS updates. The error message is

"Unable to Verify Update.

iOS 7.1 failed verification because you are no longer connected to the Internet."

The internet connection is fine.

The download of the iOS update happens properly, and Safari has no troubles getting pages *while* the verification process is attempted.

I have been through the following:

Forgotton Wifi network and reconnected.

Reset Network Settings (Settings -> General -> Reset -> Reset Network)

Factory restore using iTunes

Nothing works.

The problem I am trying to solve is using Over The Air updates. I am well aware that connecting an iPad to a computer with iTunes on it will do the job, but that isn't a solution that will work for us, as the teachers *do not have* computers to connect their ipads to. Nor is bringing them in to a central area a viable alternative, as they are geographically disparate. I need to fix this specific issue, and get them working wirelessly.

Two thoughts occur to me:

The iPad needs a valid iCloud account (although a test ipad from the same batch but connected to a different network did not).

The School firewall and content filter is blocking some portion of the update process.

We put another iPad on a fixed IP address, and removed all firewall restrictions for that IP address which allowed the update to work, so I'm concluding something in the firewall is blocking the update process.

I have run a packet capture on the firewall's interface provided for the school network, and have seen many connections to apple.com, akamai.com and amazonws.com. I have whitelisted *.apple.com in the firewall, but am quite reluctant to whitelist the whole of the others.

Hence, I'd like to narrow down which sites the iOS update process uses, so that I may open specific holes for those services.

Googling generally, and searching the Apple Support knowledgebase not been entirely productive, except to produce a handful of apple sites.

Thanks,

James