How to recover after iOS update? Being silly I have agreed to update my iPhone 5c to latest iOS and now my phone looks dead.

When boots, it displays the following screen 



If I connect it to my notebook, iTunes proposes to update phone and starts long term operation, which fails with error 1671.

Next time operation takes longer, now it is 60 mins.

What is it doing for 60 mins? Calculating the mass of proton with QCD? How to avoid this calculation? 

How to recover my phone?

If I agree to reset my phone, will I loose all my photos?
When iTunes offers to update, tell it to download only.
If that is successful, at least you have the download on your machine, instead of trying to re-fetch it every time there's a fail.

If you have to reset the phone in order to restore, then you will lose any data since your last backup.

If regular Recovery Mode doesn't work, then try DFU (Device Firmware Update) mode.
'Connect to iTunes' is Recovery, black screen is DFU.

To force the phone into DFU mode for restoration  


Plug into iTunes
Turn the phone off
Hold power &amp; home for 10 seconds
release power but continue to hold home
wait for the computer to recognise the device
if the screen lights up while you're doing this, you didn't get to DFU mode &amp; will have to try again; reports say the 10 seconds needs to be fairly accurate


iTunes should recognise it has a device in DFU Mode &amp; restore should now work.

BTW - Golden rule for OS updates is…
 in iTunes


Sync
Backup
if you really want to be thorough
Download all app updates
Sync again
Backup again
Download update file
Update


That way if anything goes wrong you can be back where you were in minutes.