Fix iTunes Error 53, Restore Loop While Updating to iOS 9

Tunes player on Windows / Mac shows error 53 when you are:

• Restoring the iOS firmware
• Updating to new iOS firmware
• Downgrading to another iOS firmware

We have received several reports from users (especially iPhone 6 and 6 Plus) that the error was visible while updating their devices to iOS 9 firmware.
Interesting fact is that error 53 is related to hardware, as iOS 8 Release points out:

Error message 53 appears because of the hardware fault in your iPhone or iPad. If you have a broken screen or any issues with Touch ID / Home button with your iOS device, then iTunes shows you this 53 error.

But if you are absolutely certain that your iOS device has no Touch ID or hardware issues…
You are not using any fake / non-geniune USB or lightning cable when connecting your device to your computer…
And never had to replace any internal parts, or get a new screen…
Then follow these solutions to fix the iTunes error 53:
(Note that doing a clean install fixed the problem, but we are outlining several generic solution).
Mandatory step:
-> Update your iTunes player – this is very important as Apple has released a newer version of iTunes player for Windows and Mac.

• Get iTunes 12.3 for Windows 7, 8, 10 and Mac OS X
• Get iTunes 12.1.3 for Windows XP / Vista

Troubleshooting steps:
-> Attempt a hard reset.
-> Uninstall and reinstall iTunes once again – this may sound silly, yet we confirm that it works!
-> If your iPhone / iPad is stuck with iTunes logo (or asking to “Connect to iTunes”), then your device is in “recovery mode.” In such cases, you have to first get the device out of the recovery mode and then try to restore it. Learn more about it here.