If you need to downgrade iOS 8.3 to iOS 8.1.3 on your iOS device then unfortunately it is impossible now only if you have got SHSH blobs of 8.1.3 saved in TinyUmbrella. Apple has closed iOS 8.1.3 singing window. But you can downgrade to older version as iOS 8.2 on your iPhone, iPad or iPod touch.
Those iOS users who have already updated their iOS devices to iOS 8.3 and want to roll back to older versions here is easy steps to follow.
Remember that downgrading from iOS 8.3 is possible as Apple is still signing the iOS 8.2 firmware.
Apple company had patched quite a few exploits in iOS 8.2, but has followed with even more patching of exploits in iOS 8.3 now, making iOS 8.3 jailbreak even more difficult. So if TaiG will release a jailbreak for versions older than iOS 8.3, this downgrade will be useful.
Step 1: Please make sure you backup your personal data to iCloud or locally to your PC before proceeding the downgrading process.
Step 2: Now download iOS 8.2 firmware file that is suitable for your device.
Step 3: Launch iTunes, go to the device’s Summary page.
Step 4: Now hold down the Option / Alt key on your Mac’s keyboard, Shift key if you are on Windows, and tap the Restore iPhone button.
Step 5: You will now be prompted to browse and pick the iOS 8.2 IPSW file you downloaded in step 2.
Step 6: Choose and open the file, which should start the downgrading / restoring to iOS 8.2 process.
The entire downgrade iOS 8.3 to iOS 8.1.3 process will take several minutes. After it will be completed you will have successfully installed iOS 8.2 version on your iOS device.