There is no 8.1 activation key, as it was a free OS upgrade (essentially, it's Windows 9). With this being said, many have been confused about the licensing structure change Microsoft made with Windows 8 and Office 2013.
First the background
Microsoft completely changed it's licensing structure with the release of Windows 8 [Office 2013 as well, although the Windows change was more significant]. My guess here is that Microsoft, in an [failed] attempt at clamping down on piracy, decided to make
some ill-fated changes to how Windows installs and activates. Microsoft prevented the lay user launching Windows 8/8.1 installer without first providing a product key [not to be confused with an activation key, as the two are very different]; however, this
backfired: When users who upgraded to Windows 8 first installed 8, they were permitted to access the installer with their activation key; however, once they did so, they could no longer use the activation key to access the installer because Microsoft changed
it's licensing structure from 3 users to a 1 user license. So if a user needed to reinstall Windows for whatever reason, their activation key no longer allowed them access to the installer to do so.
Whether Microsoft planned to do the following all along or not, about a week after the release of Windows 8 and loud outcries from consumers, Microsoft released the generic product keys for each Windows version installer [again, for the lay person, as an
answer file easily bypasses the necessity of a product key to access the installer]. These product keys are not the same as activation keys, as the sole purpose of these product keys is to allow access to the installer, nothing more. Once a person installs
Windows with the generic product keys, they will need to activate Windows via PC Settings - Activate and will need to manually change the product key listed to their activation key.
The generic keys can be found by googling "Windows [8 or 8.1] [edition - Core, Pro, etc.] generic product key".
Generic Product Keys:
8.1 Core: 334NH-RXG76-64THK-C7CKG-D3VPT
8.1 Pro: XHQ8N-C3MCJ-RQXB6-WCHYG-C9WKB