This error shows up when computer restarts for first time after update download via Windows Store app.
There are two ways to fix this problem :
1. Firstly most easier and sure shot one is to perform a clean install, on an empty partition.
For this download windows 8 upgrade assistant enter windows 8 key and select media
in later steps to make a iso of windows 8.1.
2. Another approach to this issue is pointed out by Dell to an official Microsoft advisory which claims cause of error to 'certain dynamic-link library files (.dll files) are not registered correctly or if there is a firewall between the computer and the Internet that does not allow HTTPS (SSL) connections'.
To fix this you can use regsvr32 command to reregister several .dll files.
a) For this press Ctrl+R then Run Box appears,there type cmd and click OK.Alternatively you can open cmd prompt by right clicking to open with administrative privileges.
b) Now in command prompt type following commands and press enter after each line.
c) Now restart your computer and try to install windows 8.1 once again.
There can be other workarounds also for this problem,please be free to share if this post helped in your problem and also share other ways to this issue by commenting on this post.