After some testing, I realize that there could be some compromise.
It seems that applicationDidBecomeActive: is only balanced with applicationDidEnterBackground:
In my case this means that the blurring should take place in the latter method. At the end of the day, this means that there will be no screen blurring if the user "leaves" my app by calling the Notification Center or by calling the task manager. However, concerning data security, this should not be a heavy-weighting problem because it's obvious that only the user who had access to my app can perform theses steps.
When the app is left by clicking HOME once, going to standby or by changing the foreground app by the task manager, applicationDidEnterBackground: gets called, and after some testing, it seems it gets enough time from the OS to perform the blurring on the main loop.
However, if you stick to the original problem, this is still unsolved.