Fixing package_index.json file Signature Verification Problem in Arduino
As it's said, once you solve problem #1, problem #2 gets a promotion. So, after fixing the problem with downloading package_index.json file, Arduino IDE immediately started complaining about file integrity.
To be honest, I'm not sure why this mess has happened but this is a really annoying thing. Fortunately, the problem can be solved easily if you have correct files.
So, let's get back to the problem. The problem happens when you open the board manager in Arduino IDE. This is exactly the error that I was getting.
https://downloads.arduino.cc/packages/package_index.json file signature verification failed. File ignored.
Fixing the Problem
So it's really easy to fix this problem provided that you have correct file. This fix applies to Windows.
First off, remove everything in c:\Users\YOURUSER\AppData\Local\Arduino15\ folder.
Download correct package_index.json file and place it in the above mentioned folder.
Restart Arduino IDE.
If this does not help, then I suggest you running a local web server or uploading the file to some sort of web server and specify the URL in Arduino IDE. This can be done from File > Preferences menu.
As you can see on the screen shot below, I have a local web server running and serving the JSON file from it.
Once you do this, you should be able to access Arduino board manager normally.