I think the problem is caused by the server where they are hosting the Boards Manager files. Even after I did a workaround for the "file signature verification failed. File ignored." error I just ran into another error when actually trying to install the package.
I think the easiest workaround is to do a manual installation:
- Download http://www.4dsystems.com.au/downloads/4Duino/4dsystems-1.8.1.tar.bz2
- Extract the downloaded file. This will result in a folder named 1.8.1.
- Create the following folder structure: {sketchbook folder}/hardware/4D Systems AVR Boards/avr. You can find the location of {sketchbook folder} in the Arduino IDE at File > Preferences > Sketchbook location.
- Copy the contents of the 1.8.1 folder to {sketchbook folder}/hardware/4D Systems AVR Boards/avr.
- Restart the Arduino IDE if it's running.
You should report this problem to 4D Systems so they can fix their Boards Manager installation support.