I having been collecting the treasure chests, but I am not getting any key fragments... making it impossible to open any of them. I believe they should be easier to obtain and based on your performance like getting an S grants you a treasure chest. Maybe the grading system can determine you getting a key fragment~ how often. Should be increased, or some kind of system should be in place beyond just randomized. 
Apparantly it gets harder and harder to earn key fragments, each time you earn one.
Similar to increasing amounts of exp to level up, the chances of getting keys become rarer. It resets at the end of the month.
Hey all,
Just want to help clarify some things about key drop rates:
Key drop rates are NOT linear and only wins have a chance of dropping a key. So you will earn key fragments much faster in your earlier wins than you will in your later wins. Or said another way, each incremental key fragment drop is harder than the last (on average... there is variance). This resets on a monthly basis for each player individually. The goal is to create a nice ebb and flow.
Grade does NOT impact key drop chance.
Premades DO increase drop chance.
Chests earned has no impact on key drop chance.
There is variance and randomness (with limits). It's unlikely that what happened to your friend will happen to you.
Hope that helps clarify :)
