The private keys are something that nobody will obtain. (No the keys are not in Sony's headquarters) They are in the ps3 just like the public keys because at a time Geohot/Failoverflow gained access to them.
(Logic behind the private key)
Sony intended for the key to be random its just the developers overlooked it. It's like a pass code that you have stored but it can be found out. That was the same concept. Thanks to the help of Geohot/Failoverflow by telling Sony how stupid they were for using that key "which was very old" they gave Sony the thing to fix the problem.
Question of the day: How can you break into a security vault that will always have a random password?
You cant. There IS no way around this and there is no way of cracking something that is random. It's the same concept as the lottery you will never see all 6 winning numbers drawn twice and over 20-30 years that has never been done. So your odds are -4 out of a Trillion
Nobody on the face of the earth can figure out something like that. Which is why all future advancements need the same key from 3.55 to even gain public keys and the lv0 key.
Don't waste your time trying to figure out the impossible
Ps3 Phat 250gb 4.46 OFW (Might sell or downgrade)
Ps3 Phat 80gb Rebug 4.46 Lite (Currently playing Devil May Cry / Far Cry 3/ Assassins Creed 3/ WWE 2K14)