You have to really know the "importance" of what a private key is and what it does and what it prevents. The Ps3 "could have been unhackable" If Sony used the private key in the 1st place.
The importance if the private key is to prevent piracy. The public key can be found only through the help of the lv0 key. Thing is you cant get the lv0 key unless you had the private key in the first place. With the private key you get the public key. The private key is a master key. Reason why 3.55 was found was becasue geohot found the private key. "Sony changed keys ever since 3.41" But the key was never a random key.
So with that being said if the key was intended like how Sony had intended it to be the Ps3 Scene would of been stopped dead in their tracks since 3.41. Just like how it's stopped dead in their tracks with 3.55.
The reality of the situation the scene only lasted externally for 5 months because Sony fixed the major problem. The scene only expanded/ benefit internal users (people with 3.55 or below) because that's where the progression continue.
The private keys give you access to everything on the ps3 to the point you can run whatever pirated game/blu ray you want. Public key gets generated by the firmware. Private key gives you access to everything. It is a random key.
So obtaining the private key will be remotely impossible.
Ps3 Phat 250gb 4.31 OFW (Currently Playing Dead Space 3 [Chapter 10] / Hitman Absolution / COD MW3 )
Ps3 Phat 80gb 3.55 CFW