It's virtually impossible to break a public key cypher nowadays. In fact the death knell of the PSP security is not the cypher, its cypher is intact and has never been broken into. It is actually a vunerability of the firmware. Crackers were able to circumvent this by fooling the PSP into running their custom built cracking codes. Thus circumventing the need to authenticate your games. The gist of it is to get PSP to run the cracker's code in privilege mode that allows you to put a non-authenticated EBOOT into the PSP system space, that non-authenticated EBOOT is modified to run your pirated UMDs without requiring any authentication.

You can get more information here

EDIT: This is the same reason for the need to reflash your NDS firmware to play ROMs and pirated cartridges, essentially to place cracking codes that circumvents authentication.

A 1024-bit keysize will take 300,000,000,000 MIPS-year to crack. That is, it takes a CPU running at 1,000,000 million instructions per year 300,000,000,000 years to crack. To put things in perspective, the current lean-and-mean 1billion transistors Itanium would probably have a best estimate of 125,000 million instructions per second. You'll need a super-computer to get any result at all. That is a very long time to deduce a private key.

But the hash function (MD5/SHA-1)  required for text signing does seems easier to break. In fact, I've heard of one successful attempt. Using collision detection, one could spoof your signature. Still this is pretty hard, and it gets harder as the hash digest size increases. There's 4 billion chance you could get a collision with a 32-bit hash digest and SHA-1 uses 160-bit hash!

You can get more info on public key crypto attacks here. PGP is a popular public key encryption program.

You seem pretty adamant.