I've gotten so many good replies for technical questions before that I have to abuse the good brains on this forum some more.
Why is it hard to track backwards from public address to private key?
I don't have a higher degree in math, but in the kind of math I'm used to, if I have a formula and the unknowns, I'm usually able to solve this given a little time.
Why doesn't this hold true in cryptography, and especially in elliptic curve cryptography?
Why is it hard to find the private key when you have both the formula and the output?