PKI concept trouble.

line

I've got the theory down pat, I don't question the veracity of the material, but I still don't quite grasp how it works.

PKI - User JohnDoe Public Key: A10 Private Key: A1010
User SmithySmith Public Key: A20 Private Key: A2020

According to most PKI conceptual material I've read, user JohnDoe would encrypt a message going to SmithySmith with SmithySmith's PUBLIC KEY. When SmithySmith receives this message, he will then DECRYPT it with his mathematically-similar Private Key.

How in the hell do you decrypt a message with a key it was not encrypted with. I understand it is mathematically similiar, but if the decryption algorithm compensated for this, then wouldnt the whole encyption process just be bunk, as the encyption scheme is known?

broc

You need to read about Asymmetric Encryption. http://en.wikipedia.org/wiki/Public-key_cryptography