Random thuds on cracking public key encryption
Let T be a plaintext which Alice must convey to Bob.
Let ¤ represent exclusive-or, or some similar operation which is reversible when twice applied (or at least symmetric, like TEA, where encode and decode work jes' fine.)
Let P be Alice's public key, and p be her private key.
Let P ← M¤p, where M is mysterious†.
Let Q be Bob's public key, and q his private key.
Let Q ← M¤q, where M is still mysterious.
Alice cleverly enciphers C ← T¤Q¤p.
Alice pops C into an envelope and sends it to Bob, awaiting anxiously.
Bob deduces Alice's private key, p ← (M¤p)¤(M¤q)¤q ← P¤Q¤q.
Bob deciphers T ← C¤Q¤p.
Ok. This probably ain't how public key encryption works, but if it reduces to this case, kiddies, the jig is up!
†M is not my favorite pseudorandom number generator, Mersenne Twister. M is mysterious! Like this.