Soft question: What are examples of beautiful proofs in cryptography? These may include any proofs, reductions, constructions, etc. For example, simple solutions to problems which at first sight seem difficult. Elegant construction that hide deep mathematical concepts, but once presented are easy to use.   

Anything which you deem elegant and clever. 

Proofs with nice graphics are especially welcome.

(preferably ones that can fit reasonably into a StackExchange answer).
Theorem.  The ECB mode of a block cipher is distinguishable under chosen-plaintext attack with laughably high advantage.

Proof.