Public-key cryptography is magic. Zero-knowledge proofs are a consequence that's difficult to find on your own but easy to understand once you've seen it.

I remember seeing someone (probably Avi Wigderson) demonstrating a zero-knowledge proof for graph coloring on an overhead projector when I was starting my second year studying CS. He had a slide with a graph, multiple slides with different permutations of the same valid coloring of the vertices, and a piece of paper with "doors" over the vertices to cover everything. The audience could ask him to open the doors over the vertices connected by any edge, and he would show that the coloring is valid, as far as those two vertices are concerned. And then he would replace the coloring with another permutation for the next iteration. The idea felt clever but kind of obvious in retrospect.