Diffie-Hellman is the thing where Alice and Bob first agree on a huge prime number p and a number g, then Alice picks a secret a and sends Bob ga (mod p), and Bob picks a secret b and sends Alice gb (mod p), and then Alice and Bob can both compute (ga)b=(gb)a=gab (mod p), but an eavesdropper who’s listening in only knows p, g, ga (mod p), and gb (mod p), and one can plausibly conjecture that it’s hard from those things alone to get gab (mod p). So then Alice and Bob share a secret unknown to the eavesdropper, which they didn’t before, and they can use that secret to start doing cryptography.

Source: *Shtetl-Optimized » Blog Archive » NSA in P/poly: The Power of Precomputation*