Easy one way,
hard the other
Strip cryptography down to a single idea and this is what remains: a function anyone can compute forward, but no one can practically reverse. Every cipher, signature, and key exchange in the building is downstream of this one asymmetry.
Multiply, then try to undo it
The friendliest one-way function is multiplication of primes. Multiplying two large primes is instant. Recovering them from the product — factoring — is, as far as anyone knows, brutally slow. Move the slider to enlarge the primes and watch the two costs diverge.
The trapdoor twist
A plain one-way function locks the door for everyone. Cryptography needs a little more: a trapdoor — a secret that makes the reverse easy for the one who holds it. In RSA, knowing the two primes is the trapdoor; without them you factor, with them you divide.
That is the shape of every public-key scheme: a wall everyone faces, with a hidden gate only the key-holder can walk through.
The bet under everything
RSA bets on factoring. Diffie–Hellman and ECC bet on discrete logs. The post-quantum standards bet on lattice problems instead — because a quantum computer would win the factoring and discrete-log bets. Different walls, same architecture: easy forward, hard back, secret gate.
One family deliberately omits the gate. SHA-256 is meant to be one-way with no trapdoor at all — nobody, including its designers, should be able to run it backwards. That makes a hash the purest example on this page: all wall, no door. Public-key cryptography is the harder trick, because it needs the wall and a way through for exactly one person.
Next: Reduction & Proof — how we argue one wall is at least as tall as another.