Public-key cryptography

How a stranger can send you a secret without ever meeting you

Public-key cryptography uses two linked keys: a public key you give everyone and a private key you keep. Whatever the public key locks, only the private key opens, like a padlock anyone can snap shut but only you can open.

With AES from the symmetric lesson, Alice and Bob must already share one key. Here Bob just publishes his public key; Alice locks her message with it, and even Alice can't unlock it again. Only Bob's private key can.

Unlike Diffie–Hellman, Bob doesn't have to be online to take part in an exchange: his key is published once and works for anyone, any time. And 100 people need just 100 key pairs, not one shared key for every pair of people.

Public-key cryptography

Newsrooms post a PGP key so anyone can send a secret tip

Many newsrooms publish a PGP public key on their website. PGP (Pretty Good Privacy, usually run via the free GnuPG tool) lets a source who never met the reporter send a message only the reporter's private key can open.

PGP doesn't push the whole message through slow public-key maths. It encrypts the message with a random symmetric key, then locks just that small key with the reporter's public key. This mix is called hybrid encryption.

Public-key cryptography

Multiplying two primes is easy, but splitting the result back is not

RSA, the classic scheme, rests on a trapdoor: easy one way, infeasible backwards without a secret. Bob picks huge primes p and q, publishes n = p × q and an exponent e; locking raises the message to the power e mod n.

Unlocking needs a second exponent d that undoes e, and working out d requires knowing p and q. Anyone can see n, but splitting a 2048-bit n back into its primes would take known methods far too long, so only Bob can compute d.