A lock everyone can close, and only you can open
Public-key cryptography lets you publish the method of locking a message. Strangers can lock things to you. They cannot unlock them.
Diffie and Hellman showed that two people can agree a shared secret in public, with eavesdroppers watching every message, and the eavesdroppers still cannot compute the secret. RSA, soon after, made the lock and the key different objects: a public key that encrypts, a private key that decrypts. The web’s padlock is this idea, in a protocol that also has to survive bad clocks, stolen certificates, and bored implementers.
The security is not a law of physics. It is the belief, tested hard and not disproved, that certain mathematical problems are infeasible to reverse. Factoring a large number, or taking a discrete logarithm, is easy if you chose the number and kept a factor. It is brutal if you did not.
Caveats
- A sufficiently large quantum computer would break the schemes now in wide use. That machine does not exist. Schemes believed to resist it are already being deployed beside the old ones.
- Most real failures are not a break of the mathematics. They are a bug, a reused key, or a lie about who owns the public half.
Sources
- 1Diffie W., Hellman M. E.. New Directions in Cryptography. IEEE Transactions on Information Theory 22, 1976.