Public-key cryptography
A method of secret communication using two mathematically linked keys: a public one, which anyone may use to lock a message or check a signature, and a private one, kept secret, which alone can unlock or sign. Because the locking key can be published openly, two strangers can communicate securely without ever sharing a secret in advance.
✦ Wait, really?
The impossible-seeming trick of publishing your lock while keeping your key secret was invented twice. Whitfield Diffie and Martin Hellman announced it to the world in 1976, and Rivest, Shamir and Adleman built the first complete system, RSA, in 1977. But inside Britain's GCHQ, Clifford Cocks had already worked out essentially the same scheme as RSA in 1973 — reportedly in under half an hour, after a colleague described the puzzle to him. It was stamped secret. Cocks watched others take the credit for more than twenty years, until GCHQ finally declassified the work in 1997.
What it is
Public-key cryptography breaks the oldest assumption in secret-keeping: that to share a secret you must first share a key. Every classical cipher used one key for both locking and unlocking, so the sender and receiver had to somehow exchange that key privately beforehand — the very problem the cipher was meant to solve. Public-key schemes use a *pair* of keys that are mathematically bound but not derivable from one another in any practical time. Publish one — the public key — for all the world to see; keep its partner, the private key, to yourself. Anything locked with the public key can be opened only by the private key, and anything the private key signs can be verified by the public key. So a stranger can send you a message only you can read, and you can sign a message anyone can confirm came from you.
Why it mattered
Before this, secure communication at scale was strangled by key distribution. Every pair of parties who wanted privacy needed a shared secret delivered through some trusted channel — couriers, sealed pouches, prior meetings — and the number of secrets grew impossibly with the number of participants. That is workable for two governments; it is hopeless for millions of strangers who want to buy and sell online. Public keys cut the knot: you can hand your locking key to the entire world and lose nothing, because it cannot undo what it does. This is what made commerce and confidential communication possible between people who have never met and share no prior trust — the mathematical precondition for a usable, secure internet.
What it unlocked
Nearly every secure interaction on the internet. The padlock in a browser, online banking and shopping, encrypted messaging, software updates that prove they came from their maker, and the digital signatures underpinning cryptocurrencies all rest on public-key cryptography. It let strangers transact and communicate in confidence without any prior arrangement — the foundation on which electronic commerce and private communication were built. The whole architecture of trust online is, at bottom, the bet that multiplying is easy and factoring is hard.
Minimum viable version
A Diffie–Hellman key exchange: two people who have never met each mix a private secret into a shared public number and swap the results; combining the other's result with their own secret, both arrive at the same key, while an eavesdropper who saw only the public exchange cannot. No secret ever crossed the wire, yet both now share one.
This entry is awaiting its full account — the cartographers are at work. Its place in the graph is already verified.
Unlocked
Frontier — nothing charted yet.
Sources
- — Whitfield Diffie & Martin E. Hellman, 'New Directions in Cryptography,' *IEEE Transactions on Information Theory* 22, no. 6 (November 1976): 644–654
- — R. L. Rivest, A. Shamir & L. Adleman, 'A Method for Obtaining Digital Signatures and Public-Key Cryptosystems,' *Communications of the ACM* 21, no. 2 (1978): 120–126
- — Simon Singh, *The Code Book* (1999)
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