From Caesar's battlefield ciphers to quantum key distribution, cryptography is the ancient art of keeping secrets — and the mathematics underlying it shapes every secure communication on the internet today.
The Caesar cipher shifts each letter by a fixed number — Julius Caesar used a shift of 3.
Shift: 3Caesar Cipher (58 BCE): Julius Caesar shifted letters by 3 to send military messages. Simple but effective against an illiterate enemy.
Scytale (Sparta, 700 BCE): Wrap a strip of leather around a rod — the message only makes sense on a rod of identical diameter. The world's first device-dependent cipher.
Kama Sutra (400 CE): Recommends women learn cryptography as one of 64 arts. Secret writing for personal communications.
Enigma: Nazi Germany's electromechanical cipher machine with 158 quintillion possible settings daily. Generated seemingly unbreakable messages for submarines and high command.
The Bombe: Alan Turing designed a machine that exploited Enigma's one fatal flaw — it could never encode a letter as itself. That constraint allowed mathematical elimination of most settings.
Impact: Cracking Enigma is estimated to have shortened WWII by 2–4 years and saved 14 million lives. Turing was later prosecuted for being gay and chemically castrated. He died in 1954.
Lorenz cipher: Even more complex than Enigma, used for Hitler's High Command. Cracked by Colossus — the world's first programmable electronic computer.
The Key Distribution Problem: How do you share a secret key with someone if all your communications are monitored? For centuries, this seemed impossible.
Diffie-Hellman (1976): Proved two parties could agree on a shared secret over a public channel — like mixing paint colours. Revolutionary. Nobody had believed it possible.
RSA (1977): Based on the mathematical difficulty of factoring large numbers. Multiply two 300-digit primes in seconds; factor the result in millions of years. The lock on virtually every HTTPS connection.
AES: The symmetric cipher protecting most encrypted data today. So secure that brute-forcing a 256-bit key would take longer than the age of the universe, even on all computers on Earth simultaneously.
The Threat: A sufficiently powerful quantum computer running Shor's algorithm could factor large numbers exponentially faster, breaking RSA and most modern encryption.
Timeline: Current quantum computers have ~1000 qubits. Breaking RSA-2048 requires ~4,000 stable logical qubits. We likely have years, possibly decades.
The Response: NIST standardised post-quantum cryptographic algorithms in 2024 — lattice-based cryptography and hash-based signatures that resist quantum attacks.
Quantum Key Distribution: Uses quantum mechanics itself for perfect security — any eavesdropping physically disturbs the quantum state and reveals itself. Physics as security.
Prime Numbers: Primes are the atoms of cryptography. RSA security depends entirely on the difficulty of prime factorisation.
Modular Arithmetic: Clock arithmetic where 13:00 = 1:00 PM. The basis for most modern ciphers.
Elliptic Curves: Points on algebraic curves over finite fields. ECC achieves equivalent RSA security with far smaller keys.
One-Way Functions: Easy to compute, practically impossible to reverse. The fundamental building block of all cryptography.
Cryptography is the quiet infrastructure of the modern world — every password, every bank transfer, every private message, every HTTPS padlock depends on mathematical problems that have no known efficient solution. It's the application of pure mathematics to the very human desire for privacy.