Without public key cryptography, we would not have the internet as we know it, economist Tim Harford says on his BBC-produced 50 Things That Made the Modern Economy podcast. We use cryptography every time we send a work email, buy something online, or use a banking app. Harford tells the story of public key cryptography – and the battle between the geeks who developed it, and the government which tried to control it. It all started with scientists who managed to turn the Diffie–Hellman theory into a practical technique called RSA encryption “Some mathematics are much easier to perform in one direction than another. Take a very large prime number … then take another. Multiply them together. That’s simple enough and gives you a very, very large ‘semi-prime’ number. That’s a number that’s divisible only by two prime numbers. Now, challenge someone else to take that semi-prime number a figure out which two prime numbers were multiplied together to produce it. That, it turns out, is exceptionally hard. Public key cryptography works by exploiting this difference” (runtime 09:10).

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