The Quiet Math Problem That Runs the Planet

How Diffie-Hellman key exchange secures everything from your text messages to government secrets

- BY JACK MURTAGH

ON OCTOBER 30, 1942, a group of destroyer warships from the British Royal Navy hunted down a Nazi submarine near the Nile Delta. The warships pounded the submarine with underwater explosions until it floated to the surface, where it started filling with water and sinking. As its German crew scrambled to escape, three British heroes-Lieutenant Anthony Fasson, sailor Colin Grazier and 16-year-old canteen assistant Tommy Brown-did something that defied all instinct. They jumped from their ship onto the sinking vessel and climbed inside.

They were after the sub's most valuable cargo: not weapons, not prisoners, but books. The pages contained codes for tuning the Nazi "Enigma machine" that allowed the German forces to communicate in secret. Deep inside the flooding commanding officers' quarters, the men seized the volumes before the water-soluble ink dissolved into the sea. Only the teenager made it out alive. Less than two months later English mathematician Alan Turing's team of code breakers used the codes to decipher Nazi messages, an effort estimated to have shortened the war by two years, saving millions of lives.

Jack Murtagh is a freelance math writer and puzzle creator. He writes a column on mathematical curiosities for Scientific American and creates daily puzzles for the Morning Brew newsletter. He holds a Ph.D. in theoretical computer science from Harvard University. Follow him on X @JackPMurtagh