The Japanese helped them by making an uncharacteristically careless mistake.

Delivery of the new code books for JN-25b was delayed to some far-flung units. So, for a fatal few weeks, the Japanese high command sent out some messages in both codes. Since the Americans had broken much of the original JN-25, they were able to translate the message in the old code, set the decrypt alongside the message in the new code, and figure out the meanings of the five-digit groups of the new code. For a while they progressed by leaps and bounds.

The original eight cryptanalysts were supplemented, after Pearl Harbor, by some of the musicians from the band of the sunk battleship California. For reasons no one understood, musicians were good at decoding.

Every signal was kept and every decrypt filed. Comparison of one with another was crucial to the work. An analyst might ask for all the signals from a particular day, or all the signals to one ship, or all the signals that mentioned Hawaii. Chuck and the other clerical staff developed ever-more-complex systems of cross-indexing to help them find whatever the analysts needed.

The unit predicted that in the first week of May the Japanese would attack Port Moresby, the Allied base in Papua. They were right, and the US Navy intercepted the invasion fleet in the Coral Sea. Both sides claimed victory, but the Japanese did not take Port Moresby. And Admiral Nimitz, Commander-in-Chief of the Pacific, began to trust his codebreakers.

The Japanese did not use regular names for locations in the Pacific Ocean. Every important place had a designation consisting of two letters – in fact, two characters or kanas of the Japanese alphabet, although the codebreakers usually used equivalents from the Roman A to Z. The men in the basement struggled to figure out the meaning of each of these two-kana designators. They made slow progress: MO was Port Moresby, AH was Oahu, but many were unknown.

In May, evidence was fast building up of a major Japanese assault at a location they called AF.

The best guess of the unit was that AF meant Midway, the atoll at the western end of the fifteen-hundred-mile-long chain of islands that started at Hawaii. Midway was halfway between Los Angeles and Tokyo.

A guess was not enough, of course. Given the numerical superiority of the Japanese navy, Admiral Nimitz had to know.

Day by day, the men Chuck was working with built up an ominous picture of the Japanese order of battle. New planes were delivered to aircraft carriers. An ‘occupation force’ was embarked: the Japanese were planning to hold on to whatever territory they won.

It looked as if this was the big one. But where would the attack come?

The men in the basement were particularly proud of decoding a signal from the Japanese fleet urging Tokyo: ‘Expedite delivery of fuelling hose.’ They were pleased partly because of the specialized language but mainly because the signal proved that a long-range mid-ocean manoeuvre was imminent.