From Code Girls, by Liza Mundy (Hachette, 2017), Kindle pp. 88-90:
On June 1, 1939, the Japanese fleet began using a code that the Allies came to call JN-25. The Japanese—who had moved to using numbers rather than characters—now employed a massive codebook containing about thirty thousand five-digit groups. They also had a new way of enciphering. Before the code was sent, each code group was enciphered by using math to apply an “additive.”
Here is how the additive method worked: When a Japanese cryptographer began encoding a single message, he would look in the codebook and find the five-digit group that stood for the word (or syllable or phrase or punctuation mark) he wanted. He would repeat that process until he got to the end of the message. Then he would get out a different book, called an additive book, turn to a page—selected at random—pick a five-digit number, and add that to the first code group. He would add the next additive to the second. And so on. The Japanese code makers used a peculiar kind of math called noncarrying or “false” addition. There was no carrying of digits, so 8 plus 7 would equal 5, rather than 15. If the code group for “maru” was, say, 13563, and the additive was 24968, the resulting group would be 37421 (1 + 2 =3; 3 + 4 = 7; 5 + 9 = 4; 6 + 6 = 2; 3 + 8 = 1). That was the group of digits that would be radioed. To crack a message, the Americans had to figure out the additive and subtract it to get the code group. Then they had to figure out what the code group stood for.
Once again, it was Agnes Driscoll who diagnosed the new system. Neither she nor anybody in the Navy operation had seen an additive cipher—everything up to then had been transposition, or switching—but she figured it out. It took her less than a year to make a dent. A March 1 status report for the unit “GYP-1” stated that for the “5-number system”—an early title for JN-25—“First break [was] made by Mrs. Driscoll. Solution progressing satisfactorily.” She worked on it for several more months before being transferred in late 1940 to German systems—a promotion in the sense that the Atlantic was beginning to emerge as the hot spot. The research team continued working their way through JN-25, using her methods.
The process of stripping additives and discerning the meaning of code groups was laborious and excruciating. Years after World War II ended, American code breakers who worked in Hawaii and Australia were still arguing with their D.C. counterparts over what certain code groups stood for. Much like the women who trained the men who would get to do the wartime flying, much like Elizebeth Friedman over at the Coast Guard, Agnes Driscoll taught the men in the field who did this. “In the Navy she was without peer as a cryptanalyst,” wrote Edwin Layton, who headed naval intelligence for Admiral Nimitz, the chief naval commander in the Pacific during the war. In December 1940, both code and cipher were changed, to a system the Allies called JN-25B; the team stripped the additives and built a partial bank of code words. Then, in early December 1941—days before Pearl Harbor—the additive books were changed. The codebooks were not. The U.S. Navy was able to recover a certain amount of the new system—but not enough—before the attack on Pearl Harbor happened and all hell broke loose.
“If the Japanese Navy had changed the code-book along with the cipher keys on 1 December 1941, there is no telling how badly the war in the Pacific would have gone,” said Laurance Safford.
As crushing as Pearl Harbor was, it was thanks in large part to Driscoll’s decades-long detective work—and to the example Elizebeth Friedman set for other women—that America did not enter the Second World War quite as blind as it might have seemed.