There are some big names in the history of cryptography — Caesar, Vignere, Turing, Diffie — but any student of twentieth century cryptography should know the name Friedman. Or perhaps I should say the names Friedman, because William and Elizebeth (no, that’s not a typo. Her mother wanted to make sure that nobody called her Eliza.) Friedman were a married couple who, both as individuals and together, made enormous contributions to the field. William Friedman is probably best known for leading the team that broke the Japanese PURPLE cipher and later for developing the American SIGABA cipher machine during World War II, and he went on to be one of the founders of the National Security Agency. Many versions of his story portray his wife simply as his assistant or as an interesting footnote to his story, but Jason Fagone’s excellent new biography of Elizebeth, The Woman Who Smashed Codes, fleshes out her story and argues successfully that she belongs high on any list of famous cryptographers.

To briefly summarize her story: as a young woman, Elizebeth Smith was recruited by George Fabyan to work at Riverbank Laboratories, a think-tank of sorts in rural Illinois. To say Fabyan was eccentric would be an understatement, and he was recruiting Elizebeth to join a team dedicated to proving thet Francis Bacon really wrote all of Shakespeare’s plays. These investigations involved looking at the different styles that different letters were written in, and finding messages that could be decrypted using Bacon’s Biliteral Cipher. As she worked on this project, Elizebeth grew very skeptical of the claims, but she also developed many techniques that cryptographers use to this very day in deciphering encrypted messages. She also started working closely with William Friedman, a geneticist who had originally been brought to Riverbank for projects but who eventually contributed to the Bacon project. And who fell in love with Elizebeth, with the two eventually getting married.

The two budding cryptographers were eventually enlisted to help with government efforts, and Elizebeth achieved some level of fame putting her skills to use to bring down smugglers and bootleggers during the era of prohibition while her husband was overseas working for the military. She worked for the Navy, the Treasury Department, and the Coast Guard, and is given credit for decrypting thousands of messages from rum-runners during the era leading to the downfall of many rings. Later, she was recruited by the military during World War II where she contributed to bringing down Nazi and Japanese spies and to solving some of the Enigma machine codes. Fagone argues that the work that her team did was invaluable to the Allies during the war, she has not gotten the credit she was due, largely due to the ego and sexism of J. Edgar Hoover.

In other words, this story has it all: love, Nazis, sexism, spies, and quirky characters, not to mention cameos by people like Ian Fleming and Roald Dahl. Even a mediocre writer could turn the story of Elizebeth Friedman into a great read, and in the hands of a writer as good as Fagone the book is one that I could not put down. A journalist whose previous books and magazine articles cover topics such as competitive eating, Nerf weapons, and gun violence, Fagone is clearly good at finding interesting topics to write about. He is also very good at structuring his story to give it good pacing, and also at crafting elegant sentences that would stick with me even days later — one example is when he describes science as “a check against the natural human tendency to see patterns that might not be there.’

I’m writing this review for the MAA, so I should say a few words about how Fagone describes the mathematical aspects of cryptography. He brings an outsider’s eye to some of the techniques of cryptography, and I suspect that many mathematicians will wish that he gave more details in some place and feel like he gives too much in other places, or find places they could nitpick. But given that this book is being written for general audiences and is primarily a history book, I found his descriptions to be reasonably detailed and accurate, while still being ready to move on to the next chapter of this exciting life instead of getting bogged down in the mathematical details that can be found elsewhere. It is also worth noting that since it is the 21st century, Fagone has an active social media presence and engages regularly with his readers on Twitter. He has also put many of the original documents that he has compiled online at archive.org, which is a great way to spend some time.

Much like last year’s Hidden Figures, Elizebeth Friedman’s story is one that is worth knowing first and foremost because it is a fascinating story about an important moment in American history, but also because it is a story that has not been told enough due to societal biases, and it is easy to see Friedman being an inspiration to the next generation of cryptographers, both boys and girls. Whether or not you already know about Friedman, The Woman Who Smashed Codes is a great read, and a book that belongs on every shelf.

Darren Glass is a Professor of Mathematics at Gettysburg College who teaches a First-Year Seminar on Cryptography. After reading Fagone’s book in October, he reconfigured a part of his course this fall to include more about both of the Friedmans.