The two Americans in question are Herbert Osborne Yardley and Wolfe/William Friedman. It is thanks to these two chaps that the United States caught up to (and dare I say, exceeded) the world in cryptology.
Yardley is known for popularizing American cryptology with his book: The American Black Chamber. In it, he dramatized the inner workings of the black chamber he led during and after the first world war. The public response to his book is best illustrated by the opposing views two Japanese papers took on his work. From the Japan Chronicle: “It is so much like steaming open people’s letters — a thing which is distinctly not done”. Then from the Japan Times: “trying to decipher the other nation’s code is part of the game”.
I’ll side with the Japan Times on this one.
Friedman’s contributions caused less fanfare but were more impactful. The author clearly has a favourite: “Yardley’s career was like an amazing skyrocket that explodes in fantastic patterns against the heavens. Friedman’s was like the sun”. Personally, I think Friedman had a huge leg up; he married cryptologist Elizebeth Smith (her mother named her with an “e” because “she was not going to have anyone calling her child Eliza). Two cryptologists are better than one. Take this episode from when Friedman was trying to guess at the key of cryptogram. He had figured out the first part of the key was “Cipher”, but could not figure out what the second part:
He turned to the new Mrs. Friedman, and asked her to make her mind blank.
“Now,” he went on “I want you to tell me the first word that comes into your mind when I say a word”. He paused. “Cipher,” he said.
“Machine,” she replied
It turned out to be the very key desired.(page 374)
This is a damn good reason to marry someone with similar career interests.
More concretely though, Friedman came up with techniques for statistical-based cryptanalysis. I have not dived deep enough to really understand them, but from what I glean, his methods are based on the fact that any text in a human language is distinguishable from random. The combination of letter frequencies, idioms, and common word endings make it such that you can differentiate enciphered text from plain text (or monoalphabetically enciphered text, because it’s basically plain text) based on statistical properties alone. Key words: “kappa test”, “index of coincidence”.
It would be disrespectful to omit that the Friedmans did so much more. But this is not a book, so it will be sufficient to note that David Khan considers William Friedman to be the “greatest cryptologist” due to his various contributions to the field.