December 16, 2021

Friedman Christmas Cards: Finding the Message

Some of the William and Elizebeth Smith Friedman Christmas cards in the archives at the Marshall Foundation didn’t have solutions, so we enlisted the help of long-time Friedman fan, cryptanalyst Justin Troutman, and this is how he solved the 1934 card:

Context. Context was one of the most valuable tools available to classical cryptanalysts—especially those breaking codes during wartime, where speed and accuracy were paramount to time-sensitive decryption. Think of context as experience + intelligence; over time, you learn a lot about your adversary, the patterns and content of their communication, and how you might anticipate bits and pieces of what’s next. That’s how I solved the Friedman’s 1934 Christmas card, albeit without the pressures faced by Elizebeth and William during their pioneering days in the field.

I first learned about this outstanding puzzle from Melissa Davis, Director of Library and Archives at the George C. Marshall Foundation, home of the Friedman archives. Fortunately, I had two pieces of key context:

  • Photographs of their Christmas cards from 1928, ‘29, ‘31, ‘33, ‘34, and ‘35
  • Knowledge that the ciphertext within an actual Christmas card

This is an incredible treasure trove of context to be given; in fact, it reduced my solution time from potentially hours down to about 30 minutes. Let’s break down the steps I took, based on what I knew. (Note: This is undoubtedly something Elizebeth would have been fantastic at doing; that is, leveraging the wealth of experience and intelligence amassed over the decryption of myriad ciphertexts.)

Firstly, this is a Christmas card, which means it’s going out to friends and family—most, if not all, of whom are not cryptanalysts. Because of that, the Friedmans would have wanted the cipher to be mildly challenging, but solvable by all recipients in a reasonable amount of time.

Secondly, while each of their Christmas cards’ respective puzzles were unique, there was something shared by each of them, and I knew this even before seeing it: they’re Christmas cards and they must all contain some form of a Christmas greeting. We call this “known plaintext” in the cryptography world. What’s unique about the 1934 Christmas card is that it’s the only one without such a greeting in plaintext, so my working assumption is that it must be in the ciphertext.

For reference, here’s text you’ll see in the other cards that indicate it’s a Christmas card, without needing to solve the puzzle:

  • 1928: “XMAS”
  • 1929: “Merry Christmas / Happy New Year”
  • 1931: “Our Season’s”
  • 1933: “Greetings”
  • 1934:  Nothing
  • 1935: “Our Holiday Greetings To You”

Taking a look at the card, you’ll see a sketch of what appears to be a nutcracker (the vintage metal handheld type), where the top is shaped like a bird’s head with a speech bubble containing “Those Friedmans are here again!” The characters are tossed about at every angle, seemingly at random, around this sketch.


My first observation is that this isn’t a lot of text, which can make things really hard for a cryptanalyst; that, and it’s not arranged in a way that reveals patterns, like word length (e.g., _ _ _ is probably “the” or “and”) or double letters (e.g., “zrggp” is probably a five-letter word containing two “n’s” or “l’s”). What I didn’t know is if the placement of the characters mattered, or if there was any significance to the fact that some letters seemed to be grouped on the left, some on the right, and some in the middle.

I made a critical pivot: maybe this isn’t encrypted. Maybe what I’m looking at is actually the message itself, or plaintext, but scrambled in order. (We call this “diffusion”, where the letters themselves haven’t been changed, but their locations have; in other words, it’s like putting a sentence in a blender, where all the letters are still there, but the structure of the words they used to spell is gone.)

I almost fell into my first rabbit hole when I anagrammed the right-most grouping of letters—A, R, E, N, I, W, P, S Y—as “I spy a wren.” A-ha! The head of the nutcracker is a wren! Bletchley Park’s workforce was largely composed of women enlisted in the Women’s Royal Navy Service (WRNS), known as “Wrens”. This seemed a bit too on-trail to be off-trail. I was about 10 minutes in at this point and started finding other messages that seemed promising, but unrelated; it was hard letting go of my find, but I couldn’t extend it beyond that. Time to try another path.

I then took a look at all of the Christmas cards together, and I spent a little longer looking at them than before I had started. Remember a little earlier where I mentioned that this card (1934) was the only one not to have some Christmas-related text on the card itself? This card just contains strewn gobbledygook, with the family’s first names positioned on each side of the card. There’s no way to know it’s a Christmas card—unless the greeting is within the puzzle.

I was confident I had found my first big break; now, to find the message. To test this, I took the longest probable word it likely contained and treated this as a word search: Christmas. Why the longest? Because there’s not much plaintext for me to work with, and if this is a word search, and each letter of “Christmas” is in there, that’s a really good sign I’ve found a solution. Sure enough, every letter I needed to form “Christmas” was there. How about “Merry”? It’s there too! Noticing that the letters “Y”, “W”, and two “P’s” were still available, it was clear “Happy New Year” must be the rest.

So, there you have it: Merry Christmas / Happy New Year was their 1934 season’s greeting, truly hidden in plain sight. (Coincidentally, this turned out to be the same message printed at the top of their 1928 Christmas card.) What took me 30 minutes would have taken much longer without the other Christmas cards to compare and contrast; the Friedmans were incredibly clever, to the extent that they could create legitimately fun puzzles for their recipients to solve. There’s no doubt their ingenuity would have led me down numerous paths of possible solutions.

(It’s unclear to me if the arrangement of the letters was intentional; to me, their placement and angles seem random, but I didn’t give much thought to this, as it wasn’t required for solving the puzzle. However, it was the first thing I noticed and I did wonder if I needed to turn the card in certain ways to find clues.)

In closing, imagine for a moment that you’re Elizebeth Friedman, and your ability to quickly decrypt a message quickly and accurately determined whether or not rum runners, drug smugglers, or Nazi spies remained on the loose, or were apprehended. To be this good under that kind of pressure is a testament to her incredible ability to adapt efficiently when the codes are changing and the clock is ticking. She was truly a master of her craft and a pioneer of the field of cryptanalysis.

Guest blogger Justin Troutman is an applied cryptographer in the Bay area with research interests in the design of modern block ciphers, the history of classical field ciphers, and the application of cryptography to data’s role in social marginalization. He’s presently working in the autonomous vehicle security industry.