How to Make Anything Signify Anything

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For much of his long and largely secret career, Colonel William F. Friedman kept a very special photograph under the glass plate that covered his desk. As desks go, this one saw some impressive action. By the time he retired from the National Security Agency in 1955, Friedman had served for more than thirty years as his government’s chief cryptographer, and—as leader of the team that broke the Japanese PURPLE code in World War II, co-inventor of the US Army’s best cipher machine, author of the papers that gave the field its mathematical foundations, and coiner of the very term cryptanalysis —he had arguably become the most important code-breaker in modern history.1

At first glance, the photo looks like a standard-issue keepsake of the kind owned by anyone who has served in the military. Yet Friedman found it so significant that he had a second, larger copy framed for the wall of his study. When he looked at the oblong image, taken in Aurora, Illinois, on a winter’s day in 1918, what did Friedman see? He saw seventy-one officers, soon to be sent to the war in France, for whom he had designed a crash course on the theory and practice of cryptology. He saw his younger self at one end of the mysterious group of black-clad civilians seated in the center; and at the other end he saw the formidable figure of George Fabyan, the director of Riverbank Laboratories in nearby Geneva, where Friedman found not just his cryptographic calling but also his wife Elizebeth (flanked here by two other instructors from Riverbank’s Department of Ciphers). And he saw a coded message, hiding in plain sight. As a note on the back of the larger print explains, the image is a cryptogram in which people stand in for letters; and thanks to Friedman’s careful positioning, they spell out the words “KNOWLEDGE IS POWER.” (Or rather they almost do: for one thing, they were four people short of the number needed to complete the “R.”)

The photograph was an enduring reminder, then, of Friedman’s favorite axiom—and he was so fond of the phrase that some fifty years later he had it inscribed as the epitaph on his tomb in Arlington National Cemetery.2 It captures a formative moment in a life spent looking for more than meets the eye, and it remained Friedman’s most cherished example of how, using the art and science of codes, it was possible to make anything signify anything. This idea will no doubt strike us as quintessentially modern, if not postmodern, but Friedman took it straight from the great Renaissance scholar-statesman Sir Francis Bacon (1561–1626), along with both the hidden motto in the image and the method used to convey it. In other words, the graduation photo from Friedman’s earliest course in military cryptanalysis is at once a tribute to Bacon’s philosophy and a master class in the use of his biliteral cipher .

Bacon devised this ingenious code in the late 1570s (when he spent three years in the entourage of the English ambassador in France), but he did not describe its workings until 1623.3 The cipher was based, as the name “biliteral” suggests, on a system using only two letters—or, more precisely, one where each letter in the alphabet is represented by some combination of a ’s and b ’s. When Bacon realized that it was possible to represent all twenty-six letters in permutations of only two by using groups of five, he generated the following key:4

A = aaaaa
B = aaaab
C = aaaba
D = aaabb
E = aabaa
F = aabab
G = aabba
H = aabbb
I/J = abaaa
K = abaab
L = ababa
M = ababb
N = abbaa
O = abbab
P = abbba
Q = abbbb
R = baaaa
S = baaab
T = baaba
U/V = baabb
W = babaa
X = babab
Y = babba
Z = babbb

The crucial point in Bacon’s system is that the a ’s and b ’s in the ciphered text are not represented by those actual letters. If they were (using what is known as a straightforward substitution cipher5), a message reading “Hi” would simply appear as “aabbb abaaa”: anyone intercepting the text would quickly see that it was in code, and—given enough text and time—would easily discover the key. His way around this problem was as powerful as it was simple: he allowed the a ’s and b ’s in his system to designate the different forms of anything that can be divided into two classes, sorts, or types (which Bacon referred to as the a-form and the b-form ).