Portrait of Thomas Jefferson in 1791
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Thomas Jefferson (yes, our third president) invented his "wheel cypher" in the 1790s and a deceptively innovative little device it
is. In fact, this machine was so far ahead of its time, it was still in active use in the US military 150 years later at the beginning of
WW2.
The Jefferson cipher had 36 wheels arranged around an axle with a different random alphabet printed on the outside of each wheel. This is
a polyalphabetic cipher and at first pass it may seem to be similar in function to a Vigenère disk with a 36 character keyword, but
it is not. Each of the wheels has a different substitution alphabet, unlike using the same Vigenère wheel 36 times. You could
keep up a secure correspondence with many others by having a different wheel arrangement with each person.
The key is not a repeating keyword but the order of the 36 wheels on the axle, each wheel having a different cipher. There are
36 X 35 X 34 X...X 2 X 1 (= 36! or 36 factorial) ways to arrange 36 wheels on an axle, which is 3.72 X 1041. Jefferson calculated
this number exactly, calling it "372 with 39 cyphers [zeros] added to it". This compares favorably to the 3-rotor Enigma machine which has a
key space of about 1023.
Read Thomas Jefferson's description of his cypher wheel.
The sender of a cipher message using the Jefferson cipher wheel would arrange her disks in the agreed upon order and then simply spin each
disk to spell out the first 36 letters of her message, using any of the other 25 lines as the cipher. There were no numbers or punctuation
or spaces. The receiver of the message would arrange his cipher wheels in the prescribed order and then spell out the enciphered message
across one horizontal line. By scanning across the other 25 horizontal lines, the one with the message will clearly stand out from the rest
of the gibberish. This procedure would have to be repeated for the next 36 letters of the message, and so on.
Chinese combination lock with rotating characters
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Cipher wheel found in a home near Monticello, now at NSA Museum |
Detail showing bracket where rod would be inserted through the 36 wheels
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Jefferson's cipher wheel was beyond a doubt the most advanced, secure and user friendly cipher system of its time. He
seems to have invented it out of the clear blue, as his existing papers and letters do not show a study of the science of cryptology. He may
have gotten his inspiration for this cipher device by reading about or seeing the Chinese combination lock like the one pictured above. It is
known that Jefferson subscribed to a magazine which had an article explaining this lock, which was popular in France while he was there in
the early 1790s.
Jefferson was familar with a variety of ciphers. As the first Secretary of State for the new United States of America, he used a cipher
system called nomenclator, which was the cipher system in vogue for over 450 years, until around 1850. Nomenclator is a combination of
cipher and codes. As President, he selected the Vigenère cipher as the official cipher for the Lewis and Clark expedition.
Dr. Robert Patterson, a mathematics professor and President of the Philosophical Society, sent Jefferson a letter in 1802 recommending a
cipher system which is called columnar transposition, with nulls at the beginnings of the columns. Jefferson responded back to Dr. Patterson,
"I have thoroughly considered your cypher, and find it so much more convenient in practice than my wheel cypher, that I am proposing it to
the Secretary of state for use in his office." Later, he followed up in another letter, "We are introducing your cypher into our foreign
correspondences."
That Jefferson did not recognize his wheel cypher to be far superior to Patterson's cipher does not speak too highly of his cryptologic
understanding. If he would have recommended his own cipher, the US would have benefited from a much more secure system well into the 20th
century. Instead, his cipher was buried in history until it was rediscovered among his papers in the Library of Congress in 1922.
The cipher wheel above was found in a home near Monticello and is an exact match to Jefferson's description of his "wheel cypher". The 36
wheels are made of wood and it has been dated to the late 1700s. This device now resides in the NSA National Cryptologic Museum in Fort
Meade, Maryland. It is a French language cipher device with 40 characters around the circumference rather than 26. The
extra 14 characters may be the 14 French letters that have accent marks but the letters are too faint to tell from the photographs. The
left side of this device has a bracket with a hole in it which is used to insert a rod. The rod would then go through all 36 disks and
into the right side of the frame, keeping the letters lined up for enciphering or deciphering a message. As of this writing (April 2012),
this detail has not been displayed or mentioned in any known article. The link below will display the highest resolution pictures available
anywhere online for this unique and rare cipher machine.
Joseph O. Mauborgne (1881-1971)
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US Army Pamphlet published in Feb. 1922
Courtesy of David Stroud
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Jefferson's wheel cipher was to be reinvented at least twice. Etienne Bazeries, a French military cryptanalyst, invented his Bazeries
cylinder in 1891 but it was never adopted by the military. Then Captain Parker Hitt of the US Army invented it in strip form in 1913. The
strip form was made into a cipher called the M-138A. About 1917, Major Joseph Mauborgne redesigned it into the 25 wheels of the M-94, which
became the main battlefield cipher for the US military in 1922 and was in use until 1943.
Mauborgne would go on to cryptologic fame with several breakthroughs to his credit. The first involved the Playfair cipher, used by the
British as their field cipher. It was the first digraphic cipher, meaning that the cipher was based on pairs of letters in plaintext being
enciphered into another pair. Two pairs of plaintext letters with letters in common could produce ciphered text with no letter in common.
Mauborgne had the first recorded solution to this cipher in 1914, authoring the first work on cryptology published by the US government.
He also developed the first theoretically unbreakable cipher, called the one-time pad, along with co-inventor Gilbert Vernam.
Mauborgne was the first person to demonstrate the use of two-way radio communications from an aircraft to a ground station in 1914. This
innovation changed air warfare from individual airplanes into a coordinated air force. Later, as a two-star general and Chief Signal Officer,
he built and directed the team, led by William Friedman, that solved the Japanese Purple cipher in 1940. He retired a few months before Pearl
Harbor.
Etching by Joseph O. Mauborgne signed and dated 1951
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Mauborgne was also an accomplished artist, his portraits and etchings are displayed in several prominent galleries as well as private
collections. Mauborgne was also interested in music and violin making, for which he won an international competition in The Hague in 1949.
The US M-94, except for the number of wheels, is an exact replica of Jefferson's cipher wheel. Jefferson's invention of this 120 years
earlier, while being somewhat preoccupied with the founding of a new country, is testament to his extraordinary genius. The concept of a
rotor device with interchangeable wheels was the precursor to the various electrical, rotor-based cipher machines, such as the Enigma and
Hagelin machines, which were developed just after WW1.
See the Entire Collection of Cipher Machines
See detailed pictures of the US Army M-94 cipher, the Jefferson Wheel Cypher and 2 Mauborgne etchings.
This is the US Army M-94 cipher wheel first produced in 1922 and used until 1943, when it was replaced by the M-209. These were made
of all alumninum construction, except for the brass threads inside the knurled nut, and a total of 9,432 were manufactured. There are 25
wheels, numbered inside from 1 to 25 (also B to Z) and the daily key is the order of these 25 wheels on the spindle. The key space is 25!
(25 factorial = 25 X 24 X 23 X ... X 2 X 1 = 1.55 X 1025) which is larger than the German Army Enigma machine's key space.
After putting the wheels in the correct order for the day, you could send an enciphered message by aligning your message along the
straight-edge. Note this straight-edge has a notch every 5 characters to help keep track of the letters. The enciphered message can
be any of the other 25 rows of letters. To decipher, just line up the enciphered message along the straight-edge and read the other
lines until the one line with plain text becomes obvious.