## Section 3.5 Presidential Secrets

###### Objectives

- Jefferson's Biography
- Jefferson's Letter with Vigenère's Cipher
- Jefferson's Wheel Cipher

### Subsection 3.5.1 Thomas Jefferson's Biography

A brief biography of Thomas Jefferson.

### Subsection 3.5.2 Thomas Jefferson and Vigenère's Cipher

Among Thomas Jefferson's papers in the library of congress there are atleast 63 distinct items which discuss ciphers. In one of these, a letter from Jefferson to Meriwether Lewis (Thomas Jefferson to Meriwether Lewis, April 20, 1803), Jefferson suggests that they use Vigenère's cipher for their correspondence.

Suppose the keyword to be “antipodes”

write it thus to be cyphered

a n t i p o d e s a n t i p o d e s a n t i p o d e s t h e m a n w h o s e m i n d o n v i r t u e b e n t u v y v q b & m g t s f r e s s s n j e m c u q i t m

then copy out the cyphered line thus, uvyvqb&mgtsfresssnjemcuqitm

numbers are thus, 18 is `bv`

1798 is thus `bubq`

the method is this.

look for `t`

in the \(1^{st}\) vertical column & `a`

in the \(1^{st}\) horizontal one gives `u`

. . . `h`

. . . `e`

. . . `m`

. . . `a`

. . . `n`

. . . `n`

. . . `t`

. . . `i`

. . . `p`

. . . `o`

. . . `v`

. . . `y`

. . . `v`

. . . `q`

. . . `b`

*Comprehension Check:*

- Look carefully at Jefferson's work, can you find his error?
- How did Jefferson turn 18 into
`bv`

? - How did Jefferson turn 1798 into
`bubq`

?

###### Checkpoint 3.5.1.

Below is the rest of the quote from Thomas Blacklock that Jefferson started enciphering. Try to complete the enciphering.

The man, whose mind on virtue bent,Pursues some greatly good intent,With undiverted aim,Serene, beholds the angry crowd;Nor can their clamors, fierce and loud,His stubborn honor tame.

UVYVQB &MGTSF RCSSSN JEMCUQ ISLQHK AJTWXG NS&&UP XQQHBH MYBXJF UJBBXI RIAWSK BUSENE TSKNCT FJ&PZX AIWIFF HERLGC &IFPEW JCHLJA SQEJBC VXYJSK LUPRID PHXQYG WYMCPH &CWSSG SGUVU

Start by writing out the plaintext with the key text above it, just as Jefferson did:

antipod esan tipodes anti podesa ... pursues some greatly good intent ...

Next, using the key letter to tell you the column and the plaintext to tell you the row, look up the cipher letters inside the table:

antipod esan tipodes anti podesa ... pursues some greatly good intent ... QHKAJTW XG ...

###### Checkpoint 3.5.2.

Use the key word `happy`

to enchipher Jefferson's birthday of April 13, 1743.

### Subsection 3.5.3 Thomas Jefferson's Wheel Cipher

Here is a brief description of Thomas Jefferson's wheel cipher, and here is his description Jefferson's Wheel Cipher, that we examine below.

From a cylinder of white wood of about 2 inches in diameter and 6 to 8 long bore through the center a hole sufficient to receive an iron spindle or axis of 1/3 or 1/2 inch diameter. Divide the perimeter into 26 equal parts (for the 26 letters of the alphabet) and with a sharp point draw parallel lines through all the points of the division from one end to the other of the cylinder, and trace those lines with ink to make them plain. Then cut the cylinder end wise into pieces of about 1/6 of an inch thick, they all resemble backgammon men with plane sides. Number each of them as they are cut off, on one side, that they may be arranged in any order you please. On the perimeter of each & between the black lines, put all the letters of the alphabet, not in their established order, but jumbled & without order so that no two shall be alike. Now string them in their numerical order on an iron axis, one end of which has a head and the other a nut or crew the use of which is to hold them firm in any given position when you chose it. They are now ready for use, your correspondent having a similar cylinder similarly arranged.

Suppose I have to cypher this phrase “Your favor of the \(22^{nd}\) is received.”

I turn the \(1^{st}\) wheel till the letter `y`

presents itself

turn the \(2^{nd}\) and place it's `o`

by the side of the `y`

of the \(1^{st}\)

turn the \(3^{rd}\) and place it's `u`

by the side of the `o`

of the \(2^{nd}\)

turn the \(4^{th}\) and place it's `r`

by the side of the `u`

of the \(3^{rd}\)

turn the \(5^{th}\) and place it's `f`

by the side of the `r`

of the \(4^{th}\)

turn the \(6^{th}\) and place it's `a`

by the side of the `f`

of the \(5^{th}\)

and so on till I have got all the words of the phrase arranged in one line, fix them with the screw. You will observe that the cylinder then presents 25 other lines of letters, not in any regualr sense, but jumbled & without order or meaning. Copy one of them in the letter to your correspondent. Then he receiving it, he takes his cylinder and arranges the wheels so as to present the same jumbled letters in the same order in one line. He then fixes them with the screw and examines the other 25 lines and finds one of them presenting him these words “Your favor of the \(22^{nd}\) is received” which he understands. As the others will be jumbled & have no meaning he cannot mistake the true one intended.

*Comprehension Check*

- If the cylinder we start with is 8 inches long, how many discs do we get following Jefferson's directions?
- Using factorials (see Definition 1.1.10), in how many ways could you rearrange the number of discs you found in the previous problem?
- In his description Jefferson says that we should write the alphabet around the edge of each disk “not in their established order, but jumbled & without order so that no two shall be alike”, how many ways can we rearrange the letters of the alphabet so that they are not in their usual order?
- Jefferson was unfortunately wrong when he said “As the others will be jumbled & have no meaning he cannot mistake the true one intended.” Why did he believe this was the case, what did he mean by this? Can you construct a way to arrange letters on a disk so that you could end up with more than one message?

While his cipher was not used while Jefferson was in office a variation of it was employed from about 1920 to 1945 in the form of the M-94 Cipher Cylinder.

###### Checkpoint 3.5.3.

Use the Jefferson Wheel simulator below to encipher the message “Jefferson”.

Because after lining up the letters you want you can choose to write down any other row, there are multiple different asnwers. One posibility is: `MMIHODVWR9RN`

###### Checkpoint 3.5.4.

Decipher the message `LY2VAALYQVCV`

below using the simulator.

attack at dawn