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Section 3.3 An Automatic Hit

Subsection 3.3.1 Biography of Blaise de Vigenère

Insert biography when available

Subsection 3.3.2 The Autokey Cipher

Description of Alberti's autokey from Kahn ...

Below is a description of Vigenère's more secure variation on an autokey cipher.  1  Read carefully through the passage above, you will need to use Figure 3.3.1 in order to follow along.

This translation is mostly from Charles Mendelsohn in [11, p. 128], I have supplemented with material from the original description by Vigenère is in [16, pp.49-49b].

“Each letter may be enciphered by the preceding letter, thus: with the . . . text. . . . “Au nom de l'eternel” and the key D, we say, a [the first letter of the text] from D [the key letter] gives x; u [the second letter of the text] from A [the first letter of the text, which now becomes the key] gives i; n from U, a; o from N, h; m from O, g; d from M, u; e from D, p; l from E, t; e from L; m, t from E, l; e from T, s; r from E, h; n from R, i; e from N, x; l from E, t. By which method, taking D for the key, we would arrive at DXIAHGUPTMLSHIXT. The other method, which is more secret, is to encipher each letter of the clear text not by the letter [of that text] which precedes it, but by the letter by which the preceding letter is enciphered. Thus, a from D, which is the key, gives x; u from X [the first letter of the cipher text] h; n from H, e; o from E, e; m from E, c; d from C, o; e from O, u; l from U, m; ... etc.” [16, pp. 49-49b] [11, p. 128]

This is the table that Vigenère used for his Autokey Cipher
Figure 3.3.1. Table used for Vigenère's Autokey Cipher

Comprehension Check: It will be easier to follow what is happening in this passage if we write out the message as follows:

Text for the first cipher method:

Plaintext:    a u n o m d e l e t e r n e l
Key Letter:   D A U N O M D E L E T E R N E
Ciphertext: D X I A H G U P T M L S H I X T
  • Vigenère uses a D as the key to encipher the first letter, in the first method described where does he get the subsequent letters for the key?
  • The letter D enciphers a as X, but the a is not in row D of Figure 3.3.1 so how do we know that the a should be X ?
  • At one point Vigenère uses a key letter of U but there is no row U on his table, looking at how the U enciphers the n, what row is he using in place of U?
  • The a was enciphered as X, but the first letter of the ciphertext is D, also the ciphertext is one character longer than the plaintext, what is the explanation for both of these? Where did the leading D come from?

Text for the second cipher method:

Plaintext:    a u n o m d e l e t e r n e l
Key Letter:   D X H E E C O U ...
Ciphertext: D X H E E C O U M ...
  • In the second method described he again starts with a key of D but then where does he get the the next key letter X? What about the key letter H? Try to complete the cipher using the second method.
  • Vigenère believes his second method is more secure, looking at the key for the second method why do you think he believes this?
  • If you compare the key for his second method to the cipher text he generates why is Vigenère wrong about his second method being more secure?

Check your understanding by enciphering the message “automatic confusion” using Vigenère's first and second autokey methods, use Q for the initial key letter.

Answer

Method 1:

Plaintext:    a u t o m a t i c c o n f u s i o n
Key Letter:   Q A U T O M A T I C C O N F U S I O
Ciphertext: Q P I G A G R H M U N D H M A F M G H

Method 2:

Plaintext:    a u t o m a t i c c o n f u s i o n
Key Letter:   Q P E L G D X G R N T A B R F I Q L
Ciphertext: Q P E L G D X G R R R L F P E I Q L F

The message CHFABH CXNXM GFMRR MDDMR was enciphered using Vigenère's first autokey method, check your understanding of the method by deciphering it.

Answer
Ciphertext: C H F A B H C X N X M G F M R R M D D M R
Key Letter:   C S T O R M T H E B A S T I L L E N U L
Plaintext:    s t o r m t h e b a s t i l l e n u l l

The message QMPTM GPOHG SOOHL QXUGC was enciphered using Vigenère's second autokey method, check your understanding of the method by deciphering it.

Answer
Ciphertext: Q M P T M G P O H G S O O H L Q X U G C
Key Letter:   Q M P T M G P O H G S O O H L Q X U G
Plaintext:    h i d i n g i n p l a i n s i g h t x

Reflection: If you go back and look carefully at the preceding couple of exercises you will notice that deciphering a message enciphered using the first autokey method is equivalent to second method and vice versa. In what way does this weaken the cipher?