Cryptography, Information Theory, and Error-Correction. Aiden A. Bruen

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Cryptography, Information Theory, and Error-Correction - Aiden A. Bruen


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and the keyword letter is upper E (equals 4), then the cipher text letter corresponds to 24 plus 4 equals 28. However, 28 is larger than 26, so we subtract 26 to get 2, which is upper C. Thus, y enciphers to upper C.

Keyword: E N C O D E E N C O D E E N C
Message: t h e s k y i s f a l l i n g
Cipher text: X U G G N C M F H O O P M A I

      To decipher, simply subtract the value of the respective key letters from each cipher text letter. For example, to decrypt the cipher text “XUGGNCMFHOOPMAI” from above, we use the keyword “ENCODE” as follows:

StartLayout 1st Row 1st Column normal upper X minus normal upper E 2nd Column equals 23 minus 4 3rd Column equals 19 4th Column equals t 2nd Row 1st Column normal upper U minus normal upper N 2nd Column equals 20 minus 13 3rd Column equals 7 4th Column equals h 3rd Row 1st Column normal upper G minus normal upper C 2nd Column equals 6 minus 2 3rd Column equals 4 4th Column equals e 4th Row 1st Column normal upper G minus normal upper O 2nd Column equals 6 minus 14 3rd Column equals negative 8 equals 18 4th Column equals s EndLayout

      Repeat the process until all plain text characters have been determined. This enciphering process is easy if one has knowledge of the key. However, it can be difficult to break the cipher without such information. This will be investigated in Section 2.6.

      The Vigenère cipher is known as a type of block cipher, where the block length is equivalent to the key length. In a block cipher procedure, the plain text or message is encrypted block by block, rather than character by character.

      There are a few important remarks to be made regarding the use of the Vigenère cipher. First, because the same plain text character enciphers to different characters depending on the position, the cryptanalysis of such a cipher is much more complex than for a simple monoalphabetic substitution cipher. We also point out that the Vigenère cipher was invented to hide the frequencies of letters in the English language. The Caesar cipher, for example, does not do this. Also, if the key phrase “VIGENERECIPHERX” had been used instead of “ENCODE,” in our previous example, the encrypted message would have had perfect secrecy. Perfect secrecy is achieved if the cipher text yields no information about the plain text, and this occurs, roughly speaking, when the keyword is as long as the message itself. Such a secure system can be obtained using one‐time pads, which we investigate later in the book.

Letter Frequency (%) Letter Frequency (%)
a 7.44 b 1.46
c 2.52 d 3.53
e 12.22 f 2.68
g 1.84 h 5.97
i 6.82 j 0.20
k 0.65 l 4.28
m 2.71 n 6.32
o 8.25 p 1.97
q 0.12 r 6.21
s 6.99 t 9.85
u 3.67 v 0.12
w 2.09 x 0.18
y 1.87
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