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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rel="nofollow" href="#fb3_img_img_679798b2-cb04-5aba-a887-86cc24ed8354.png" alt="1 comma 8 comma 15 comma ellipsis"/>, this will still be the case. Therefore, the most frequent cipher text letter in positions 1 comma 8 comma 15 comma ellipsis will have come from the enciphering of the letter “e”. Thus, by computing the number of occurrences of each cipher text letter at intervals of 7 letters, we can determine the most frequently occurring cipher text letter and assign it to the plain text letter “e”. Hence, we will have determined the first letter of the keyword. Similar remarks apply to positions {2 comma 9 comma 16 comma ellipsis}, {3 comma 10 comma 17 comma ellipsis}. In general, if we know the period n, we can capture the key using frequency analysis.

      We will first try the case where the period is 4, and we will determine the character frequencies for the {1 Superscript s t Baseline comma 5 Superscript t h Baseline comma 9 Superscript t h Baseline comma ellipsis} letters, {2 Superscript n d Baseline comma 6 Superscript t h Baseline comma 1 0 Superscript t h Baseline comma ellipsis} letters, and so on. Taking the 1 Superscript s t Baseline comma 5 Superscript t h Baseline comma 9 Superscript t h Baseline comma ellipsis letters, we get

VKGKT EVPUG JVCCP GDGPD DMGKG PVPA

      from which we obtain the following table of frequencies:

A B C D E F G H I J K L M
1 0 2 3 1 0 6 0 0 1 2 0 1
N O P Q R S T U V W X Y Z
0 0 5 0 0 0 1 1 4 0 0 0 0

      Since G is the most frequently occurring letter, we make the assumption that “e” enciphers to G. Thus the first key letter might be “C.” Similarly, for the second set of letters (i.e. the 2 Superscript n d Baseline comma 6 Superscript t h Baseline comma 1 0 Superscript t h Baseline comma ellipsis letters), we obtain the following table:

A B C D E F G H I J K L M
0 1 0 1 0 5 2 4 2 0 1 0 1
N O P Q R S T U V W X Y Z
0 1 0 1 0 4 0 1 2 1 0 0 1

      For the 3 Superscript r d Baseline comma 7 Superscript t h Baseline comma 1 1 Superscript t h Baseline comma ellipsis letters, we obtain the following frequency table:

A B C D E F G H

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