Cryptography Reference
In-Depth Information
3.5
3.21
3.05
3
2.3
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2.13
1.81
1.9
1.83
2
1.53
1.51
1.32
1.36
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1.22 1.3
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0.5
0
AN
AT ED EN ER ES HE IN ON OR RE ST TE TH TI
FIGURE 1.3
Percentage of Common Digraphs in English Text
1.17
BREAKING SIMPLE POLYGRAM CIPHERS
The Playfair cipher, for all its complicated rules, is not secure. Digraphs are not large enough
blocks to rule out the use of frequency analysis. Tables that record the relative frequency of
digraphs in typical English text exist (as well as for many other languages). For example,
the most common digraph in English text is “TH,” followed by “HE.” Using such tables,
one can break a Playfair cipher given enough ciphertext. A complete table is often not even
necessary; a partial table will often be enough, such as the chart shown in Figure 1.3.
Relative frequency tables for English exist even for trigraphs (3-letter blocks); the most
common is “THE,” followed by “AND” and “THA.” Such tables exist for even larger blocks.
Modern polygram ciphers use a block size of at least 8 characters.
1.18
THE JEFFERSON CYLINDER
None other than the American statesman Thomas Jefferson invented the Jefferson cylinder.
It was an ingenious device that provided very secure ciphers, and it was used for many
years. The cylinder consisted of 36 wheels. Each wheel had printed on it a complete (scram-
bled) alphabet. A simplified drawing of a typical Jefferson cylinder is shown in Figure 1.4.
To encipher, one needed to rotate the wheels so that the plaintext appeared along one of
the rows in the cylinder. To select the ciphertext, one would simply select any of the other
25 rows. Rotating the wheels so that the ciphertext would appear in one of the rows did
deciphering. Then they would search the other 25 rows of the cylinder for meaningful text.
What made the Jefferson cylinder so powerful was the huge size of its rows, or blocks;
frequency analysis on such blocks, each consisting of 36 characters, was literally impossi-
ble at the time.
The Jefferson cylinder eventually fell into disuse because of its impracticality. (This is
why most of the excellent classical ciphers were rejected; they were too hard to implement.)
Every authorized user of the cryptosystem would need his or her own cylinder. If a single
 
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