Cryptography Reference
In-Depth Information
able messages), or just enumerate all possibilities for k and then check to see if any words are formed by taking
characters that are k.
To protect messages more without increasing the complexity of the algorithm too much, it is possible to use
two columnar transpositions, one right after the other. We simply take the resulting ciphertext from the single
columnar transposition above and run it through the columnar transposition again with a different value of k .
We refer to these values now as k 1 and k 2 .
For example, if we take the encrypted string, shown earlier, from all work and no play makes
johnny a dull boy , encrypt it with k = 6 (as above, obtaining the ciphertext from the previous section),
and encrypt it again with k 2 = 8, we get:
ALYOA KEBNH PNWMU KLDON LYDLN JYLAA RASOO
To show how jumbled things get quite easily, we will take the plaintext P to be the alphabet:
abcde fghij klmno pqrst uvwxy z
Encrypting with k 1 = 5, we get the ciphertext C 1 :
AFKPU ZBGLQ VCHMR WDINS XEJOT Y
And we encrypt the ciphertext C 1 with k 2 = 9 to obtain the next and final ciphertext C 2 :
AQNFV SKCXP HEUMJ ZROBW TGDYL I
1.5 Cryptanalysis
In the previous sections, we explored the evolution of several simple cryptographic systems, many of which
were used up until the previous century (and some still find limited use, such as ROT13). Now we will discuss
the weaknesses in the above methods and how to defeat these codes.
1.5.1 Breaking Monoalphabetic Ciphers
The first topic we covered was monoalphabetic ciphers. These simple ciphers have several weaknesses, a few
of which were alluded to previously. There are a few important tools and techniques that are commonly used in
the evaluation and breaking of monoalphabetic ciphers, which we explore in the following sections.
1.5.1.1 Frequency Analysis
The most obvious method is called frequency analysis — counting how often individual letters appear in the
text.
Frequency analysis is based on patterns that have evolved within the language over time. Most speakers of
English know that certain letters occur more often than others. For example, any vowel occurs more often than
X or Z in normal writing. Every language has similar character properties like this, which we can use to our
advantage when analyzing texts.
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