Transposition Ciphers
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Transposition Ciphers
So far all the examples given have taken the message and substituted letters, or blocks of letters, with other letters or blocks. Thus they all come under the general heading of Substitution Ciphers. There are, however, other families of ciphers which are based on the idea of transposing the order in which the letters are written. These are known as Transposition Ciphers. We give a very simple example.
In our example the key is a small number. We use 5 as the key. In order to encrypt a message using this key, we write the key in rows of 5 letters and encrypt by writing the letters of the first column first, then the second column etc. If the length of the message is not a multiple of 5 then we add the appropriate number of Zs at the end before we encrypt. The process is most easily understood by working through a small example.
We encrypt the message WHAT WAS THE WEATHER LIKE ON FRIDAY. Since the key is 5 the first step involves writing the message in rows of 5 letters. This is:
WHATW
ASTHE
WEATH
ERLIK
EONFR
IDAY
Since the length of the message is not a multiple of 5, we must add one Z to get:
WHATW
ASTHE
WEATH
ERLIK
EONFRIDAYZ
We now read down each column in turn to get the following cryptogram:
WAWEEIHSERODATALNATHUFYWEHKRZ
To obtain the decryption key we merely divide the length of the message by the key. In this case we divide 30 by 5 to get 6. The deciphering algorithm is then identical to encryption. So, for this example, we write the cryptogram in rows of 6 to get:
WAWEEI
HSEROD
ATALNA
THTIFY
WEHKRZ
It is now easy to verify that reading down each column in turn gives the original message.
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Transposition Ciphers
Transposition Ciphers of the type given here are easy to break. Since the key must be a divisor of the cryptogram length, an attacker has only to count the length of the cryptogram and try each divisor in turn.
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Super-encryption
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Super-encryption
So far in this chapter we have provided a number of simple ciphers, most of which are easy to break. We now introduce a concept that can be used to combine two or more weak ciphers to obtain one that is considerably stronger than either. It is known as super-encryption. The basic idea is very simple. If, say, we want to super-encrypt using a Simple Substitution Cipher and a Transposition Cipher, then we first encrypt the message using the Simple Substitution Cipher, and then encrypt the resultant cryptogram using the Transposition Cipher. Once again a simple example should clarify the situation.
We encrypt the message ROYAL HOLLOWAYby super-encrypting a Caesar Cipher with key 2 with a Transposition Cipher with key 4. For the Caesar Cipher with key 2 we have:
Message: ROYAL HOLLOWAY
Cryptogram: TQACN JQNNQYCA
For the Transposition Cipher with key 4 we have:
Message: TQACN JQNNQYCA
Cryptogram: TNNAQ JQZAQYZCNCZ
Super-enciphering is a very important technique and many modern strong encryption algorithms can be regarded as resulting from superencryption using a number of comparatively weak algorithms.
Team-Fly
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Some conclusions
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Some conclusions
From the numerous examples discussed in the last sections it is clear that there are many factors that influence an attacker's chances of breaking a cipher system. We have also seen that, although the main prize for an attacker is knowledge of the decryption key, if the underlying language is highly structured then he may be able to determine a particular message without needing to discover the entire key. In fact our early examples indicate quite clearly that the structure of the underlying language is an extremely important factor when trying to assess an attacker's likelihood of success. For instance, it is clearly much easier to disguise random data than to successfully encrypt English text. It is also clearly true that, for English text, it is much easier to secure short messages than long ones. Indeed for a single short message, say three or four letters, there are many weak encryption algorithms that are probably sufficient.
Team-Fly
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