Cryptology: Monoalphabetic Substitution

Cryptology

Monoalphabetic Substitution

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Introductory Example

The key of a monoalphabetic substition is a permutation of the alphabet, for example:

   ABCDEFGHIJKLMNOPQRSTUVWXYZ
   UNIVERSTABCDFGHJKLMOPQWXYZ

For encryption locate each letter of the plaintext in the first row of this table, and replace it by the letter below it. In our example this becomes:

   ENGLI SHAST RONOM ERWIL LIAML ASSEL LDISC OVERE DTRIT ON
   EGSDA MTUMO LHGHF ELWAD DAUFD UMMED DVAMI HQELE VOLAO HG

For decryption we use the inverse permutation, given by the table

   ABCDEFGHIJKLMNOPQRSTUVWXYZ
   IJKLEMNOCPQRSBTUVFGHADWXYZ

that is a rearrangement of the key permutation: Exchange the two rows and sort the first row.

Historically cryptographers often used mysterious symbols for the ciphertext (look here for an example). This is an »illusory complication«, that is, it has no influence on the security of the cipher.

FAQ: Can we improve encryption by using strange symbols instead of normal letters?

Monalphabetic Cipher

A monoalphabetic cipher has as key space a selection of permutations.

The mathematical description is here.

Examples

The key space of the shift cipher consists of the simple translations (or shifts of the alphabet).
The general monoalphabetic cipher uses all permutations. Therefore for an n-letter alphabet we have n! keys.
In practice usually one uses only a restricted selection of permutations as keys. For example a usual rule is: Take a »keyword«, discard all letters that occur at an earlier position, and append all unused letters in alphabetical order [ARGENTI ca 1590].

The advantage of this rule is that the key is easily memorized. The secret agent doesn't need to carry around a suspicious sheet of paper and stomach it in case of getting caught. An example for the rule is in the introductory example using the (German) keyword »Universitaet«:

   UNIVERSITAET
   UNIVERSTA
   UNIVERSTABCDFGHJKLMOPQWXYZ

Questions: What is bad about this key? How to avoid this weakness?

As is shown in the mathematical part the key length of the general monoalphabetic cipher is about 88 for our 26 letter standard alphabet. Therefore exhaustion is out of the capabilities even of the best computers. In spite of this we'll see that the monoalphabetic cipher is not secure.

Practical Execution

You may use web forms for monoalphabetic encryption and decryption.

Exercise: Encrypt and decrypt some texts of your choice with the help of this web service.

[The next page gives a description of these programs. There you can also download them for local execution.]

Author: Klaus Pommerening, 1999-Sep-29; last change: 2014-Jun-12.