of this common secret key.
For a numerical explanation, suppose we label
Figure 2.1 Caesar cipher wheel.
Note that in the above example,
To decipher the message, reverse the operation (shift left by
In this case, we have
The Caesar cipher is a simple example of a type of cipher known as a monoalphabetic cipher. Monoalphabetic ciphers belong to a class of ciphers known as substitution ciphers, in which all of the plain text characters in the message are substituted for another letter. Mathematically speaking, the enciphering process of a monoalphabetic cipher can be represented by the mapping of a plain text character to a cipher text character:
Similarly, deciphering is represented by the mapping
where
To break such a cipher, one can decrypt the message by trying all 26 keys (this is referred to as an exhaustive search). For long messages, the likelihood of a cipher text decrypting to two intelligible messages is small.
We mention here briefly affine ciphers. They are similar to Caesar ciphers in that they are simple substitution ciphers, but they differ in that enciphering involves not only addition, but also multiplication as well.
2.3 The Scytale Cipher
The Scytale cipher was introduced around 500 BCE by the Spartans, who used this rather simple but effective method to send crucial planning data between generals and bureaucrats. Both the sender and receiver were in possession of a cylindrical tube of the same diameter. To encode the message, the sender would wrap a thin strip of paper around the tube, with the paper spiraling its way down the length of the tube. The message was then written on the strip, with letters being written one beneath the other until the end of the tube was reached. (The message was then continued by starting a new column of letters, and this process was repeated until the message was finished.) To encode, the sender would simply unwrap the paper, leaving a thin strip of unintelligible letters. To decode, the receiver only had to wrap the paper around their similar tube and read the message off in columns.
It is often much simpler to duplicate the Scytale process with pencil and paper. Using a preselected number of rows (this number is the cipher key), write the message in columns. Then, “unwrap” the message by writing a string of characters consisting of the concatenated rows. For example, the message “THE ENEMY WILL ATTACK AT DAWN” is encrypted as follows:
Knowledge of the cipher key reduces the decryption process to a trivial matter. Using the fact that the key for this example is six, count up the total number of characters and divide by six. Doing so yields the period of the sequence,
