The unbreakable cipher
One of the simplest ways to encrypt messages is by means of a shift cipher. When using a shift cipher, each letter of the plaintext is replaced by another letter a fixed number of positions down in the alphabet, in order to yield the ciphertext. This number of positions is called the shift.
For example, if the shift is 3, then each A of the plaintext is replaced by a D, each B by an E, each C by an F, and so on. The substitions of letters can be illustrated by aligning two alphabets, the plain alphabet and the cipher alphabet. The plain alphabet is simply the usual alphabet, while the cipher alphabet is the plain alphabet rotated three steps to the left:
Plain alphabet: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Cipher alphabet: DEFGHIJKLMNOPQRSTUVWXYZABC
Using the table above, the plaintext "GEOCACHINGISFUN" becomes the ciphertext "JHRFDFKLQJLVIXQ".
The Vigenère cipher is another method of encrypting alphabetic texts. This method was originally described by Giovan Battista Bellaso (1505-?) in 1553, but was in the 19th century misattributed to the French diplomat Blaise de Vigenère (1523-1596), and is nowadays therefore widely known as the Vigenère cipher.
 |
In the Vigenère cipher, one uses a series of different shift ciphers, where the length of the shifts are based on the letters of a keyword. As an aid for encrypting a message using this cipher, one can use a tabula recta or Vigenère table, which is a quadratic table of alphabets, as shown in the table to the left. In the first row of the Vigenère table, the ordinary alphabet is listed. Any other row is then obtained by rotating the previous row one step to the left. For instance we find the alphabet that we used in the example above to encrypt "GEOCACHINGISFUN", in the row labeled D of the Vigenère table.
At different points in the encryption process, one uses the different alphabets from one of the rows of the table. Which row (and thereby which alphabet) to use at each point, depends on the letters of the keyword.
|
We illustrate the encryption process by means of an example. Suppose that we again wish to encrypt the plaintext "GEOCACHINGISFUN". We will use the keyword "NANO". First we repeat the keyword until it matches the length of the plaintext:
GEOCACHINGISFUN
NANONANONANONAN
Then we pair the first letter of the plaintext, G, with the first letter of the repeated keyword, N. This means that we look up the row labeled N and column labeled G of the Vigenère table. In that cell of the table we find T, which will be the first letter of the ciphertext. Next, we combine the second letter of the plaintext, E, and the second letter of the repeated keyword, A, in the same way; the letter at row A and column E of the table is E. Continuing in this manner finally yields
Plaintext: GEOCACHINGISFUN
Repeated keyword: NANONANONANONAN
Ciphertext: TEBQNCUWAGVGSUA
Hence the ciphertext will be "TEBQNCUWAGVGSUA".
For more than 300 years, the Vigenère cipher was believed to be impossible to break, and was therefore called the unbreakable cipher, (in French: "le chiffre indéchiffrable"). In fact, it took over 300 years after its invention, before the first successfull attack was published in 1863 by Friedrich Kasiski (1805-1881). However, it was later found out that Charles Babbage (1791-1871) had discovered the very same method to break the cipher, already in 1854.
