Classic Cryptography:Vigenère

Vigenère
The Vigenère cipher is a polyalphabetic substitution. Blaise de Vigenère actually produced a more sophisticated autokey cipher, but through an accident of history his name has become attached to this weaker cipher.

For the above reason, the Vigenère cipher is reasonably secure - requiring more work than a simple monoalphabetic substitution. Yet it is still possible to break by pencil and paper methods. I have heard that a well known scientific magazine said that it was "uncrackable" as late as 1917 - even though it had been broken before then. The Vigenère cipher makes use of a tableau.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
B C D E F G H I J K L M N O P Q R S T U V W X Y Z A
C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
E F G H I J K L M N O P Q R S T U V W X Y Z A B C D
F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
G H I J K L M N O P Q R S T U V W X Y Z A B C D E F
H I J K L M N O P Q R S T U V W X Y Z A B C D E F G
I J K L M N O P Q R S T U V W X Y Z A B C D E F G H
J K L M N O P Q R S T U V W X Y Z A B C D E F G H I
K L M N O P Q R S T U V W X Y Z A B C D E F G H I J
L M N O P Q R S T U V W X Y Z A B C D E F G H I J K
M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
N O P Q R S T U V W X Y Z A B C D E F G H I J K L M
O P Q R S T U V W X Y Z A B C D E F G H I J K L M N
P Q R S T U V W X Y Z A B C D E F G H I J K L M N O
Q R S T U V W X Y Z A B C D E F G H I J K L M N O P
R S T U V W X Y Z A B C D E F G H I J K L M N O P S
S T U V W X Y Z A B C D E F G H I J K L M N O P Q R
T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
U V W X Y Z A B C D E F G H I J K L M N O P Q R S T
V W X Y Z A B C D E F G H I J K L M N O P Q R S T U
W X Y Z A B C D E F G H I J K L M N O P Q R S T U V
X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
Y Z A B C D E F G H I J K L M N O P Q R S T U V W X
Z A B C D E F G H I J K L M N O P Q R S T U V W X Y

How is the ciphertext formed?

The cipher also requires a key, the cipher text is formed by first writing the key underneath the plain text. In the following example we will use the plain text "encryption rocks" and the key "alabaster".

plaintext     encryption rocks 
key(repeated) alabastera labas

Now, we will demonstrate how to form the cipher text. First, find the letter of the plain text on the top of the table, then drop down to the
letter row of the key letter. The first letter from the table is ‘e’, so

plain text encryption rocks
key(repeated) alabastera labas
cipher text eycsyhmmfn codkk

Seems pretty secure? Remember, there are plenty of people who would be able to crack this with paper and pencil, but it’s great for passing notes to friends. Now imagine coupling this techniques you’ve learned before it. Imagine an algorithm hundreds of times stronger than a Vigenère and a Polybius combined. That’s what your web browser is probably doing as you put your credit card into Amazon.com.

To form the ciphertext we need to use the Vigenère tableau, the plaintext is encrypted letter by letter using the correspponding key letter.

Using the tableau, a paper copy is useful, locate the first plaintext letter, "E", along the left hand side of the table, then locate the corresponding letter of the key, "G", along the top of the table.

How can it be broken?

What cryptanalysts would do first is to find the key’s length. The original cipher text is shifted against itself. The more letters match, the more likely that the number that shift is a multiple of the key length. The method is called the method of coincidences.

original text eYcsyhmmfn codkk
shifted text sYhmmfncod kkeyc

Since there is one match, after a shift of 3, 3 could possibly be a multiple of the key length. Let's assume that we went ahead and got the key length, a likely multiple of 9, as always, the more cipher text to work with, the more accurate the results. So we have the key length, now what? Decoding is easy for anyone with the key. Then we break up the cipher text into groups of 9, in which we can assume that all of the first letters in each group were encrypted with the same letter, all the second letters were encrypted with the same letter, and so on. Each group of firsts, seconds, and thirds, are then simply Caeser ciphers, and then are more readily broken down ( think about what would happen if you encrypted a Vigenère with the key ‘aaaaa’ ). Now it is simply a matter of solving each "group."

Being a polyalphabetic substitution, obviously a Vigenère cipher is more secure than a straightforward monoalphabetic substitution. Nevertheless, the cipher is still vulnerable to attack.