To best understand the very fascinating Vigenere-Square Cipher, we must first lay a basic groundwork of knowledge through some basic definitions and explanations.

Encryption – The process of obscuring information to make it unreadable without specific or special knowledge.

Cipher – An algorithm for performing encryption and decryption through a series of defined-steps which follow a set procedure.

Substitution Cipher – A method of encryption by which units of plaintext are substituted with cipher text according to a regular system. The units may be single letters (as is in most common cases), pairs of letters, triplets of letters, mixtures of the above, etc. The receiver will decipher the text by performing an inverse substitution.

Caesar Cipher – Also known as the shift cipher, or Caesar Shift, the Caesar Cipher is one of the most basic and widely-known encryption techniques. It is a type of substitution cipher in which each letter in plaintext is replaced by a letter some fixed number of positions further down the alphabet.

The Caesar cipher is named after Julius Caesar, who used it with a three letter shift formula to protect messages during battle, according to Suetonius, a prominent Roman historian.

Polyalphabetic Cipher – A cipher based on substitution, using multiple substitution alphabets. The best example is the Vigenere cipher described below.

The Vigenere cipher is a method of encryption which uses several different Caesar ciphers based on the letters of a keyword and is considered a simple form of polyalphabetic substitution.

The Vigenere cipher has been recreated and reinvented many times over the centuries. The concept was first seen in the book La Cifra Del. Sig. Giovan Batista Belaso, by Giovan Batista Belaso in 1553. Later, in the 19th century, the concept was misattributed to Blaise de Vigenere in the 19th and the name stuck as such ever since.

The cipher is extremely well known due to its easily understandable construction and theory. The cipher was considered unbreakable until the 19th century. Interestingly enough, the Confederacy used a brass cipher disk to implement the Vigenere cipher during the American Civil War. Throughout the war, the Union consistently cracked the messages leading to the widespread knowledge of its penetrable nature.

In a Caesar cipher, each letter of the alphabet is shifting along a specific number of places. For example, a shift of 4 would have an A become E, a B be F, etc. The Vigenere Cipher furthers this idea by using several Caesar ciphers of varying shift values.

To encrypt, a table of alphabets called a Vigenere square, is used. This table consists of the alphabet written out 26 times in different rows, with each alphabet shifted cyclically to the left compared to the previous and corresponds with the 26 possible Ceasar ciphers. Throughout the encryption process, the cipher uses a different alphabet from a certain row. The selection of which alphabet to use depends on repeating word.

Lets look at an example. Suppose we want to encrypt the plaintext: Trustwave ISGREAT. First, we select a keyword. In this example we will use the word "HOUSE". The person who is sending the message must repeat the word until it matches the number of characters of the plaintext message. In this example, the key would be HOUSEHOUSEHO.

Plaintext:     Trustwave ISGREAT
Key:             HOUSEHOUSEHO
Ciphertext:  EFUETPGAJIHH

The first letter of plaintext, X, is encrypted using the alphabet in row H which is the first letter of the key. The easest way to think of it is as follows. X is found in the top row and H is found in the left column so follow the two together to lead to E, your first cipher place. Repeat until the message is completely encrypted. You can see that without computers, this can be a very long and tedious process!

The relative power behind the Vignere Cipher lies in its ability to make frequency analysis more difficult. Frequency analysis is defined as the decrypting of a message by counting the frequency of ciphertext letters, and linking it to the letter frequency of normal text. For example, if L is the most commonly found letter in the ciphertext, one could estimate that if the original plaintext was in English, E, the most common letter in the English alphabet, could be represented by the L. However, the overall weakness in the Vigenere cipher is due to its relatively short and repeated nature of its key.

The Vigenere cipher was compromised over 140 years ago, first by Friedrich Kasiski in 1863. The Kasiski examination takes advantage of the fact that certain common words like "and" and "the" are encrypted using the same key letters, leading to repeated groups in the cipher text. The Kasiski test is effective with longer messages, as they usually will contain more repeated cipher text segments.

Later in 1925, William F. Friedman invented the Friedman test which uses the index of coincidence theorem which focuses on the probability of any two randomly chosen letters in English are the same as a about 6.5%. The test is an approximation which has proven sufficiently effective.