What is a Polyalphabetic Cipher?

A Polyalphabetic Substitution Cipher is simply a cipher in which more than one alphabet is used. This means that though the plaintext letter 'E' is sometimes replaced with the ciphertext letter 'R' it isn't always replaced with the ciphertext letter 'R'.

A field cipher is a simple, usually paper based, cipher that can be used by soldiers with very little training.

The Vigenère Cipher

The Vigenère Cipher is a simple and popular PSC. It is simply a grid¹ containing all the twenty-six possible Julius Caesar Cipher alphabets. A keyword is chosen and each letter of the keyword is used in sequence to determine which alphabet is to be used.

For example: if the keyword was 'CAT' then the first character of the plaintext would be encrypted using the third possible Julius Caesar alphabet, identified by the keyword letter 'C'. The second letter of the plaintext would be encrypted using the first possible Julius Caesar alphabet, identified by the keyword letter 'A'. The third letter of the plaintext would be encrypted using the twentieth possible Julius Caesar alphabet, identified by the keyword letter 'T'. The fourth letter of the plaintext would be encrypted as the first, because the keyword repeats until the end of the message.

An important consequence of this system is that one of the possible alphabets replaces each plaintext letter with itself in the ciphertext, this means that there is a possible weakness in the system. However, if the key is long enough it actually makes little difference as the obvious letters are spread so thinly through the text. Having a cipher system in which the plaintext letter can never be encrypted as itself is a serious weakness in a cipher as it eases the use of 'Cribs' in cryptanalysis. The German Enigma cipher machine suffered this exact weakness.

The Vigenère Cipher is much more secure than the Julius Caesar Cipher, nonetheless cryptanalysis was used to break it and the first person to successfully do so was none other than Charles Babbage, the spiritual father of computing.

The Vigenère Tableau

ABCDEFGHIJKLMNOPQRSTUVWXYZ
==========================
BCDEFGHIJKLMNOPQRSTUVWXYZA
CDEFGHIJKLMNOPQRSTUVWXYZAB
DEFGHIJKLMNOPQRSTUVWXYZABC
EFGHIJKLMNOPQRSTUVWXYZABCD
FGHIJKLMNOPQRSTUVWXYZABCDE
GHIJKLMNOPQRSTUVWXYZABCDEF
HIJKLMNOPQRSTUVWXYZABCDEFG
IJKLMNOPQRSTUVWXYZABCDEFGH
JKLMNOPQRSTUVWXYZABCDEFGHI
KLMNOPQRSTUVWXYZABCDEFGHIJ
LMNOPQRSTUVWXYZABCDEFGHIJK
MNOPQRSTUVWXYZABCDEFGHIJKL
NOPQRSTUVWXYZABCDEFGHIJKLM
OPQRSTUVWXYZABCDEFGHIJKLMN
PQRSTUVWXYZABCDEFGHIJKLMNO
QRSTUVWXYZABCDEFGHIJKLMNOP
RSTUVWXYZABCDEFGHIJKLMNOPQ
STUVWXYZABCDEFGHIJKLMNOPQR
TUVWXYZABCDEFGHIJKLMNOPQRS
UVWXYZABCDEFGHIJKLMNOPQRST
VWXYZABCDEFGHIJKLMNOPQRSTU
WXYZABCDEFGHIJKLMNOPQRSTUV
XYZABCDEFGHIJKLMNOPQRSTUVW
YZABCDEFGHIJKLMNOPQRSTUVWX
ZABCDEFGHIJKLMNOPQRSTUVWXY
ABCDEFGHIJKLMNOPQRSTUVWXYZ


As an example, assume the key was 'DOG'. Taking out just those rows of the tableau needed to encrypt we have a rather more limited table:

ABCDEFGHIJKLMNOPQRSTUVWXYZ
==========================
DEFGHIJKLMNOPQRSTUVWXYZABC
OPQRSTUVWXYZABCDEFGHIJKLMN
GHIJKLMNOPQRSTUVWXYZABCDEF


We then take the message 'SEND FOOD' and write the key below it, repeating until the end of the plaintext:

Plaintext : SENDFOOD
Key       : DOGDOGDO

Then encrypt each letter using the keyletter associated with it:

Plaintext : SENDFOOD
Key       : DOGDOGDO
Ciphertext: VSTGTURR

Note that the double 'O' in the plaintext is encrypted as 'UR' and the double 'R' at the end if the ciphertext actually represents 'OD'.

The Statistics of the Vigenère Cipher

• Alphabets: 26
• Blocklength: 1
• Keyspace: Infinite

ADFGVX

ADFGVX is one of the most famous ciphers ever designed. It was widely used by the German Army during much of the First World War and it justifiably held a reputation for security. It was nevertheless broken, by a French cryptanalyst called Georges Painvin.

ADFGVX gets its name from the fact that only those six letters appeared in any message encrypted with it. The reason for this was because the inventor of the cipher found those six letters the easiest to memorise when he learned Morse Code. ADFGVX is a checkerboard cipher, a relatively common type of paper-based field cipher.

The cipher works by the construction of a thirty-six character checkerboard, each character being identified by its co-ordinates. Each character becomes two letters in this first stage. For illustration look at the grid below.

 ADFGVX
A8dhaq0
Dxnow2f
Flse71k
G4rp5zb
Vt9j6cu
X3myivg

Plaintext : S E N D F O O D
Ciphertext: FDFFDDADDXDFDFAD

This ciphertext is then split into columns in a predefined grid and read off in rows to mix up the order.

Painvin became obsessed with the task of breaking ADFGVX, becoming quite ill in the process, but he cemented a reputation as a dedicated cryptanalyst.

The Statistics of the ADFGVX Cipher

• Alphabets: 36
• Blocklength: 1 - 4 variable
• Keyspace: 3.7x10⁴¹

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¹ Usually called a Vigenère Tableau.