Classic Cryptography: Playfair

Playfair
The Playfair cipher was actually invented by a someone named Wheatstone, but Playfair’s name is attached to it because he was its most avid supporter in the government circles. Playfair first demonstrated this cipher at a dinner in 1854. A Lord Granville gave the dinner, and a notable guest was Lord Palmerston. Hence, 'PALMERSTON' was the first keyword used to demonstrate this system.

The cipher is a form of mono-alphabetic substitution, but relies on digraphs rather than single letters, and it is simple to master. The Playfair cipher is believed to be the first digraphic system. We start with a keyword and then place the remaining letters in underneath, for instance using "cryptogram" as a keyword we will then get the following.

c  r  y  p  t  o  g  a  m

b d e f h i k l n
q s u v w x z

(the ‘R’ appears twice in cryptogram, and is skipped the second time, the i and the j share the same location)

The box is then read by columns.

c b q r d s y e u p f v t h w o ij x g k z a l m n

The new string of 26 letters is then transposed on a 5x5 grid, with the i and the j sharing the same location.

c b q r d
s y e u p
f v t h w
o i x g k
z a l m n

Now, forget all that stuff we just did, another method, which we are going to use, is to place the keyword as the first series of letters in a 5x5 grid, and fill the remaining letters in.

c r y p t
o g a m b
d e f h ij
k l n q s
u v w x z

Using this system, the message to be encrypted is broken up into groups of two letters, a sample message: ‘cows cannot encrypt’ would be encrypted by ‘co ws ca nn ot en cr yp tz’. The ‘z’ is thrown in because it would easily be recognized as a ‘junk’ letter after decryption. Now that you have broken up the message, you must take each message pair, and find the letters on the chart, take the row of the first letter, and the column of the second letter, and take the intersecting letter. Next, take the row of the second, the column of the first, and get that intersecting letter. Done, that is how to encrypt a pair, now let's encrypt our message with the chart.

plain text   co ws ca nn ot en cr yp tz 
cipher text  co zn yo nn bc fl rc py tz

The main advantage of this system is that it robs a cryptanalyst of it main weapon, as they are no longer able to look for recurring encoding, as in an ‘e’ can be encrypted as a different letter each time. This method is relatively secure, and a large amount of sample cipher text is required in order to run a
proper digraph frequency analysis. This cipher has many advantages, it is relatively secure, and requires but paper and pencil to encrypt large sections of text.