Playfair Ciphers and PLAYFAIR.EXE
                         Charles Shapiro
                      Compuserve 72300,3632
                        23 November 1988


Introduction

The playfair cipher was invented in 1854 by Charles Wheatstone, 
the physicist who was also responsible for the measurement tool 
known as the Wheatstone Bridge. But it bears the name of Lyon 
Playfair, a British politician who tried to get his foreign 
office to adopt it.   The playfair cipher is a good medium-
security cipher system for alphabetic  text.  You can easily 
encipher and decipher messages manually  with it, and enciphered 
messages are more secure than they are under a monalphabetic code 
(such as the Caesar cipher), and easier to encipher and decipher than
a book code message.

The playfair cipher works on letter pairs; this makes it less 
vulnerable to solution by frequency analysis, since the 
most common letter pairs in english (th and he) comprise a much 
smaller portion of the possible letter pairs than the most 
common letters do of the possible letters. It also means that a 
garbled code group affects only two letters of the message you 
are trying to send.

Using the playfair cipher

To encipher a message with the playfair cipher, you must first 
construct the key grid.  This grid must be a square; usually, "i" 
and "j" are equivalent in encoded text so that the key grid 
is 5 letters on a side.  To construct the grid, first think of a 
key phrase or word with no duplicated letters in it.  In our 
example, we will use the phrase "man bites dog".  

To construct a playfair grid from the key phrase, first write 
down the key phrase in 5 letter rows, so:

     m a n b i
     t e s d o
     g

Next, fill in the rest of the grid with the letters of the 
alphabet not found in the phrase:

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

Next, divide your message into letter pairs, inserting a null 
letter (such as "x") wherever a letter pair consists of two of 
the same letter or the message ends without another letter:


     i see no tourists only soldiers
     is ex en ot ou ri st so nl ys ol di er sx

The second group and the last group in this sample message 
contain nulls to make encoding it possible.

You can find every letter in the message on the code grid.  Each 
pair of letters on the grid can stand in only three relationships 
to each other: they can share a grid row, they can share a grid
column, or they can share neither a row nor a column.  To 
encipher a pair of letters which share a row, write down the grid 
letter to the right of each member of the pair.  To encipher a 
pair of letters which share a column, write down the grid letter 
below each member of the pair.   In these cases, the grid wraps 
around; hence, the letter to the right of "i" in the code grid 
given above is "m".   If the pair of letters to encipher share 
neither a row nor a column, their enciphered equivalents are the 
letters which are in the same row as the enciphered letter, and 
the same column as its mate.

Hence, to encipher the letter pair "is", you will first find "i" 
and "s" in the cipher grid, above:

     m a n b I
     t e S d o

The enciphered letter pair is "no", as follows:

     m a N b i
     t e s d O

The full enciphered text of the message given above with the key 
"man bites dog" is as follows:

     is ex en ot ou ri st so nl ys ol di er sx
     no sw sa te kz ub de dt mq xd tu ob dp fn

To decipher an encoded message, simply reverse the process 
explained above; take each coded pair of letters, find them in 
your grid, and look at their relationship.  If they share a row, 
the plaintext letters are to their left; if the share a column, 
the plaintext letters are above them.  If they share neither, the 
plaintext letter lies in the same row as the code letter and the 
column of its partner.

For added security, you can "transpose" your playfair key before 
constructing the code grid.  To transpose a key, write it out 
and write the rest of the alphabet beneath it:

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

Construct your code grid by reading down this primary grid, as
follows:

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

This method eliminates the regular structure of the grid for 
letters not in your key phrase.

Once you have spent about 15 minutes to master this cipher 
system, you can encipher and decipher quickly with pencil
and paper.  

Playfair.c

I have written "PLAYFAIR.C" to automate the process of 
enciphering and deciphering with the playfair cipher. It is 
limited in the same ways as the example cipher used above. 
Enciphered messages contain only lowercase letters; numbers, 
punctuation, and white space in plaintext are ignored. 

PLAYFAIR.C  takes  two  arguments:  an option string  and  a  key 
string.   The  key string must be enclosed by quotes; duplicate letters,
spaces, and punctuation marks are automatically removed from it.
A  "-" must precede the option string.   At this writing, there are
three option strings:   "-p" prints out a copy of the playfair cipher
table, "-d" decodes a message with the argument key, and "-t" transposes
the argument key as explained above.  Options can be combined in logical
orders -- "-pt" prints a transposed table, "-dt" decodes using a transposed
table.  All I/O happens through stdin and stdout.

Conclusion

I wrote this program for fun and entertainment, so I expect no 
remuneration for its use.  If you make enhancements to the code, 
please let me know about them.  Please note that I will accept no 
responsibility for the use or misuse of this encipherment method 
or this program. I also make no specific claims about the 
security or correctness of the PLAYFAIR.C code or any version of 
the playfair program.