Cryptology - Unofficial St. Mary's College of California Web Site

9.4. PLAYFAIR 177
Playfair Ciphers: Pick a keyword. Using the Keyword Mixed method
Section 5.2 to mix the alphabet, arrange the the alphabet in a 5 × 5 array,
considering i and j to be the same letter.
To encipher, the plaintext is replaced two letters at time using the following
rules.
1. If the letters are in the same column, replace each by the letter below
it.
2. If the letters are in the same row, replace each by the letter to its
right.
3. If the letters are in neither the same row or column, then use them to
form a rectangle. The individual letters are replaced by the opposing
corners of the same height, i.e., the opposing corner in the same row.
(Notice that we must pretend that leaving the bottom of the array to be
entering its top, and leaving the right-hand-side to be entering its left-handside.)
Deciphering is simply the opposite: replace by the letters above, to the left,
and by the opposing corners.
For example, if we use the alphabet in its usual order (with J omitted) the
array is
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
Then examples of each of the three enciphering steps are as follows:
1. bm→GR, uz→ZE
2. lo→MP, gk→HF
3. ls→NQ, er→BU
Similarly, here are examples of the three deciphering steps.
1. LA→fv, JO→dj
2. QU→ut, CE→bd
3. TW→ry, LI→ of
If there are repeated letters in a pair, insert a null, often x, to break them up.
So balloon becomes ba lx lo on. Notice that oo is naturally broken, so no x
is needed. If the message contains an odd number of letters either send the last
letter un-enciphered, or add a final null letter before enciphering.