Playfair cipher
With 600[1] possible bigrams rather than the 26 possible monograms (single symbols, usually letters in this context), a considerably larger cipher text is required in order to be useful.
Wheatstone offered to demonstrate that three out of four boys in a nearby school could learn to use it in 15 minutes, but the Under Secretary of the Foreign Office responded, "That is very possible, but you could never teach it to attachés.
A typical scenario for Playfair use was to protect important but non-critical secrets during actual combat e.g. the fact that an artillery barrage of smoke shells would commence within 30 minutes to cover soldiers' advance towards the next objective.
By the time enemy cryptanalysts could decode such messages hours later, such information would be useless to them because it was no longer relevant.
The key can be written in the top rows of the table, from left to right, or in some other pattern, such as a spiral beginning in the upper-left-hand corner and ending in the center.
The first rule can only be reversed by dropping any extra instances of the chosen insert letter — generally "X"s or "Q"s — that do not make sense in the final message when finished.
The first step of encrypting the message "hide the gold in the tree stump" is to convert it to the pairs of letters "HI DE TH EG OL DI NT HE TR EX ES TU MP" (with the null "X" used to separate the repeated "E"s).
Then: Thus the message "hide the gold in the tree stump" becomes "BM OD ZB XD NA BE KU DM UI XM MO UV IF", which may be restructured as "BMODZ BXDNA BEKUD MUIXM MOUVI F" for ease of reading the cipher text.
Most notably, a Playfair digraph and its reverse (e.g. AB and BA) will decrypt to the same letter pattern in the plaintext (e.g. RE and ER).
This is obviously beyond the range of typical human patience, but computers can adopt this algorithm to crack Playfair ciphers with a relatively small amount of text.
If there are no double letter digrams in the ciphertext and the length of the message is long enough to make this statistically significant, it is very likely that the method of encryption is Playfair.
A good tutorial on reconstructing the key for a Playfair cipher can be found in chapter 7, "Solution to Polygraphic Substitution Systems," of Field Manual 34-40-2, produced by the United States Army.
Sayers' book includes a detailed description of the mechanics of Playfair encryption, as well as a step-by-step account of manual cryptanalysis.
As the German numbers 1 (eins) to twelve (zwölf) contain all but eight of the letters in the Double Playfair squares, pro forma traffic was relatively easy to break (Smith, page 74-75) Advanced thematic cryptic crosswords like The Listener Crossword (published in the Saturday edition of the British newspaper The Times) occasionally incorporate Playfair ciphers.
