Cryptography in Japan

The cipher system that Uesugi used is basically a simple substitution usually known as a Polybius square or “checkerboard.” The i-ro-ha alphabet contains forty-eight letters, so a seven-by-seven square is used, with one of the cells left blank. The rows and columns are labeled with a number or a letter. In the table below, the numbers start in the top left, as does the i-ro-ha alphabet. In practice these could start in any corner.

To encipher, find the plaintext letter in the square and replace it with the number of that row and column. So using the square above, kougeki becomes 55 43 53 63 or 55 34 35 36 if the correspondents decided ahead of time on column-row order. The problem of what to do in the case of letters such as “ga,” “de,” and “pe” that do not appear in the i-ro-ha alphabet is avoided by using the base form of the letter instead – as above where “kougeki” becomes koukeki. Technically, this is a serious flaw because some messages may have two or more equally valid decipherments. To avoid this the encipherer may have had to rephrase messages.

The column and row headers do not have to be numbers. One common variation is to use letters. This was common in European cryptography and is found in the Uesugi cipher as well. However, the Japanese cipher had a twist that never seems to have been used in the West: using the last 14 letters of a waka poem to fill in the row and column headers. The table shown below gives an example of this, using “tsurenakumieshiakinoyufukure”.

This system of using a “checkerboard” to convert an alphabet into numbers or letters was described by Polybius over 2000 years ago. There are three main advantages to this system. First, converting letters into numbers allows for various mathematical transformations which are not possible or not as easy with letters – super-enciphering for example. Second, the checkerboard system reduces the total number of characters. Whether converting to numbers or letters, the Polybius square reduces 25 English letters to five characters. Uesugi's square reduces to seven. This reduction makes crytanalysis slightly more difficult than simple one-to-one substitution. Another benefit of the reduction in the number of letters is that it reduces the chance of error in communicating the message. The letters of the German ADGFX system in World War I were chosen because in morse code they are quite distinct and thus it was unlikely that an error in the morse code transmission would accidentally turn one letter into another. This would have been important for a sengoku daimyō, for instance, if he experimented with sending coded messages over long distances by torches, flags, poles, or similar system.

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