Japanese Cryptology From The 1500s To Meiji
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.
8 i-ro-ha Alphabet, 1-7 Checkerboard Cipher 1 2 3 4 5 6 7 1 i ro ha ni ho he to 2 chi ri nu ru wo wa ka 3 yo ta re so tsu ne na 4 ra mu u i1 no o ku 5 ya ma ke fu ko e te 6 a sa ki yu me mi shi 7 e hi mo se su n
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”.
Checkerboard Cipher Using Waka Poem re ku fu yu no ki a e a ya ra yo chi i tsu hi sa ma mu ta ri ro re mo ki ke u re nu ha na se yu fu i so ru ni ku su me ko no tsu wo ho mi n mi e o ne wa he e shi te ku na ka to shi
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.
Finally, although the checkerboard system doubles the length of messages, breaking each plaintext letter into two ciphertext letters allows for separate transformations on each of the halves. However, this does not seem to have been used much in American or European cryptology and Japanese cryptologists apparently did not use it at all.
It is not known how or even if Uesugi actually used the seven-by-seven checkerboard system. The scarcity of evidence makes it impossible to draw any firm conclusions but tentatively it seems that senkoku period daimyō did not have much use for cryptology. Of course it is possible that they did have their “black chambers” and that those chambers were shrouded in such secrecy that no hint of their existence escaped. This seems unlikely however. Several daimyō compiled codes of conduct or books of advice on governing for their offspring. Had cryptology been an important factor in the success of such men, they might be expected to pass that advantage along to their successor. The fact that they did not do so, in writing at least, does not prove anything but, in light of the other evidence – and lack of it – does make the existence of black chambers of the European sort seem unlikely.
The history of cryptology in Japan shows two things. First, the fact that substitution ciphers existed makes the failure of the Japanese to improve on the substitution cipher or to invent the transposition cipher much harder to explain. Second, the lack of a strong cryptographic tradition suggests – almost requires – a correspondingly weak cryptanalytic tradition. In fact there seems to be no cryptanalysis in Japanese history before the late 19th century.
Read more about Japanese Cryptology From The 1500s To Meiji: The Bakumatsu and Early Meiji Periods, World War I As Turning Point, The American “Black Chamber” and The Two-Letter Code, Analysis of The Two-Letter Code, Code Improvements in The Nineteen Twenties and Thirties, Jan Kowalewski, Learning From Warsaw and Then in Warsaw, Discrepancies, The Two-Letter, Ten-Chart Code, Hara Hisashi's Pseudo-Random Number Code, Two-Part Codes, Random Numbers, Hara's Pseudo-Random Number Generator, The State of Japanese Army Cryptology Around 1941, Conclusions
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