This cipher has been documented since 1937 when the Swede Per Meurling used it during the Spanish Civil War using the name of Manuel Del Vajo, a Communist fighter in that war, as a password; it was used after World War II during the Cold War, in particularly by Soviet agents. It is known by the English name of straddling checkerboard or straddle checkerboard.
It was, as stated above, used by Soviet spies, the most famous case, though far from certain, is that of Rudolf Ivanovich Abel (*) the Soviet spy arrested in New York in 1957 and then exchanged in 1962 with Francis Powers, the pilot of the U2 US spy plane shot down by the Russians in 1960. The case was recently, 2016, recalled in the film "The Bridge of Spies".
The idea is similar to the one of some Argenti's ciphers, with encrypting signs of one or two digits, to be written without spaces or separators, so the cryptanalyst will not be able to distinguish the single encrypting signs. But at the same time these ciphers can also cause difficulties for the legitimate decipher operator who must strive to distinguish ambiguous cases based on context.
This cipher was designed to avoid any ambiguity. In fact, a table is used, with a little imagination it can be seen as a chessboard, with ten columns and three lines, built by randomly distributing the 26 letters of the international alphabet (*) on the three lines leaving two blank boxes in the first line, and two in the other two lines; the two column numbers with blanks in the first line, are used as identifiers for the last two lines.
To avoid the problem to have to keep safe a leaflet with the table, you can also use an easy-to-remember keyword to write at the beginning, discarding duplicate letters, always leaving blanks at two agreed places in the first line, followed orderly by letters not present in the word. In this way one have easier security, provided you always keep the keyword in memory and destroy the leaflet with the table after each use. But, at the same time, the last positions of the table will contain letters placed at the end of the alphabet and this is a weakness.
An interactive example, with a random generated table, is in the figure on the right: you find instructions in the popup note.
As can be easily seen from these examples, each letter is encrypted searching for it in the chessboard and using as the first decimal digit the one indicating the line (or no digit for the first line) and as a second digit the one indicating the column, as in Polybius's board. In this way the two pilot numbers are used only in the bigraphs as initials, and never in the single digits, thus avoiding any ambiguity.
This cipher is easier to use but also weaker than Argenti's or Medici's ones; first of all the two numbers used to indicate the second and third lines will often be the two most frequent of the cryptogram, and therefore easy to identify with statistical cryptanalysis; it can happen especially for languages where there is a letter, typically E, with a very high frequency, that this letter can be between the two most frequent ones, meddling things a little. For this reason it could be a good practice to insert the E and some other very frequent letter in the first line.
Using single digits for the most frequent letters gives also a no bad advantage: the messages are on average shorter, a bit like in the Morse code, and this spares some time in telegraphic transmission.
To increase security it is advisable to use super-encryption, for example a transposition, and that's what the Soviets did with VIC, a rather cumbersome cipher built around a straddle checkerboard similar to this one (but of course using the Cyrillic alphabet).
Battle name of William August Fisher. See for instance Wikipedia Rudolf Abel.
Of course the Russian agents like Abel used the Cyrillic alphabet that has more than 30 letters and would require four rows, and three numbers to be used as the first digit.
As in the example, the key should contain two spaces in the first row at the agreed place; it must have exactly 3 rows of 10 characters each, including all letters once and only once and other two spaces. Alternatively one can insert a key word; the remaining places are to be filled with the remaining alphabet, written downward to increase security a bit.
Leaving the “key” field blank, a random key is generated.