Variable size (straddling) ciphers

Matteo Argenti's variable Vatican ciphers
- Ottavian Medici's variable Venetian ciphers
- The straddling checkerboard cipher

The mono-alphabetic substitution ciphers (shortly MASC) are relatively easy to decrypt, the easier the longer the encrypted message (or the sum of the encrypted messages available).

One way to complicate the work of the cryptanalyst is to use ciphers of varying length and then write the message thus encrypted in a continuous way, without spaces or other separator signs, so that the single ciphering signs are not evident.

A MASC requires ciphers of at least two decimal digits, from 00 to 99; even if you write them without separators, the cryptanalyst will not have much trouble recognizing the individual signs. But if you mix two-digit signs and single-digit signs, it's much more complicated. We can distinguish two variants of this method:

- Some letters are encrypted with a single digit, others with two, without any well defined rule; the decipherer will have to strive to tell them apart according to the context. Mathematically the cipher function is not injective, it must be believed that among the different possible decodes there is only one that gives sensible sentences.
- Only a few digits, usually two, are used as the first digit of the two-lines; in this way the cipher function returns to be injective, and the decipher operator should have no difficulty. But the cryptanalyst also could meet less difficulties ...

Below are three examples of such ciphers, the first of the first kind, the others of the second.

Vatican ciphers of the XVI Century, by Matteo Argenti

An example of such a cipher by Matteo Argenti is the following n. 19 of the Meister book: *Cifra con monsignor eletto vescovo di Savona, nuntio in Savoya*.

a | b | c | d | e | f | g | h | i | l | m | n | o | p | q | r | s | t | u | z |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

13 4 42 | 14 | 16 | 15 |
1 36 43 | 19 | 18 | 21 |
22 38 5 | 23 |
25 94 |
24 82 |
2 26 39 | 28 |
30 91 |
31 92 |
33 93 |
3 32 41 | 35 |

Note that there are homophones for some frequent letters; furthermore the single digit **4** which stands for **a** is distinct from the two-digits **04** which stands for ** catholic cantons ** (indeed this cipher included a small nomenclator that used other available two-digits ciphers and some three-digits ones, not reported here).

More details on the Variable Length Ciphers by Matteo Argenti .

Venetian XVII Century cipher

In the XVII century, the Venetian cryptographers used mostly three-digit nomenclators, with dictionary, syllabary and alphabet, rather ordered, altogether simpler and easier to use but also weaker than those of the previous century.

A cipher with signs of variable length, designed by Ottavian Medici, was approved by the Council of Ten on 10-12-1624, and was used by the Venetian embassies in the following years. The numerical signs vary in length from two to four digits, and always begin with 5 or 6; in this way the function is injective ie the decipher is univocal. It is fundamental to write everything without intermediate spaces. Among the cipher keys in the State Archives of Venice, the *key* of this cipher has so far not been found, but I have largely recovered it comparing the encrypted dispatches found in the archive with the chancellery deciphers. Below the recovered cipher alphabet (the rarest letters have been deduced, following the clearly visible regular pattern) and the first line of the syllabary.

a | b | c | d | e | f | g | h | i | l | m | n | o | p | q | r | s | t | u | z |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

680 681 |
682 683 |
5180 5181 |
5182 5183 |
6280 6281 |
6282 6283 |
5380 5381 |
5382 5383 |
6480 6481 |
6482 6483 |
690 691 |
692 693 |
5190 5191 |
5192 5193 |
6190 6191 |
6292 6293 |
5390 5391 |
5392 5393 |
6490 6491 |
6492 6493 |

ba | be | bi | bo | bu | ca | ce | ci | co | cu | da | de | di | do | du | |||||

67 | 5107 | 6207 | 5307 | 6407 | 68 | 5108 | 6208 | 5308 | 6408 | 610 | 5110 | 6210 | 5310 | 6410 |

As you can see, both the alphabet and the syllabary are regular, but not too much. The cipher also includes a dictionary with dozens of words, perhaps hundreds.

This cipher was used for a few years, there are dispatches coded by several Venetian embassies from European capitals; some follow the CX recommendations and the numbers are written without interruptions, while others have cipher groups well separated by spaces, thus negating the basic idea of this cipher. The insufficient training of the cipher operators is confirmed also in this case the most frequent flaw in the history of cryptography.

More details and examples at this page: Ottavian Medici's variable Venetian ciphers.

The “straddling checkerboard”

After another three centuries, such an idea was the basis of this cipher, used for the first time during the Spanish civil war. It was later used in the Cold War period by Soviet agents. It is known by the English name of * straddling checkerboard * or also (* straddle checkerboard *).

The idea is more similar to the Venetian one, with two * pilot * numbers, than to Argenti's one, but there are no dictionaries or syllabaries. The cipher is designed in such a way as to avoid any ambiguity. In fact, a table is used, the chessboard, with ten columns and three rows, built by randomly distributing the 26 letters of the international alphabet on the three lines, leaving two blanks in the first row, and two in the other two rows; the column numbers, with a blank at the first row, are used as identifiers for the last two lines. You can also generate the chessboard by memory using an easy-to-remember keyword and by first writing this and then orderly the alphabet letters not present in the word, but this is detrimental to security. Here is an example of a randomly generated table with short encrypted messages (reload to generate a different table):

As one can see from this example, each letter is encrypted by searching for it in the chessboard and using as the first decimal digit the one indicating the row and as a second digit the one indicating the column. In this way the two pilot digits are used only in the double digit ciphers as initials, and never in the single ones, thus avoiding any ambiguity.

More details and examples at this page: La cifra straddling checkerboard.

Riferimenti bibliografici

- Friedrich Ludwig Bauer, Decrypted secrets: Methods and Maxims of Cryptology, Springer, Berlin, 1991 − 2007, pag. 55 - 57 → info
- David Kahn, The codebreakers, Scribner, New York, 1967 − 1996, pag. 635 - 636 → eBook
- Aloys Meister, Die Geheimschrift Im Dienste Der Papstlichen Kurie Von Ihren Anfängen Bis Zum Ende Des XVI. Jahrhunderts, Ferdinand Schöningh, Paderborn, 1906, pag. 343 - 344 → eBook

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