Nihilist Cipher

The nihilist cipher is a super-cipher of the Polybius square. The Polybius square is a substitution cipher where each letter is replaced by a pair of numerical coordinates (row, column) in a grid. The nihilist cipher adds a repeated numerical key to these coordinates, according to a term-by-term addition.

The nihilist's cipher uses a grid (usually 5x5 = 25 cells) that is filled with letters of the alphabet (often a deranged alphabet). For a 5x5 grid and the 26-letter latin alphabet, choose a letter to omit, often the J, V or W are omitted. The grid has digit headers for its rows and columns (typically 1 to 5).

To encrypt a text, it is necessary to replace each letter of the initial text, by its coordinates in the grid. Generally, the coordinates [row, column] (and more rarely [column, row]) are used. A numerical code consisting of pairs of digits is obtained.

The particularity of the Nihilist cipher in relation to the Polybius cipher is its over-encryption. The nihilists use a key that is added for each couple of digits previously created.

Decryption requires to know the grid and the over-encryption key.

The message can have the form of a list of numbers (2 or 3 digits) or of a large series of digits, in the second case, separate them into pairs of 2 digits.

To decrypt, the coded key is subtracted from each pair of 2 digits and each number obtained is replaced by the corresponding letter with these coordinates in the grid.

In the general case of using a 5x5 grid with coordinates from 1 to 5, the message is composed of numbers with the following properties:

— If the encryption is without a separator, the numbers are between 00 and 99 and the message is composed of an even number of digits.

— If the encryption is with separating spaces, the numbers are between 22 and 110

— In all cases, the numbers 11,12,13,14,15,16,17,18,19,20,21,31,41,51,61,71,81,91 can never appear by addition because they contain only one ten or only one unit.

Any reference to Russia (USSR), tsars or Russians traditions is a clue.

The presence of historical figures like Sergei Nechaev or other key figures of Russian nihilism is a significant indicator.

The word nihilist is generally associated with a philisophic doctrine, but in Russian the word нигилизм has a Latin root meaning nothing.

Without the key, the user must exploit the repeated additive structure. Each block is the sum of two numbers between 11 and 55. It is possible to test hypotheses about key length and then examine the differences between blocks spaced a multiple of that length apart.

dCode analyzes the pairs of digits in the message to extract the potential sums they formed. It is then possible to find all possible combinations and deduce the potential keys using the grid.

If the key is known but not the grid, subtraction allows us to recover numerical coordinates.

These coordinates correspond to an unknown grid: the resulting message is then equivalent to a Polybius square, that is, a text encrypted by a monoalphabetic substitution depending on the internal permutation of the grid.

A standard frequency analysis then allows us to progressively reconstruct the grid; see the page dedicated to the Polybius cipher.

It is possible to make several variants:

— Inversion of coordinates: rather than using [row, column], it is possible to use [column,row].

— Change of coordinates names: the digits from 1 to 5 can very well be mixed or replaced by other digits.

— Multiple keys, it is possible to use several keys, summed successively, but this only extends the process time and does not complicate a brute-force attack.

The number of nihilists is associated with 19th-century Russian revolutionary movements, particularly during the period 1860-1880.