Nihilist cipher

The Nihilist cipher was used by Russian revolutionaries in the late 19th century to correspond under the Tsarist police’s watch. The name comes from the nihilist political movement — those who rejected the established order, notably Dostoevsky’s The Possessed.

It is a composite cipher: it combines Polybius (coordinate substitution) with a key addition (like Vigenère, but on numbers).

Principle

The method runs in two steps:

1. Polybius encoding

The plaintext is first encoded with a classic 5×5 grid (I/J merged):

     1  2  3  4  5
  1  A  B  C  D  E
  2  F  G  H  I/J K
  3  L  M  N  O  P
  4  Q  R  S  T  U
  5  V  W  X  Y  Z

Each letter becomes a (row, column) pair → (1,3), (2,4), etc., read as a two-digit number: 13, 24.

2. Key addition

A text key is also encoded in Polybius, then cycled beneath the plaintext. Each pair is summed:

C_i = P_i + K_i      (arithmetic sum, no modulo)

The result can exceed two digits (say 45 + 55 = 100), yielding the ciphertext.

Example

Plaintext CIPHE with key KEY:

Polybius plain :  C=13  I=24  P=35  H=23  E=15
Polybius key   :  K=25  E=15  Y=54  K=25  E=15
Sum            :  38    39    89    48    30

Ciphertext: 3839894830.

Decoding subtracts the key and reads the remaining pairs in the Polybius grid.

Variants

• Transposed Nihilist — adds a columnar transposition after the sum, scrambling the digits and complicating the attack.
• 6×6 Nihilist — enlarged grid that covers digits too (no I/J merge needed).
• VIC cipher — modern elaborate version used by Soviet spy Reino Häyhänen; combines Polybius + straddling checkerboard + transposition.

Weaknesses

• Arithmetic without modulo leaves clues: sums above 66 betray that both operands have high components.
• The short key remains periodic: Kasiski’s test applies on digit pairs.
• The Polybius grid, if standard (alphabet in order), protects nothing — a quick test reconstructs it.

In CipherChronicle

The Nihilist cipher is an excellent introduction to composite ciphers: it stacks two already-known building blocks (Polybius, Vigenère-like). Its grids can be solved in two steps — first undo the addition, then read the grid — offering a natural learning curve.