Bazeries cipher

The Bazeries cipher was published in 1898 by Étienne Bazeries, a legendary French cryptanalyst. He is best remembered for breaking Louis XIV’s Grand Cipher in 1893 — a nomenclator that had resisted decryption for two centuries — and for spending his career designing cipher devices, several of which directly anticipated the cryptographic machines of the 20th century.

Principle

The Bazeries cipher combines two operations driven by a numeric key:

1. Reversal of the plaintext in blocks whose lengths depend on the key.
2. Substitution through a 5×5 square whose alphabet is scrambled according to the number spelled out in words.

Step 1 — The key

The key is an integer (e.g. 1702). You write it out in words — here in English:

1702 → ONE THOUSAND SEVEN HUNDRED TWO
     → ONETHOUSANDSEVENHUNDREDTWO

Extract the distinct letters in order of appearance, dropping duplicates:

O N E T H U S A D V R W

Then fill in the remaining letters of the alphabet (J merged with I):

O N E T H U S A D V R W B C F G I K L M P Q X Y Z

This scrambled alphabet is written into a 5×5 square row by row:

O N E T H
U S A D V
R W B C F
G I K L M
P Q X Y Z

Step 2 — Block reversal

The plaintext is split into blocks whose lengths cycle through the digits of the key: with 1702, blocks of 1, 7, 0 (skip), 2 letters, repeating. Each block is reversed and the blocks are reconcatenated.

Step 3 — Substitution

Every letter is then replaced by the one sitting at its transposed position in the keyed square. This substitution combines a key effect (the alphabet in the square) with a geometric effect (transposition inside the grid).

Legacy

Bazeries also designed:

• A cipher cylinder with 20 discs, directly in line with the Jefferson disk — and thus with the later M-94 of the US Army.
• A two-alphabet disc combining Alberti with a multi-key system.
• The Four Square method (1901), a precursor to Delastelle’s Four-Square cipher.

His career is also marked by his controversial reading of the Man in the Iron Mask ciphers: he argued, without definitive proof, for a specific identification of the prisoner.

Strengths and weaknesses

Strengths

• Three layers (reversal + keyed square + positional substitution) resist naive monoalphabetic analysis.
• The numeric key is easy to memorise (4 to 8 digits suffice) and produces a highly scrambled alphabet.

Weaknesses

• As soon as the spelled-out key is guessed, the whole structure collapses.
• The linguistic dependency (the way numbers are spelled) exposes the cipher to dictionary attacks on common round numbers.
• Block reversal leaves a detectable fingerprint: certain positions retain their frequency signatures.

Against a modern cryptanalyst, it breaks quickly — but it still makes for a pleasing hand-solve challenge.

In CipherChronicle

Bazeries is a hybrid cipher: it stitches together the two great families of classical cryptography — substitution and transposition — into a single operation. Companion grids can ask the player to identify the numeric key from historical hints (dates, altitudes, distances), then apply all three steps.