Exhibit 15 of 37 1901 Broken

Bifid Cipher

Felix Delastelle's masterwork: fractionation meets transposition

InventorFelix Delastelle
Year1901
Key Type5×5 keyword square
Broken ByStatistical analysis · Hill climbing
Modern LessonConfusion + diffusion combined

Why This Matters

Félix Delastelle’s Bifid cipher was the first to combine substitution and transposition into a single operation, creating genuine interdependence between letter positions — a property Claude Shannon would later formalize as ‘diffusion.’

📜Historical Context

Felix Delastelle was a French amateur cryptographer who invented several remarkable ciphers in the late 19th century. The Bifid (from Latin bis = twice, fidus = split) is widely considered his masterpiece. It combines a Polybius square with a transposition technique in a way that creates genuine interdependence between letter positions — a property Shannon would later call diffusion.

⚙️How It Works

Using a 5×5 Polybius square with a keyword:

  1. Convert each plaintext letter to its (row, col) coordinates
  2. Write all row numbers in a row, then all column numbers beneath
  3. Read pairs from the combined sequence
  4. Convert each pair back to a letter using the square
HELLO → H(1,3) E(0,4) L(2,1) L(2,1) O(3,4)
Rows:    1  0  2  2  3
Cols:    3  4  1  1  4
Combined: 1 0 2 2 3 | 3 4 1 1 4
Pairs: (1,0)(2,2)(3,3)(4,1)(1,4)
Cipher: FNSZO
① Letters: H E L L O ② Coords: (1,3) (0,4) (2,1) (2,1) (3,4) ③ Rows: 1 0 2 2 3 Cols: 3 4 1 1 4 ④ Join & re-pair: 1 0 2 2 3 3 4 1 1 4 ⑤ Read pairs: (1,0) (2,2) (3,3) (4,1) (1,4) FNSZO
Bifid fractionation: coordinates are split, concatenated, and re-paired — mixing row and column information across positions
💀How It Was Broken
Statistical Cryptanalysis + Hill Climbing
Complexity: Moderate-Hard

The Bifid's fractionation mixes coordinate information across positions, making simple frequency analysis ineffective. However, because the period is the message length, modern hill climbing with bigram/trigram scoring can recover the key square. The attack requires a few hundred characters of ciphertext to work reliably.

🔬What It Teaches Modern Cryptography
Concept from Bifid CipherModern Evolution
Fractionation (split letter into coordinates)Bit diffusion: every bit of plaintext influences multiple ciphertext bits
Row/column interleavingAES MixColumns: mixes 4 bytes of each column together
Polybius square lookupS-box lookup: key-dependent non-linear substitution
Quick Facts
Exhibit15 of 37
Era1901
SecurityBroken
InventorFelix Delastelle
Year1901
Key Type5×5 keyword square
Broken ByStatistical analysis · Hill climbing
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