Exhibit 16 of 140 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 bifidus, “split in two,” from findere, “to 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
Key square (keyword SECRET):
  S E C R T
  A B D F G
  H I K L M
  N O P Q U
  V W X Y Z

HELLO → H(2,0) E(0,1) L(2,3) L(2,3) O(3,1)
Rows:    2  0  2  2  3
Cols:    0  1  3  3  1
Combined: 2 0 2 2 3 | 0 1 3 3 1
Pairs: (2,0)(2,2)(3,0)(1,3)(3,1)
Cipher: HKNFO
① Letters: H E L L O ② Coords: (2,0) (0,1) (2,3) (2,3) (3,1) ③ Rows: 2 0 2 2 3 Cols: 0 1 3 3 1 ④ Join & re-pair: 2 0 2 2 3 0 1 3 3 1 ⑤ Read pairs: (2,0) (2,2) (3,0) (1,3) (3,1) HKNFO
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
Exhibit16 of 140
Era1901
SecurityBroken
InventorFelix Delastelle
Year1901
Key Type5×5 keyword square
Broken ByStatistical analysis · Hill climbing
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