Bifid Cipher
Felix Delastelle's masterwork: fractionation meets transposition
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.’
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.
Using a 5×5 Polybius square with a keyword:
- Convert each plaintext letter to its (row, col) coordinates
- Write all row numbers in a row, then all column numbers beneath
- Read pairs from the combined sequence
- 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
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.
| Concept from Bifid Cipher | Modern Evolution |
|---|---|
| Fractionation (split letter into coordinates) | Bit diffusion: every bit of plaintext influences multiple ciphertext bits |
| Row/column interleaving | AES MixColumns: mixes 4 bytes of each column together |
| Polybius square lookup | S-box lookup: key-dependent non-linear substitution |
| Exhibit | 15 of 40 |
| Era | 1901 |
| Security | Broken |
| Inventor | Felix Delastelle |
| Year | 1901 |
| Key Type | 5×5 keyword square |
| Broken By | Statistical analysis · Hill climbing |