Bifid Cipher
Felix Delastelle's masterwork: fractionation meets transposition
Statistical analysis · Hill climbing
Why This Matters
Delastelle’s Bifid combines coordinate substitution with transposition, spreading each letter’s coordinate information across positions. This is a useful early illustration of diffusion; it is not established here as the first system ever to combine substitution and transposition.
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.
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
Bifid mixes coordinate information within a chosen period. Some variants use fixed-size groups; this demo uses its documented grouping rule. Computer attacks can search candidate squares using language scores, but success depends on period, text length, key conventions, and search effort. No fixed few-hundred-character guarantee applies universally.
| 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 | AES uses a fixed public nonlinear S-box, combined with separate key addition and diffusion |
| Exhibit | 16 of 172 |
| Era | 1902 |
| Trust | Broken |
| Inventor | Felix Delastelle |
| Year | 1902 |
| Key Type | 5×5 keyword square |
| Broken By | Statistical analysis · Hill climbing |