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Bifid Cipher

Tool to crypt/decrypt the bifid cipher. The bifid cipher uses coordinates of letters and mixes them in order to get new coordinates.

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Bifid Cipher -

Tag(s) : Polygrammic Cipher, GRID_CIPHER

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# Bifid Cipher

## Bifid Encoder

### What is the Bifid cipher? (Definition)

The bifid cipher is an encryption that combine a substitution with a Polybius square and a transposition, it is described in Traité Élémentaire de Cryptographie by Felix Delastelle.

### How to encrypt using Bifid cipher?

Bifid encryption requires a square grid (or a keyword to generate the grid, generally 5x5 or 6x6) and (optional) a number N which will serve as a period/block length (otherwise take N=1).

Example: Encrypt the plain message DCODE with the grid (generated with the word SECRET):

1 2 3 4 5 \ 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

— Choose a block size N and group the letters into blocks of size N.

Example: A period of length N=3 for DCODE gives DCO,DE(no need to complete the block if the last one is not of length N)

This text-splitting is not mandatory, but simplifies encryption/decryption for long texts. For a non split encryption, imagine a period size of N=1 (or a period size equal to or greater than the number of letters in the plain message)

— For each letter of the block, write the coordinates of the letters (row, column) in a table.

Example: Take the first block DCO. D=(2,3), C=(1,3), O=(4,2) and write it in a table:

 D 2 3 C 1 3 O 4 2

— To get new coordinates, read the numbers of the table vertically by columns.

Example: The vertical reading gives 2,1,4,3,3,2 or the coordinates (2,1),(4,3),(3,2).

— Replace the coordinates with the corresponding letters in the grid.

Example: (2,1) for A, (4,3) for P and (3,2) for I.

These steps are repeated for each block.

Example: The final encrypted message is APIAI

### How to decrypt a Bifid cipher?

Bifid decryption begins identically to encryption.

Example: The message DBAKS has been encrypted with a period N=3 and the grid (generated with the word MESSAGE):

1 2 3 4 5 \ M E S A G B C D F H I K L N O P Q R T U V W X Y Z

The message is split into period/block of size N

Example: The message is decomposed in block of 3: DBA,KS

Each letter is associated with its position in the grid as coordinates (row, column)

Example: The letters of the block D,B,A have the respective coordinates (2,3),(2,1),(1,4).

Write the coordinates on 2 rows (and thus N columns, eventually except the last block)

Example:

 2 3 2 1 1 4

Example: You get 2,1,3,1,2,4 or (2,1),(3,1),(2,4).

The new coordinates are then associated with the corresponding letters in the grid.

Example: You find the plain letters (2,1)=B, (3,1)=I and (2,4)=F

These steps are repeated for each block.

Example: The plaintext message is BIFID.

### How to recognize Bifid ciphertext?

The message has a low coincidence index around 0.04 to 0.05.

If the grid is 5x5 then it can have at most 25 distinct characters.

### What does bifid mean?

Bifid means 'that is cut in half lengthwise', which applies to the Delastelle cipher: the coordinates are cut in 2 during the encryption and decryption steps.

### Why should the period not be N=1?

With a period of 1, the encryption or decryption algorithm has no effect (because the principle of column writing and row reading does not produce a shuffling effect)

### When was the Bifid cipher invented?

Felix-Marie Delastelle, civil engineer, described this process in 1902.

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