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Burrows–Wheeler Transform

Tools that apply Burrows-Wheeler algorithm. Burrows-Wheeler transform (BWT) is an algorithm maximizing repeated letters in a text, which is useful in data compression.

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Burrows–Wheeler Transform -

Tag(s) : Compression, Algorithm

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Burrows–Wheeler Transform

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Tools that apply Burrows-Wheeler algorithm. Burrows-Wheeler transform (BWT) is an algorithm maximizing repeated letters in a text, which is useful in data compression.

Answers to Questions

How to encrypt using BWT cipher?

BWT ciphering rearranges letters in the message and associate it a key.

The first step consists in listing all possible rotations the the message.

Example:

DECODE
EDECOD
DEDECO
ODEDEC
CODEDE
ECODED

The second step is sorting this list in alphabetical order.

Example:

CODEDE
DECODE
DEDECO
ECODED
EDECOD
ODEDEC

The ciphered message is constituted of the last letters of each rotation. The associated key is the rank of the original message in the list.

Example: The encrypted message is EEODDC. The key is 2 (DECODE, the original text, is on the line 2 if the table).

dCode ignores all characters other than letters and digits, replacing them by a dot .

How to decrypt BWT cipher?

Decryption requires to know the key and the ciphered message.

Example: Consider the ciphetext EODC and the key 1

To decrypt, imagine an empty table, and repeat the following algorithm (A,B) as many times as the number of letter in the message:

A) Write the message in the first column of the table (shifting the others columns)

B) Sort the lines of the table by alphabetic order

Example:

A(1)B(1)A(2)B(2)A(3)B(3)A(4)B(4)
E
O
D
C
C
D
E
O
EC
OD
DE
CO
CO
DE
EC
OD
ECO
ODE
DEC
COD
COD
DEC
ECO
ODE
ECOD
ODEC
DECO
CODE
CODE
DECO
ECOD
ODEC

When finished, the plaintext is at the line number key of the table.

Example: At the row 1, after the last step of the algorithm, is the plain message: CODE

How to recognize BWT ciphertext?

The ciphered message has a high number of repeated letters and a classic index of coincidencehref.

The message is sometimes overencrypted with a RLEhref encoding.

How to decipher BWT without key?

The key is not really important for intelligible text, because when decrypting, all lines of the table are in fact rotations of the original text.

What are the variants of the BWT cipher?

BWT can be used without key, but in this case, a unique character of the original text and its position are needed, for instance in computer EOF is used for last one.

When BWT have been invented?

In 1994 by Michael Burrows and David Wheeler

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Source code

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