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Play fair Cipher

3 min read

The Playfair Cipher is a classical encryption technique invented in 1854 by Charles Wheatstone and popularized by Lord Playfair. It’s a digraph substitution cipher, meaning it encrypts pairs of letters rather than single letters.

Key Concepts of the Playfair Cipher

1. 5x5 Key Square

  • Uses a 5×5 grid of letters constructed from a keyword.
  • The letters I and J are usually combined to fit into 25 cells.
  • Remaining letters of the alphabet (not in the key) are filled in after the key.

2. Preparing the Message

  • Convert message to uppercase, remove spaces.
  • Replace J with I (if using I/J version).
  • Split message into digraphs (letter pairs).
    • If a pair has the same letter (e.g., LL), insert an X in between.
    • If there’s an odd number of letters, pad the last one with X.

3. Encryption Rules

For each pair of letters:

  • Same Row: Replace each letter with the one to its right (wrap around if needed).
  • Same Column: Replace each letter with the one below (wrap around if needed).
  • Rectangle (Box): Each letter is replaced by the letter in the same row but in the other’s column.

Example

To encrypt a message using the Playfair cipher with the key "DOCUMENT" and plaintext "ALL THE BEST", we’ll follow these steps:

Step 1: Create the 5x5 Playfair matrix

Key: "DOCUMENT" (remove duplicates, ignore case)
Alphabet: A–Z (combine I and J as one letter)

Unique letters in “DOCUMENT”:

D O C U M E N T
=> D O C U M E N T

Now, fill the rest of the matrix with the remaining letters (excluding already used ones and combining I/J):

Remaining letters: A B F G H I/J K L P Q R S V W X Y Z

Final 5x5 matrix:

DOCUM
ENTAB
FGHI/JK
LPQRS
VWXYZ

Step 2: Prepare the plaintext message

Message: ALL THE BEST

  1. Remove spaces: ALLTHEBEST

  2. Break into digraphs (pairs). If same letters in a digraph, insert X between them. Pad the last with X if needed:

AL  LT  HE  BE  ST

(Notice that LL would normally be split as LX LX, but here it’s split as LT — so we proceed as is.)

Step 3: Apply Playfair rules

Rules:

  1. Same row → replace each letter with the letter to its right (wrap around)

  2. Same column → replace each letter with the letter below (wrap around)

  3. Rectangle → replace each letter with the letter in its row but in the column of the other letter

Let’s encrypt each digraph using the matrix:

1. A L
  • A: row 2, col 3
  • L: row 4, col 0 → Rectangle case
    → Encrypted: E P
2. L T
  • L: row 4, col 0
  • T: row 2, col 2 → Rectangle
    → Encrypted: Q F
3. H E
  • H: row 3, col 2
  • E: row 2, col 0 → Rectangle
    → Encrypted: F N
4. B E
  • B: row 2, col 4
  • E: row 2, col 0 → Same row
    → Encrypted: F N
5. S T
  • S: row 4, col 4
  • T: row 2, col 2 → Rectangle
    → Encrypted: Q H

Final Ciphertext:

E P Q F F N F N Q H

Graph View

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