5x5 Checkerboard Cipher (Polybius Square)

Summary: A substitution cipher using a 5x5 grid (Polybius square) with a keyword. I and J share one cell. Each letter is encoded as its (row, column) coordinates.

Example:

• Keyword: CIPHER
• Build square by placing keyword first (removing duplicates), then remaining alphabet:

Polybius Square:

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

Encryption:

• Plaintext: HELLO
• Look up each letter:
  • H = row 1, col 4 -> 14
  • E = row 1, col 5 -> 15
  • L = row 3, col 3 -> 33
  • L = row 3, col 3 -> 33
  • O = row 4, col 1 -> 41
• Ciphertext: 14 15 33 33 41 (or written as: 1415333341)

Decryption (given key CIPHER):

1. Build the Polybius square with keyword CIPHER
2. Split ciphertext into pairs: 14, 15, 33, 33, 41
3. Look up coordinates:
   • (1,4) = H
   • (1,5) = E
   • (3,3) = L
   • (3,3) = L
   • (4,1) = O
4. Plaintext: HELLO

Additional Example:

• Keyword: MATRIX
• Build square:

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

(Note: J is combined with I)

Encrypting "JACK":

• J = I/J at position (1,5) -> 15
• A = (1,2) -> 12
• C = (2,3) -> 23
• K = (3,4) -> 34
• Ciphertext: 15 12 23 34 (or 15122334)

Encrypting "RENDEZVOUS" (note: J becomes I):

• R = (1,4) -> 14
• E = (2,5) -> 25
• N = (4,1) -> 41
• D = (2,4) -> 24
• E = (2,5) -> 25
• Z = (5,5) -> 55
• V = (5,2) -> 52
• O = (4,2) -> 42
• U = (5,1) -> 51
• S = (4,5) -> 45
• Ciphertext: 14 25 41 24 25 55 52 42 51 45

Decrypting 32 21 25 (given keyword MATRIX):

1. Build MATRIX square (shown above)
2. Split into pairs: 32, 21, 25
3. Look up:
   • (3,2) = G
   • (2,1) = X
   • (2,5) = E
4. Plaintext: GXE (possibly a word fragment)

Practical Note: In competitions, you might see the ciphertext written as one long string: "1512233441" would be split as: 15-12-23-34-41 Always split into pairs from left to right.