Beaufort Cipher

The Beaufort Cipher is a classical substitution cipher, similar to the Vigenère Cipher but with a slight twist. It is named after the French cryptographer, Sir Francis Beaufort. Here’s a step-by-step guide on how to use the Beaufort Cipher, including an example.

Beaufort Cipher Overview

In the Beaufort Cipher:

• Each letter in the plaintext is encrypted by subtracting the corresponding letter in the key from it, using modular arithmetic with a 26-letter alphabet.

Steps to Encrypt with Beaufort Cipher

• Choose a Key: Select a keyword or key phrase. For example, let’s use the key "KEY".

• Prepare the Plaintext: Write down the message you want to encrypt. For example, let’s use "HELLO".

• Align the Key with the Plaintext: Repeat the key as many times as needed to match the length of the plaintext. If the key is shorter than the plaintext, repeat it. For "HELLO" and "KEY", it becomes:

Plaintext:  H E L L O
Key:        K E Y K E

• Encrypt Each Letter: For each letter in the plaintext, use the corresponding letter in the key to find the encrypted letter. Use the following formula for encryption:

$$C=(K−P+26)\;\;mod\;\;26$$

Where:

• C = Ciphertext letter (encrypted letter)

• K = Key letter (converted to a number, where A=0, B=1, ..., Z=25)

• P = Plaintext letter (converted to a number)

• 26 ensures the result stays within the alphabet range (0-25)

Convert each letter to its numerical value:

H = 7, E = 4, L = 11, O = 14
K = 10, E = 4, Y = 24

For each position:

• H (7) and K (10):

$$C=(10−7+26)\;mod\;26=29\;mod\;26=3 (D)$$

• E (4) and E (4):

$$C=(4−4+26)\;\;mod\;\;26=26\;\;mod\;\;26=0 (A)$$

• L (11) and Y (24):

$$C=(24−11+26)\;\;mod\;\;26=39\;\;mod\;\;26=13 (N)$$

• L (11) and K (10):

$$C=(10−11+26)\;\;mod\;\;26=25\;\;mod\;\;26=25 (Z)$$

• O (14) and E (4):

$$C=(4−14+26)\;\;mod\;\;26=16\;\;mod\;\;26=16 (Q)$$

So, the ciphertext for "HELLO" with the key "KEY" is "DANZQ".

Steps to Decrypt with Beaufort Cipher

• Use the Ciphertext and Key: Align the key with the ciphertext:

Ciphertext: D A N Z Q
Key:        K E Y K E

• Decrypt Each Letter: Use the following formula for decryption:

$$P=(K−C+26)\;\;mod\;\;26$$

Where:

• P = Plaintext letter (decrypted letter)

• C = Ciphertext letter

• K = Key letter

Convert each letter to its numerical value:

D = 3, A = 0, N = 13, Z = 25, Q = 16
K = 10, E = 4, Y = 24

For each position:

• D (3) and K (10):

$$P=(10−3+26)\;\;mod\;\;26=33\;\;mod\;\;26=7 (H)$$

• A (0) and E (4):

$$P=(4−0+26)\;\;mod\;\;26=30\;\;mod\;\;26=4 (E)$$

• N (13) and Y (24):

$$P=(24−13+26)\;\;mod\;\;26=37\;\;mod\;\;26=11 (L)$$

• Z (25) and K (10):

$$P=(10−25+26)\;\;mod\;\;26=11\;\;mod\;\;26=11 (L)$$

• Q (16) and E (4):

$$P=(4−16+26)\;\;mod\;\;26=14\;\;mod\;\;26=14 (O)$$

o, the decrypted plaintext from "DANZQ" with the key "KEY" is "HELLO".

Summary

• Encryption: Uses the key to modify each letter of the plaintext by subtracting the key letter value.

• Decryption: Reverses the process using the same key to retrieve the original plaintext.

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