🔢 Nihilist Cipher — Step-by-Step Example

Welcome, codebusters! The Nihilist cipher turns letters into numbers using a special grid, then adds a secret key to scramble everything. Let's break it down!

🤔 What is the Nihilist Cipher?

The Nihilist cipher has three ingredients:

1. A Polybius Square — a 5×5 grid filled with the alphabet (I and J share a spot).
2. A keyword used to build the grid.
3. A key phrase that generates numbers to add on top.

The result? A series of two-digit numbers that hide your message!

📜 The Problem

Encrypt the message: ROCKET Grid keyword: COMET Key phrase: MARS

🕵️ Step-by-Step Encryption

Step 1: Build the Polybius Square

Take the keyword COMET and write its unique letters first, then fill in the rest of the alphabet (skipping any letters already used, and combining I/J into one cell):

Starting with C, O, M, E, T, then continue with A, B, D, F, G, H, I/J, K, L, N, P, Q, R, S, U, V, W, X, Y, Z:

     1    2    3    4    5
  ┌────┬────┬────┬────┬────┐
1 │  C │  O │  M │  E │  T │
  ├────┼────┼────┼────┼────┤
2 │  A │  B │  D │  F │  G │
  ├────┼────┼────┼────┼────┤
3 │  H │ I/J│  K │  L │  N │
  ├────┼────┼────┼────┼────┤
4 │  P │  Q │  R │  S │  U │
  ├────┼────┼────┼────┼────┤
5 │  V │  W │  X │  Y │  Z │
  └────┴────┴────┴────┴────┘

How to read it: Each letter gets a 2-digit number — the row first, then the column.

• C = Row 1, Column 1 → 11
• O = Row 1, Column 2 → 12
• R = Row 4, Column 3 → 43

Step 2: Convert the plaintext to numbers

Look up each letter of ROCKET in the grid:

Plaintext numbers: 43 12 11 33 14 15

Step 3: Convert the key phrase to numbers

Now look up each letter of the key MARS in the same grid:

Key numbers: 13 21 43 44

Step 4: Repeat the key to match the message length

Our message has 6 letters, but our key only has 4 numbers. So we repeat the key:

Plaintext:  R    O    C    K    E    T
            43   12   11   33   14   15

Key:        M    A    R    S    M    A
            13   21   43   44   13   21
            ↑ key starts over ──────↑

Step 5: Add the numbers!

Simply add each plaintext number to its matching key number:

✅ Ciphertext: 56 33 54 77 27 36

🔓 Now Let's Decrypt It!

You received this ciphertext: 56 33 54 77 27 36 You know the grid keyword is COMET and the key phrase is MARS.

Step 1: Build the same Polybius Square

(Same grid as before — use keyword COMET)

     1    2    3    4    5
  ┌────┬────┬────┬────┬────┐
1 │  C │  O │  M │  E │  T │
  ├────┼────┼────┼────┼────┤
2 │  A │  B │  D │  F │  G │
  ├────┼────┼────┼────┼────┤
3 │  H │ I/J│  K │  L │  N │
  ├────┼────┼────┼────┼────┤
4 │  P │  Q │  R │  S │  U │
  ├────┼────┼────┼────┼────┤
5 │  V │  W │  X │  Y │  Z │
  └────┴────┴────┴────┴────┘

Step 2: Convert the key phrase to numbers

MARS → 13 21 43 44 (same as before)

Repeat to match ciphertext length: 13 21 43 44 13 21

Step 3: Subtract the key from the ciphertext

This is the reverse of encryption — instead of adding, we subtract:

Step 4: Look up the numbers in the grid

✅ Plaintext: ROCKET 🚀🎉

🧠 Key Things to Remember

1. Build the grid with the keyword first — write the unique letters of the keyword, then fill in the remaining alphabet letters. I and J always share one cell.
2. Row number comes first, then column. So Row 4, Column 3 = 43 (not 34!).
3. The key repeats to match the length of the message.
4. Encrypt = ADD. Decrypt = SUBTRACT.
5. Every ciphertext number will be between 22 and 110 (smallest: 11+11=22, largest: 55+55=110).

🎯 Practice Problem

Decrypt this ciphertext using grid keyword COMET and key phrase MARS:

57  36  64  87

Hint: Build the same grid, convert MARS to numbers, and subtract!

Happy number crunching! 🔍🏆