NIHILIST SUBSTITUTION

Overview

• Used by Russian Nihilist revolutionaries in the 1800s
• Two-step cipher: Polybius square (letter → two digits) + keyword addition
• At Invitationals/Regionals: Decrypt (D) — key given
• At State/Nationals: Decrypt or Cryptanalysis (DC)

Step 1 — The Polybius Square

• A 5×5 grid of letters, labeled 1–5 on rows and columns
• I and J share one cell (25 letters fit in 5×5)
• Each letter → a two-digit number (row, column)

• A=11, B=12, C=13, … Z=55

Keyword Square

• The keyword is written into the Polybius square first (no duplicate letters)
• Remaining letters fill in alphabetical order
• This creates a non-standard Polybius square — the key

Step 2 — Keyword Addition

• Convert each plaintext letter to its two-digit Polybius number
• Write the keyword above the message, repeating
• Convert each keyword letter to its Polybius number
• Add the plaintext number and keyword number (no carrying)

Decryption

• Repeat keyword above ciphertext numbers
• Convert keyword letters to Polybius numbers
• Subtract keyword numbers from ciphertext numbers
• Look up the resulting number in the Polybius square → plaintext letter

Cryptanalysis (State level)

• Find keyword length using repeated patterns in the ciphertext
• Group ciphertext numbers by keyword position
• Use frequency analysis on each group's last digits (column info)
• The most common Polybius value in English ≈ 23 (H), 15 (E), 44 (T)

Key Takeaways

• Nihilist = Polybius square coordinates + keyword number addition
• The keyword sets the Polybius square filling order
• Decrypt by subtracting keyword numbers from ciphertext numbers
• D at Invitationals; DC at State
• Next class: Checkerboard (5×5)