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Lesson 10
COMPLETE COLUMNAR
Rearrange columns, not letters
What is Transposition?
- Unlike substitution ciphers, transposition rearranges letters — doesn't replace them
- The same letters appear in plaintext and ciphertext, just in different order
- Frequency analysis will show normal English — but words won't appear
- Complete Columnar appears as Cryptanalysis (C) at all levels
How Columnar Transposition Works
- Step 1: Write the plaintext in rows under a numeric key
- Step 2: Number the key letters alphabetically (A=1, B=2, …)
- Step 3: Read off columns in numeric key order
Key: CARGO (C=1, A=2, R=4, G=3, O=5)
C A R G O
1 2 4 3 5
W E A R E
C O D E B
U S T E R
S X X X X
Completing the Rectangle
- "Complete" means the grid is a full rectangle — null letters pad the last row if needed
- The number of rows = ⌈message length / key length⌉
- Null letters are marked on the test
Read column 1 first, then 2, 3, 4, 5 — always in key-number order.
Encryption — Reading Off Columns
Grid from previous slide (key order: 1=C, 2=A, 3=G, 4=R, 5=O)
Col 1 (C): WCUS
Col 2 (A): EOSX
Col 3 (G): EEEX
Col 4 (R): ADTE
Col 5 (O): EBER
Ciphertext
WCUS EOSX EEEX ADTE EBER
Decryption Process
- Step 1: Determine key length (given or solve)
- Step 2: Compute number of rows and which columns are longer (if message doesn't divide evenly)
- Step 3: Distribute ciphertext back into columns in key-number order
- Step 4: Read across rows to get plaintext
For C-type: you must figure out the key length. Try lengths 4–8 and see which produces readable text.
Finding Key Length (Cryptanalysis)
- Try dividing message length by 4, 5, 6, 7, 8 — look for a clean rectangle
- For each candidate length, rearrange columns and check for English digraphs
- Once rows look like partial English words, you have the right length
- Then determine column order by matching common digraphs across adjacent columns
Key Takeaways
- Columnar transposition rearranges letters — doesn't change them
- Write in rows, read out in column order (key-number order)
- Decryption: fill columns in order, read across rows
- Appears as Cryptanalysis (C) at all levels
- Next class: Nihilist Substitution
Homework: encrypt "WEARECODEBUSTERS" with key "MATH" and verify by decrypting.