Complete Columnar

What it is

• A transposition cipher: letters keep their identities; only their positions are permuted. You write plaintext row-wise under a keyword and then read columns out in the alphabetical order of the keyword’s letters (ties left-to-right).
• Two common variants: padded (fill last row) and irregular (no padding). Irregular means rightmost columns may be shorter by one.
• Hand rule (decrypt with known key): compute column heights, slice the ciphertext into columns by sorted-key order, place slices back into their original column positions, then read rows.

Key facts you need

• Column order is determined by sorting keyword letters A–Z, breaking ties left-to-right.
• Irregular column heights: with N letters and key length L, rows R=ceil(N/L) and remainder r=N mod L. In sorted order, first r columns have height R, the rest have height R−1.
• Padded columns: all columns have height R.

Decryption (known keyword)

1. Normalize letters (A–Z), note N, key length L, compute R and r.
2. Determine sorted order of columns from the keyword; compute each column’s height (irregular vs padded).
3. Slice ciphertext into L chunks by heights in sorted-key order.
4. Place each chunk back into its original column position (unsorted).
5. Read rows left-to-right to get plaintext; restore spaces/punctuation.

Worked example A (irregular)

Ciphertext: URSLEEBBIER
Keyword: PEAR (L=4)

1. N=11 → R=ceil(11/4)=3, r=11 mod 4=3 → in sorted order, first 3 columns have height 3, last has height 2.
2. Sorted-key order for PEAR is A(3), E(2), P(1), R(4) → order indices [3,2,1,4].
3. Heights by sorted order: [3,3,3,2]. Slice ciphertext accordingly: URS | LEE | BBI | ER.
4. Place into original positions (P=1,E=2,A=3,R=4):

• Col A (pos 3): URS
• Col E (pos 2): LEE
• Col P (pos 1): BBI
• Col R (pos 4): ER

5. Read rows by position 1..4:

Row1: B  L  U  E
Row2: B  E  R  R
Row3: I  E  S  -

Plaintext: BLUEBERRIES

Worked example B (irregular, unknown key length but small)

Ciphertext: HWEOLRLLD

Try L=2 and L=5 as hints.

• L=5 → R=ceil(9/5)=2, r=4 → in sorted order, heights [2,2,2,2,1]. Split into 5 chunks accordingly, then test permutations (5!=120) to reconstruct rows; HELLO WORLD emerges after reinserting a space.

Solving without the key (strategy)

1. Guess key length L (try 4–8). For each L, compute R and r, derive sorted-order heights, slice ciphertext into L chunks.
2. Anagram columns: permute the L chunks back into positional order (1..L) and score the row-wise reading for English (bigrams/trigrams, dictionary hits, word shapes). Use greedy/beam search.
3. If the best permutation yields only partial English, try neighboring L values or re-check irregular vs padded assumption.
4. Cribs: if you suspect specific words, test their placements across row boundaries; this constrains which columns can be adjacent.

Common mistakes

• Miscomputing irregular heights (r columns should be taller by 1).
• Mishandling repeated letters in the keyword (ties must be left-to-right).
• Assuming padding when the source used irregular (or vice versa).
• Over-relying on letter frequency; transposition preserves frequency, not structure.

Quick reference

• Column heights (irregular): first r (in sorted order) have R, others R−1.
• Place slices according to the sorted order mapping back to original positions.
• Read rows left-to-right for plaintext.

Practice

1. Decrypt (irregular): URSLEEBBIER with key PEAR.
2. Blind solve: HWEOLRLLD with a likely key length of 2 or 5.

Answers

1. BLUEBERRIES
2. HELLO WORLD (after spacing)