Breaking the Rail Fence

The letter statistics still look like English, because the letters did not change. That is how you recognise a transposition.

CryptanalysisTranspositiondemo

Objectives

Show that a transposition leaves both letter statistics unchanged.
Diagnose a transposition from English counts on unreadable text.
Brute-force the rail count and recover the message.

50%

A transposition changes no letter, so every letter-frequency test comes back clean.

Plaintext

Rails the sender used

ciphertext

WVOBT EEAEM LAOTH DAHAE REL

Both scorers say “English”

	IC	χ²
plaintext	0.0791	18.2
ciphertext	0.0791	18.2

Identical, to the digit. Both statistics ignore order, and order is the only thing this cipher changes, so neither one can see it at all.

That is the detection. English letter counts on text that reads as nonsense announce a transposition before you have guessed a single key.

Then brute-force the one small key

rails 2	WOVTOHBDTAEHEAAEERMELLA
rails 3	WEHAVEAMOLEABORTTHEDEAL
rails 4	WTAEOEVETRHAOEDEAMBLHLA
rails 5	WBEHRDMTVELAEHAEOAOALET
rails 6	WBETHEAHMTVELDELRAAEOAO
rails 7	WOEMTHEAHLEBVTAADELRAOE

The rail count is a small integer, so there is no search problem here at all. Reordering is only worth anything when the number of orderings is large, which is what the next section is about.

step 1/2

CPE 645 / CS 685

Breaking the Rail Fence

Two-Time Pad

Breaking Columnar Transposition