Frequency analysis of transposition ciphers

Question

Can we do frequency analysis of transposition ciphers?
If yes, please tell me the procedure and I would be happy if you provide me with some links related to it.
I heard that it can be done using bi-gram frequency.
I did it for substitution ciphers but am unable to do it for transposition ciphers.

Answer 1

I did it for substitution ciphers but am unable to do it for transposition ciphers.

When it comes to transposition ciphers, it’s not really surprising frequency analysis doesn’t turn out to be as useful as it is when looking at substitution ciphers.

See, one important strength of transposition ciphers is that they are not susceptible to frequency analysis, since transposition ciphers do not change the symbols for each letter.

Instead of replacing characters with other characters, transposition ciphers just change the order of the characters. Typically, the text to be encrypted is arranged in a number of columns. These columns are then reordered, resulting in encrypted text. This means that, to decrypt/break a ciphertext created using a transposition cipher, you need to find the number of columns (which is usually based on a common factor of the total number of characters in the text) and then rearrange the columns accordingly.

Now, don’t get me wrong – frequency distribution is interesting to look at during a transposition cipher analysis, but for other reasons… frequency analysis on a transposition cipher shows that the constituent letters are what would be expected in a standard text (example: “e” is the most common English letter).

As you’re obviously just starting out to learn how to analyze and potentially decrypt/break transposition ciphers, you could check stuff like the “Analysis of columnar transposition ciphers” section of "Introduction to Cryptology and Cryptosystems" by Prof. H. Williams, which provides a first, rather simple insight.

UPDATE: Since the original PDF of Prof. Williams went offline, here’s an excerpt containing the 3 related pages. Please note that the excerpt I am making available here is provided for reference purposes only and does not represent a complete copy of "Introduction to Cryptology and Cryptosystems".

Also (in contrast to Wikipedia’s related article), there are ample pages online which provide nice examples of the cryptanalysis and deciphering… randomly picking one of them: “Transposition Cipher : nrich.maths.org”.

Answer 2

You cannot frequency analyze a transposition cipher with padding as shown here.

Given this:

You cannot frequency analyze the above to get this:

Answer 3

Sorry to burst your bubbles but i disagree, transposition ciphers are susceptible to frequency analysis. Transpotion ciphers only change their relative position not their individual symbols, thus their frequency can be compared with other plaintext candidates to find the most probable ones. (Or by using anagram analysis)

To elaborate, transposition cipher by itself is easily detectible by using frequency analysis, if a long ciphertext is given, by looking at the frequency of individual letters and comparing it with some real world frequency distribution of each letters.

@Ilmari Karonen , yes it is a weakness

@e-sushi , transposition ciphers are easily detectible using frequency analysis. Yes, it is susceptible to it. I think you missed the point because you know that the substitution ciphers can be broken by frequency analysis, and forget that detecting transposition cipher is also possible using frequency analysis (i.e., it is a vulnerability>