Classical Cryptography

Transposition Cipher

Description

The idea behind a transposition cipher is to create a permutation (rearrangement) of the letters of the plaintext that will make the ciphertext appear to be well-encrypted. Transposition ciphers are not highly secure because they do not change the letters in the plaintext or even cover up frequencies, but they can be built upon to make more secure methods of encryption. One example of transposition cipher is the  rail fence cipher.

Example

The rail fence cipher is a very simple columnar transposition that takes a string and splits the letters into two groups by way of a zigzag pattern, as shown below:
Encipher
plaintext = When drinking water, remember its source.
compressed plaintext = whendrinkingwaterrememberitssource

zig:

W

E

D

I

K

N

W

T

R

E

E

B

R

T

S

U

C

zag:

H

N

R

N

I

G

A

E

R

M

M

E

I

S

O

R

E

zig = WEDIKNWTREEBRTSUC
zag = HNRNIGAERMMEISORE
ciphertext = zig + zag
ciphertext = WEDIKNWTREEBRTSUCHNRNIGAERMMEISORE

Decipher
To decipher, simply cut the ciphertext in half and create a new string with alternating letters from both substrings.
substring_1 = WEDIKNWTREEBRTSUC
substring_2 = HNRNIGAERMMEISORE
newstring = W + H + E + N + D + R + + U + R + C + E"

 

Scytale Cipher

In 4th century B.C., a device named a scytale was used to encrypt Spartan government and military messages. The device consisted of a cylinder of wood with a strip of paper wrapped around it. When the paper was removed, it was simply a string of jumbled letters but, while wrapped around the device, the message was clearly revealed. The scytale  takes the idea of the rail fence cipher and expands upon it by using a key of a given length to help conceal the message.


Encipher
plaintext = When drinking water, remember its source.
compressed plaintext = whendrinkingwaterrememberitssource
compressed plaintext length = 34
chosen key length = 4
Dividing the plaintext length of 34 by the key length of 4 gives 8 with a remainder 2. So we round  the length of each row of the scytale up to 9 and pad the message with two letter "z"s.

W

H

E

N

D

R

I

N

K

I

N

G

W

A

T

E

R

R

E

M

E

M

B

E

R

I

T

S

S

O

U

R

C

E

Z

Z

:: the scytale unit itself ::

By lining up the letters from each column and moving left to right we get the ciphertext:
   WIESHNMSEGEONWMUDABRRTECIERENRIZKRTZ
Looking at this ciphertext alone, the original message is disguised to the eye.

Decipher

To decrypt, knowing that the key is of size 4, so we write the first four characters from top to bottom, then the next four character adjacent to the first column and so on. Reading the letters from each row and discarding the final padded characters, we get the plaintext

 

Disadvantages

In the case of small messages, the ciphertext is easily deciphered by anyone willing to try deciphering with different key values.

Ciphertext length 36 is divisible by 3 so we first test with a key of 3, resulting in...
   WSMGNUBTIEIR
   IHSEWDREENZT
   ENEOMARCRRKZ
which when read line by line obviously proves not be English, so we can deduce that the key is not 3.

Testing with a key of 6, which also divides evenly into 36, gives us...
   WMNBII
   ISWREZ
   EEMRRK
   SGUTER
   HEDENT
   NOACRZ
which again is clearly not the correct answer. In fact, we didn't even have to plot out the entire answer here, because after putting in the second column, our first word was shown to begin with "WM," and no English language word begins that way. Therefore a key of 6 could not work.

A test using a key of length 4 will show the correct answer:
   WHENDRINK
   INGWATERR
   EMEMBERIT
   SSOURCEZZ
This becomes "WHENDRINKINGWATERREMEMBERITSSOURCEZZ," which is clearly the correct answer.

The rail fence cipher is more of a learning tool than a practical cipher, as its overly simple design allows virtually anyone to crack it. Despite this, the scytale cipher can actually be a useful tool for applications such as quick message passing and in other situations where the decoding must be done by hand.

The main problem with both of these ciphers is that the actual letters are not changed, so frequency counts reveal not only trends in letter repetition but the actual plaintext letter that the ciphertext is linked to (because they are the same letter!). Generally speaking, having the plaintext and ciphertext letters line up exactly with each other always leads to easily deciphered messages.