Last modified on 25 April 2014, at 03:29

Cryptography/Classical Cryptography

Cryptography has a long and colorful history from Caesar's encryption in first century BC to the 20th century.

Caesar CipherEdit

One of the most basic methods of encryption is the use of Caesar Ciphers. It simply consist in shifting the alphabet over a few characters and matching up the letters.

Classical cryptographyEdit

This makes transposition and substituting the two major principles in classical cryptography.

Transposition ciphersEdit

Lets look first at transposition, which is the changing in the position of the letters in the message such as a simple writing backwards

    Plaintext: THE PANEL IN THE WALL MOVES
    Encrypted: EHT LENAP NI EHT LLAW SEVOM

or as in a more complex transposition such as:

    THEPAN    
    ELINTH     
    EWALLM
    OVESAA        

then take the columns:

    TEEO HLWV EIAE PNLS ATLA NHMA

(the extra letters are called space fillers) The idea in transposition is NOT to randomize it but to transform it to something that is not recognizable with a reversible algorithm (an algorithm is just a procedure, reversible so your correspondent can read the message).

We discuss transposition ciphers in much more detail in a later chapter, Cryptography/Transposition ciphers.

Substitution ciphersEdit

The second principle is substitution. That is, substituting a Symbol for a letter of your plaintext (or word or even sentence). Slang even can sometimes be a form of cipher (the symbols replacing your plaintext), ever wonder why your parents never understood you? Slang, though, is not something you would want to store a secret in for a long time. In WWII, there were Navajo CodeTalkers who passed along info from unit to unit. From what I hear (someone verify this) the Navajo language was a very exclusive almost unknown and unwritten language. So the Japanese were not able to decipher it.

Even though this is a very loose example of substitution, whatever works works. The classical example of a substitution cipher is a shifted alphabet cipher

   Alphabet: ABCDEFGHIJKLMNOPQRSTUVWXYZ
     Cipher: BCDEFGHIJKLMNOPQRSTUVWXYZA
    Cipher2: CDEFGHIJKLMNOPQRSTUVWXYZAB
        etc...

Example:(using cipher 2)

          Plaintext: THE PANEL IN THE WALL MOVES
          Encrypted: VJG RCPGN KP VJG YCNN OQXGU

If this is the first time you've seen this it may seem like a rather secure cipher, but it's not. In fact this by itself is very insecure. For a time in the 1500-1600's this was the most secure (mainly because there were many people who were illiterate) but a man (old what's his name) in the 18th century discovered a way to crack (find the hidden message) of every cipher of this type he discovered frequency analysis.

We discuss substitution ciphers in much more detail in a later chapter, Cryptography/Substitution ciphers.

Frequency AnalysisEdit

In the shifted alphabet cipher or any simple randomized cipher, the same letter in the cipher replaces each of the same ones in your message (e.g. 'A' replaces all 'D's in the plaintext, etc.). The weakness is that English uses certain letters more than any other letter in the alphabet. 'E' is the most common, etc. Here's an exercise count all of each letter in this article. You'll find that in the previous sentence there are 2 'H's,7 'E's, 3 'R's, 3 'S's, etc. By far 'E' is the most common letter; here are the other frequencies [Frequency tables|http://rinkworks.com/words/letterfreq.shtml]. Basically you experiment with replacing different symbols with letters (the most common with 'E', etc.).

      Encrypted: VJG TCKP KP URCKP

First look for short words with limited choices of words, such as 'KP' this may be at, in, to, or, by, etc. Let us select in. Replace 'K' with 'I' and 'P' with 'N'.

      Encrypted: VJG TCIN IN URCIN

Next select VJG this is most likely the (since the huge frequency of 'the' in a normal sentence, check a couple of the preceding sentences).

      Encrypted: THE TCIN IN URCIN

generally this in much easier in long messages the plaintext is 'THE RAIN IN SPAIN'

We discuss many different ways to "attack", "break", and "solve" encrypted messages in a later section of this book, "Part III: Cryptanalysis", which includes a much more detailed section on Cryptography/Frequency analysis.


Combining transposition and substitutionEdit

A more secure encryption is a transposed substitution cipher.

Take the above message in encrypted form

      Encrypted:VJG RCPGN KP VJG YCNN OQXGU

now spiral transpose it

          VJGRC
          NNOQP
          CAAXG
          YUNGN
          GJVPK

The message starts in the upper right corner and spirals to the center (again the AA is a filler) Now take the columns:

       VNCYG JNAUJ GOANV RQXGP CPGNK

Now this is more resistant to Frequency analysis, see what we did before that started recognizable patterns results in:

       TNCYE HNAUH EOANT RQXEN CNENK

A problem for people who crack codes.