Crypto Corner
  • Home
    • Crypto Corner Challenges
    • Glossary
    • Help with Activities
    • Educational Uses
    • Downloadable Resources
  • Introduction to Cryptography
    • Steganography
    • Codes and Ciphers
    • Conventions in Cryptography
  • Monoalphabetic Substitution Ciphers
    • Atbash Cipher
    • Pigpen Cipher
    • Caesar Shift Cipher
    • Affine Cipher
    • Mixed Alphabet Cipher
    • Other Examples
    • Frequency Analysis: Breaking the Code
    • Homophonic Substitution
  • Simple Transposition Ciphers
    • Rail Fence Cipher
    • Route Cipher
    • Columnar Transposition Cipher
    • Myszkowski Transposition Cipher
    • Permutation Cipher
    • Anagramming: Jumbling words
    • Combining Monoalphabetic and Simple Transposition Ciphers
  • Polyalphabetic Substitution Ciphers
    • Vigenère Cipher
    • Kasiski Analysis: Breaking the Code
    • Autokey Cipher
    • Other Examples
  • Fractionating Ciphers
    • Polybius Square
    • Straddling Checkerboard
    • Transposing Fractionated Text
    • Other ways to Alter Fractionated Text
  • Digraph Substitution Ciphers
    • Playfair Cipher
    • Two-Square Cipher
    • Four-Square Cipher
    • Hill Cipher

Fractionating Ciphers

Fractionation is a method of splitting letters so that each plaintext letter is represented by two or more symbols. This is different to Homophonic Substitution in that the same set of symbols are used to represent each plaintext letter each time, it is just there is more than one symbol. For example, "a" could be represented by "01", "b" by "02" and so on. Carrying this on we would get the ciphertext alphabet below.
Picture
The ciphertext alphabet when each plaintext letter is represented by two digits.
We can now encrypt a plaintext message "flee at once". We get "06120505 0120 15140305" as our ciphertext. Clearly this is a simple key, and we can use a more complex ciphertext alphabet. This makes the message harder to break, however, we have still only used a simple Monoalphabetic Substitution at this point. It is still susceptible to frequency analysis, but rather than looking at individual digits, we look at pairs (or digraphs). In our ciphertext, the most frequent digraph is "05" which appears 3 times, and does indeed represent "e".
So fractionation has made our substitution a little bit more secure, but it is still vulnerable (and at this stage most definitely less secure than the Polyalphabetic Ciphers).
However, fractionation is a useful tool to help make other ciphers (namely Transposition Ciphers) much more secure. We already looked at combining a monoalphabetic substitution with a transposition cipher, and when we use a fractionating method in our substitution it turns out to be even more secure.
As a simple example, we could reverse the words, giving us the new ciphertext "50502160 0210 50304151". This is still susceptible to frequency analysis, but the words would be reverted, which makes it a little harder to spot the patterns.
Now let's try a Columnar Transposition on the original ciphertext using keyword apple. We get the grid below.
Picture
The columnar transposition grid on the original ciphertext.
From this we read off our new ciphertext "05240115205060001513".
Now if we try to decipher this message with the ciphertext alphabet above, we start fine until we get to "50" and "60" which are not available. This method has turned a plaintext of 10 letters into a ciphertext of 20 digits, which we have jumbled up so it cannot be undone without the transposition first.
This is the power of a fractionating method. It allows us to not only pull apart words (like a normal transposition) but actually pull apart the individual letters of a message! It also allows us to represent a set of letters with a smaller set of characters (in this case the 26 letters are represented by 10 digits).
In this section we will look at two methods of fractionating a plaintext:
  • Polybius Square
  • Straddling Checkerboard
We will then look at how we can combine these fractionating methods with a Transposition Cipher to make them even more secure.
​And finally another way to alter the fractionated text in a way to make it harder to break.

Previous Page: Other Examples
Next Page: Polybius Square
Information
  • About Me
  • Contact Me
  • Legal
  • Glossary
  • Help with Activities
  • Educational Uses
  • Downloadble Resources
Crypto Corner is a subsiduary of www.interactive-maths.com
©2013 - 2023 Daniel Rodriguez-Clark
All rights reserved
If you have found Crypto Corner useful, then please consider supporting my work using the button below. Thanks!
  • Home
    • Crypto Corner Challenges
    • Glossary
    • Help with Activities
    • Educational Uses
    • Downloadable Resources
  • Introduction to Cryptography
    • Steganography
    • Codes and Ciphers
    • Conventions in Cryptography
  • Monoalphabetic Substitution Ciphers
    • Atbash Cipher
    • Pigpen Cipher
    • Caesar Shift Cipher
    • Affine Cipher
    • Mixed Alphabet Cipher
    • Other Examples
    • Frequency Analysis: Breaking the Code
    • Homophonic Substitution
  • Simple Transposition Ciphers
    • Rail Fence Cipher
    • Route Cipher
    • Columnar Transposition Cipher
    • Myszkowski Transposition Cipher
    • Permutation Cipher
    • Anagramming: Jumbling words
    • Combining Monoalphabetic and Simple Transposition Ciphers
  • Polyalphabetic Substitution Ciphers
    • Vigenère Cipher
    • Kasiski Analysis: Breaking the Code
    • Autokey Cipher
    • Other Examples
  • Fractionating Ciphers
    • Polybius Square
    • Straddling Checkerboard
    • Transposing Fractionated Text
    • Other ways to Alter Fractionated Text
  • Digraph Substitution Ciphers
    • Playfair Cipher
    • Two-Square Cipher
    • Four-Square Cipher
    • Hill Cipher