12 Jun 2013

The Undecipherable Cipher: Middle Secondary Mathematics

The weakness of the substitution ciphers used in the first two questions is that the distribution of letter frequencies remains intact. However, there is a very simple yet powerful method that changes the distribution of letters, thereby making the ciphertext much harder to crack.

The most common letters in the English language form the sequence ETAON RISHD; the most common double letters are TH and HE; and the most common first letter of a word is T. If blank spaces are encoded, then the ”space” becomes the most popular symbol (for example, in Unicode the “space” is encoded as U+2420). All this statistical information is used to crack simple substitution ciphers. However, what would happen if we used a sequence of different substitutions? A 16th century French diplomat, Blaise de Vigenère, perfected just such an encryption method that now bears his name.

Imagine that instead of one alphabet disk we have a sequence of them. Both the plaintext and ciphertext letters are in alphabetical order. Now, imagine picking a keyword, let’s start with something simple such as BYTE. Set the first wheel so that the plaintext letter A is encoded into the letter B; then set the second wheel so that A encodes into Y; then set the third and fourth wheels to T and E. No further wheels are needed in this case. Now, take your plaintext and encode the first letter using the first wheel, encode the second letter using the second wheel, and so on. Once you reach the end of your keyword start from the beginning again; in this way the fifth letter of the plaintext will be encoded using the first wheel again. This very simple method destroys the frequency distribution of the letters in the plaintext.

Without computers, the Vigenère Cipher is extremely difficult to crack. Indeed, if the keyword is very long - say, a whole poem - or at least longer than the actual message, then it is impossible to crack! It became so famous as to be called the Undecipherable Cipher. However, using some brute force computing and a fairly short keyword, some new statistical patterns emerge.

Worth reading the whole section on the Vigenère Cipher at Simon Singh’s website then, using the Vigenère Cipher Cracking Tool, decrypt the following ciphertexts. Just copy and paste each of the texts below.

In this first question, I have left the punctuation intact. This should help you, but be aware that the Cracking Tool will ask you to remove it, so just delete those characters. Be careful not to accidentally delete any actual letters!

Ciphertext 1

Stvgw iah Two ejm cpsgvry i qmum teem. Npakr lsa gag ageflnvv lvgw vhqtmeiv wai lw fmp euijmnw Two mk cfmfo brw lbhwknlwleed lvi fczfwzrh gvr xg bjiddr. Azig mk bui hzbfsjvpabl xzig xzml fgbu vgty e niyyw ws xwv?

Here is an example where the chosen keyword has created a number of overlapping patterns. This time, all punctuation has been stripped, apart from the very last question mark: find the answer to the question.

Ciphertext 2



And lastly, can you crack this?

Ciphertext 3


Have fun!

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