Question

Discussion 400 words with APA Citations: Explain how to break the Vigenere Cipher.

Answer 1

Vignere Cipher:

The key is combination of letters.

We shift each character in text by the size that is specified by the next character.

The decryption is just opposite to it.

Breaking Vignere Cipher:

The plain text is encrypted using this cipher in the following manner.

We first choose set of alphabets as keyword to encrypt.

We use the alphabets and numbers associated with each character as follows.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Let us understand the process using a example.

Let the plain text be I like wiki books.

1. Now we convert the plain text to numbers based on sequence of alphabets.

This turns out as follows.

ilikewikibooks has the numbers as 8 11 8 10 4 22 8 10 8 1 14 14 10 18

2. we choose the keyword randomly. Let the keyword be cta.

cta has the numbers 2 19 0

3. We add the keyword and plain text numbers as shown below.

8 11 8 10 4 22 8 10 8 1 14 14 10 18
2 19 0 2 19 0 2 19 0 2 19 0 2 19

We add them and result is as follows.

10 30 8 12 23 22 10 23 8 3 33 14 12 37

4. Perform mod 26 operation on the result.

10 4 8 12 23 22 10 3 8 3 7 14 12 11
  
5. Use the above numbers and map the numbers back to letters.

keimxwkdodhoml
  
This is encrypted message. Using the above process we can trace back and decrypt the plain text.

When the keyword is not known, the method of breaking the cipher is generally called as kasiski test.
There are stages in determining it.

Determining the key length:

Let pi be the frequency of each character in plain text.

If key length is N, then we can make sure that every nth character is of same shift.

We consider every nth character and calculate frequency we can see permuted order of pi.

Later we consider every Mth character and calculate frequency we can get something uniform.

For some candidate distribution q0.....q255, we compute summation for squares of candidate distribution.

We try all possibilities of key length and compute the above summation values and see the maximum value.

Determining ith byte of key:

We now know the length of key.Let it be N.

See every Nth character start with ith character.consider them and form a stream.

These bytes are nothing but the bytes obtained by performing mod with plain text.

Try decrypting the stream using every possible byte values.

Though this is a long process, we need this to break vignere cipher without knowing the key.

If the key is available then the process is simple and just backtracking the encryption process.