- A variation of the shift cipher
- key for the encryption is a vector of a chosen length
- Example
- key length 6
- (21,4,2,19,14,17)
- corresponds to word vector
- To encrypt we shift by the word vector
- A known plain text attack will succeed if enough characters are known
- Cryptanalysis uses the fact that english letter frequency is not equal
- a - 0.082
- b - 0.015
- c - 0.028
- d - 0.043
- e - 0.127
- f - 0.022
- g - 0.020
- h - 0.061
- i - 0.070
- j - 0.002
- k - 0.008
- l - 0.040
- m - 0.024
- n - 0.067
- o - 0.075
- p - 0.019
- q - 0.001
- r - 0.060
- s - 0.063
- t - 0.091
- u - 0.028
- v - 0.010
- w - 0.023
- x - 0.001
- y - 0.020
- z - 0.001
- Variations can occur but usually takes effort to produce, example the book Gadsby does not contain the letter e
- However, when using a Vigenere Cipher the frequencies are distributed so that the above is not nearly as useful in decryption
- Finding Key Length
- We find the key length by matching the number of coincidences
- write the ciphertext, then rewrite it with a displacement
- Example
- VVHQ
- VVHQW
- Then we mark each time there is a match between the two rows, and after trying multiple displacements the largest number of coincidences will be closest to the key length
- Finding the Key: First Method
- take a look at the 1+5n letters and find the frequency of letters then repeat for 2+5n, 3+5n, 4+5n, 5+5n we then guess at the code by finding the difference between the most frequent letter and e to find the overall shift that is used as the key
- After finding the key we then test it by decrypting to confirm if the key was correct
- Soft Proof
- place the frequencies of the english letters into a vector A
_{0}and let A_{i}represent the frequencies shifted by i - When taking the dot product of these two vectors we arrive at 0.066 with a full match but significantly less than that for any other shift
- We can also use this knowledge to approximate the number of coincidences we should find for a given match, which would be 0.066*the number of comparisons

## Saturday, September 28, 2013

### Notes - The Vigenere Cipher

The following are notes from Introduction to Cryptography with Coding Theory.

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