How Do You Decrypt an Affine Cipher Text?

[pupeye11]

Homework Statement

Below is an example of ciphertext obtained from an Affine Cipher. Determine the plaintext.

KQEREJEBCPPCJCRKIEACUZBKRVPKRBCIBQCARBJCVFCUPKRIOFKPACUZQEPBKRXPEIIEABDKPBCPFCDCCAFIEABDKPBCPFEQPKAZ
BKRHAIBKAPCCIBURCCDKDCCJCIDFUIXPAFFERBICZDFKABICBB
ENEFCUPJCVKABPCYDCCDPKBCOCPERKIVKSCPICBRKIJPKABI

Probabilities of each letter:

E .127
T .091
A .082
O .075
I .070
N .067
S .063
H .061
R .060
D .043
L .040
C .028
U .028
M .024
W .023
F .022
G .020
Y .020
P .019
B .015
V .010
K .008
J .002
X .001
Z .001
Q .001

The Attempt at a Solution

Well, due to occurrences and the probabilities, you try mapping two letters to other letters then solve using modular arithmetic. I have tried mapping C--> E then B--> every other letter, C--> T and B--> all letter with a higher probability then R, and C--> A and B--> all letters with a higher probability then R.

Just to make sure I am doing all calculations right, assume C-->E and B--> T

Then we have the equations 2a+b=4 (mod 26)
a+b=19 (mod 26)

This means a=11, b=8 and since GCD(11,26)=1 the deciphering equation will be

d(k) = 7(y-8) (mod 26)

But, using this equation the first five letters map to OEYLE which is obviously nothing, so I have to try the next one.

I have been working on this for over 5 hours and have not come up with a solution. Any help would be greatly appreciated!

 

[mighty2000]

Hi there, thank you for sharing your attempt at solving this problem. It seems like you have a good understanding of the Affine Cipher and how to use modular arithmetic to decipher the ciphertext. However, it is important to note that there may not be a single solution to this cipher, as there are multiple combinations of letters that could have been used for the key. It is also possible that the ciphertext has been encrypted using a different cipher or a combination of ciphers.

One approach you could try is to use frequency analysis on the ciphertext. This involves comparing the frequency of letters in the ciphertext to the probabilities given in the forum post. This can give you a starting point for mapping letters and can also help you identify common letter combinations (e.g. "THE", "ING", etc.). From there, you can continue using modular arithmetic and trial and error to find the correct key.

Additionally, you could also try using a tool or program that can automatically decipher the ciphertext for you. This can help you check your work and potentially give you some insights on how to approach the problem.

I hope this helps and good luck with your decryption!