Affine Cipher

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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!
 

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