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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!