 # Decrypt Message Encrypted Using Affine Cipher

## Question

The following ciphertext was encrypted by an affine cipher modulo 26: CRWWZ. The plaintext starts ha. Decrypt the message.

## Solution Preview

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H -> C and A-> R. From here results a system of two equations, namely:
7*a+b=2 (mod 26)
0*x+b= 17 (mod 26) => b=17
We plug the value of b into the first equation to find out “a”.
7*a+17=2 (mod 26)=> 7*a= 2-17 (mod 26) = -15 (mod26) =26-15=11 (mod 26).
So 7*a= 11 (mod 26) => a= 7^(-1)* 11 (mod 26)
But the inverse of 7 (modulo 26) is 15 because 7*15=105=1 (mod 26).
So a= 15* 11 (mod 26) =165 (mod 26) = 9...
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