# Math Help - Cracking Affine Ciphers

1. ## Cracking Affine Ciphers

Hey,
I have a question to decipher an affine cipher. The cipher text is RBYDKLQTSLQJBYN and I am told that E(A)=L and E(O) = B.

Cipher
L -> 12
B -> 2
Plain
A -> 1
O -> 15

So basically I set up two equations in Z26:
$
12 = a + b
$

$
2 = 15a + b
$

I take the top and subtact the bottom:

$
10 = -14a
$

$
10 = 12a
$

Now my problem is I cannot find the inverse of 12 in Z26 because they are not relatively prime. I am not sure how to proceed from this point? Can someone point me in right direction? I've tried subtracting the equations in the reverse order, but run into the same relatively prime issue.

Thanks

2. A --> 0 not 1 and O --> 14 not 15

The correspondence between letters in the plaintext and ciphertext spaces and $Z_26$ is a,A --> 0 all the way up to z,Z --> 25

This is because it is in mod 26 form, so you can have a 0, but not a 26!

Hope this helps

3. sorry, forgot to put that L --> 11 and B --> 1