I have an encrypted message (26 letter English) that was encrypted by an affine cipher. I know the first two letters of the plaintext are "th" which map to "AE" in the ciphertext. When I try to create a system of equations to try and get an encryption key, I hit a problem.
t=19 --> A=0 && h=7 --> E=4
So I create the system of equations
- 19a + b = 0
- 7a + b = 4
Subtracting I get
- 12a = -4
Now I can't invert 12 in Mod 26 so I have no idea where to go from here.. This was how I was taught to solve it in class.