# Homework Help: Cryptography affine cipher

1. Sep 8, 2010

### Firestrider

1. The problem statement, all variables and given/known data
7) You are attempting to break an affine cipher. You believe that the ciphertext ‘a’ maps to the plaintext letter ‘E’ and that the ciphertext ‘v’ maps to the plaintext ‘T’. Determine the encryption function used based on these two pieces of information.

2. Relevant equations

Ciphertext “a” = 0, Plaintext “E” = 4
Ciphertext “v” = 21, Plaintext “T” = 19
E(x) = (ax + b) mod m; Given: m = 26.

3. The attempt at a solution

0 = (a(4) + b) mod 26 => Eq 1. Plug in 4 for x, 0 for E(x), 26 for m.
21 = (a(19) + b) mod 26 => Eq 2. Plug in 19 for x, 21 for E(x), 26 for m.
21 = (a(15)) mod 26 => Subtract Eq. 1 from Eq. 2.
7(21) = (7a(15)) mod 26 => Multiply both sides by modular multiplicative inverse of 15 mod 26, which is 7. Given from Reference Sheet.
147 = (a(105)) mod 26 => Simplified.
147 = (a) => Eq. 3. Identity:1 = aa-1 mod m.
0 = (147(4) + b) mod 26 => Plug answer (a) in from Eq. 3 to Eq. 1 to solve for b.
0 = (588 + b) mod 26 => Simplified.
b = 10. STUCK HERE, I USED WOLFRAM ALPHA TO CALCULATE THIS
0 = (147(4) + 10) mod 26 => Check.
21 = (147(19) + 10) mod 26 => Check.
Encryption Function: E(x) = (147x + 10) mod 26

Please help, I might be completely off base on my methods after Eq. 3 to solve for b.

2. Sep 12, 2010

### LCKurtz

I don't really know anything about ciphers. But I'm guessing you would want to use 52 instead of 26 since you are using both upper and lower case letters.

Disclaimer: I may not know what I'm talking about:shy: