- This is a strengthened version of a shift cipher where x -> ax+B
- example a = 9, B = 2
- affine -> CVVWPM
- Decryption involves reversing the cipher
- y = 9 x + 2
- In modular arithmetic we need to find the inverse differently than we would in algebra, more clearly described in Chapter 3
- Since we are using the alphabet, we need to work with mod 26
- therefore we need to find gcd(9,26) = 1
- What we can do is use the extended euclidean algorithm to solve for a multiplier to 9 that would result 1 mod 26 aka
- 9 x ≡ 1 (mod 26)
- we can also see that multiplying 9 by 3 will also result in a remainder of 1 which satisfies this congruence
- Therefore 3 is the desired inverse
- x ≡ 3(y-2) ≡ 3y -6 ≡ 3y +20 (mod 26)
- Example
- map the letter V
- V = 21
- 3*21 +20
- 81
- 81 ≡ 5 mod(26)
- the letter f
- This decryption will allow us to return the plaintext of affine from CVVWPM
- We must be able to find the inverse in modular arithmetic in order to have a usable key so arbitrary keys may result in multiple returns for a singular input
- Possible Attacks
- Ciphertext only
- 312 keys only means its easy for a computer to break, however difficult by hand
- Known Plaintext
- knowing even some of the plaintext reduces the possibilities and can potentially result in breaking the code even without a computer
- Chosen Plaintext
- if ab is chosen as plaintext we can immediately break the code
- Chosen Ciphertext
- again if AB is chosen as ciphertext we find the encryption key but we already have the decryption key in this case so no additional work is needed

## Saturday, September 21, 2013

### Notes - Affine Ciphers

The following are notes from Introduction to Cryptography with Coding Theory.

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