mars Question 3: Eve has a cryptotext encrypted with an offine cipher E(x) = ax+b (mod 23) from a Latin-language plaintext. The most frequent cryptotext letter has numerical value a and the second most frequent letter has numerical value . a) Show that it is likely that a = 8x +15B (mod 23) and b = 14x +100 (mod 23). Hint: The most common letter in Latin is / = 7 and the second most common is E = 4.[4 marks) b) Prove that the offine cipher E(x) = ax+b (mod m) is idempotent, i.e. that composing two affine ciphers with key pairs (a,b) and (azba) results in another affine cipher with a different key pair (azba). [2 marks]