Answer Happy

3. The affine Caesar cipher replaces each plaintext character, p, with the ciphertext character, C, determined by the following equation: C = E([a, b], p) = ap + b mod N. a and b are a pair of integers that act as the key. N is the size of the alphabet. The fundamental requirement for any cipher is reversibility, i.e., that it create a one-to-one mapping between each plaintext character and the ciphertext character to which it is encrypted. Mathematically, this implies that p = q if and only if E(p) = E(q). Does this requirement place any restrictions on the value of a for the affine Caesar cipher? What about b? Justify your answers. 4. Describe the brute force approach to breaking this cipher. In this approach, every possible key is tried until the decryption yields an intelligible message. Assume that the adversary knows the 32-character alphabet used and is capable of recognizing an intelligible message, and the only challenge is arriving on the correct key. Your answer should include the maximum number of guesses required for determining the key, with an explanation for how you determined this number.