Q2: A generalization of the Caesar cipher, knows as the affine Caesar cipher, has the following...

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Q2: A generalization of the Caesar cipher, knows as the affine Caesar cipher, has the following form: For each plaintext letter p, substitute the ciphertext letter C: C= E([a, bl, p) = (a.p + b) mod 26 A basic requirement of any encryption algorithm is that it be one-to-one. That is, if p# q, then E(k, p) # E(k, q). Otherwise, decryption is impossible, because more than one plaintext character maps into the same ciphertext character. The affine Caesar cipher is not one-to-one for all values of a. For example, if a = 2 and b = 3, then E([a, b], 0) = E([a, b], 13) = 3. (1) Are there any limitations on the value of b? Explain why or why not. (ii)Determine which values of a are not allowed. (ii) Justify your statement. (iv) (v)A ciphertext has been generated with an affine cipher. The most frequent letter of the ciphertext is 'B', and the second most frequent letter of the ciphertext is 'U'. Break this code. Provide a general statement about which values of a are and are not allowed. How many one-to-one affine Caesar ciphers are there? Q2: A generalization of the Caesar cipher, knows as the affine Caesar cipher, has the following form: For each plaintext letter p, substitute the ciphertext letter C: C= E([a, bl, p) = (a.p + b) mod 26 A basic requirement of any encryption algorithm is that it be one-to-one. That is, if p# q, then E(k, p) # E(k, q). Otherwise, decryption is impossible, because more than one plaintext character maps into the same ciphertext character. The affine Caesar cipher is not one-to-one for all values of a. For example, if a = 2 and b = 3, then E([a, b], 0) = E([a, b], 13) = 3. (1) Are there any limitations on the value of b? Explain why or why not. (ii)Determine which values of a are not allowed. (ii) Justify your statement. (iv) (v)A ciphertext has been generated with an affine cipher. The most frequent letter of the ciphertext is 'B', and the second most frequent letter of the ciphertext is 'U'. Break this code. Provide a general statement about which values of a are and are not allowed. How many one-to-one affine Caesar ciphers are there?