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Dr. Jaffe Advanced Topics in Mathematics Homework due 12/16 NAME: ____________________________________________________________ 1. If the most common letter in a long ciphertext, enciphered by a shift transformation C ≡ P + k (mod 26) is Q, then what is the most likely value of k? 2. If the two most common letters in a long ciphertext, enciphered by an affine transformation C ≡ aP + b (mod 26) are W and B, respectively, then what are the most likely values of a and b? 3. Encrypt the message THE RIGHT CHOICE using the affine transformation C ≡ 15P + 14 (mod 26). 4. CHALLENGE PROBLEM: Given two ciphers, plaintext may be enciphered by using one of the ciphers, and by then using the other cipher. This procedure produces a product cipher. Find the product cipher by using the transformation C ≡ 5P + 13 (mod 26) followed by the transformation C ≡ 17P + 3 (mod 26)