2 Discrete Mathematics Questions

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Instructions: Complete the following problems. Submit responses as a single PDF file in Blackboard. For full credit, solutions must be justified and include supporting work when appropriate. 2. Determine n between 0 and 25 for each problem below. (a) 1883 + 3421 ≡ n (mod 26) (b) (1883)(3421) ≡ n (mod 26) (c) 18833421 ≡ n (mod 26) Hint: Show 188312 ≡ 1 (mod 26) as an intermediate step. 3. Use the integers modulo 26 to encode the standard 26 letter alphabet using 1 for a, 2 for b, and so on. (a) Find the ciphertext message from encrypting the plaintext message, may the force be with you, using the affine cipher with encryption key c ≡ 5p + 2 (mod 26). Hint: The ciphertext is the message repeated with different letters as specified by the cipher. (b) Decrypt the ciphertext message, DCBCP SVGJ ZPCQAODI, into plain English using the decryption key p ≡ 9c + 4 (mod 26).
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