(d) Decrypt the ciphertext message LEWLYPLUJL PZ H NYLHA ALHJOLY that was encrypted with the shift...

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(d) Decrypt the ciphertext message LEWLYPLUJL PZ H NYLHA ALHJOLY that was encrypted with the shift cipher f(p) = (p+7) mod 26. [10 points] (e) [Extra Credit - 5 points] Encrypt the message "BA" using the RSA cryptosystem with key (n, e) = (35, 5), where n = p q = 5.7 and gcd(e, (p - 1)(q-1)) =(5,24) = 1. 6. [5 points each] (a) Is 2 a primitive root of 11? (b) Find the discrete logarithm of 3 modulo 11 to the base 2. 50 (1) (c) Use the Chinese remainder theorem to find all solutions, if any, to the system of congruences x = 2 mod 3, x = 3 mod 5, and x = 2 mod 7. [15 points] (d) Decrypt the ciphertext message LEWLYPLUJL PZ H NYLHA ALHJOLY that was encrypted with the shift cipher f(p) = (p+7) mod 26. [10 points] (e) [Extra Credit - 5 points] Encrypt the message "BA" using the RSA cryptosystem with key (n, e) = (35, 5), where n = p q = 5.7 and gcd(e, (p - 1)(q-1)) =(5,24) = 1. 6. [5 points each] (a) Is 2 a primitive root of 11? (b) Find the discrete logarithm of 3 modulo 11 to the base 2. 50 (1) (c) Use the Chinese remainder theorem to find all solutions, if any, to the system of congruences x = 2 mod 3, x = 3 mod 5, and x = 2 mod 7. [15 points]