Question

(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 (ne) = (35,5), where n = p . q 5-7 and ged(e, (p-1) 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. e) Use the Chinesrmainder theorem to find all solutions, if any, to the system of 3 mod 5, and x congruences 2-2 mod 3, x 2 mod 7. [15 points]

Answer 1

6) n goes Rrom Ito P- n av oxda らn 2 2 2. 4 2 4 165 5 32 o 6 64 9 る 7 123 7 8 256 3 9512 6 lo 1024

scsafe logaRitaro of 3 modulo I1 to tho base 2 ven 2 ere y 3 Disesete loqih of modulo to thi boy e z 2 Systemo of Conganancs 2 modT

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