Alice and Bob 2 (5) Alice and Bob agree to use the prime p = 2663 and the base a = 5 for communicationsusing the ElGamal public-key cryptosystem (as described in Cryptosystem 7.1 in Stinson's4th ed book). Let (p, a, Alice) be Alice's public key and (p, a, Bob) be Bob's public key.(a) Alice decides to choose a new private key a = 1589, so Alice51589 2598 (mod 2663).Bob encrypts a message using Alice's public key and sends her the ciphertext (y₁, 92) = (568, 2223). Decrypt the message.(b) Now Bob chooses a new private key and publishes (p, a, Bob), where Bob = 2071.Alice encrypts a message using this public key and sends the ciphertext (y₁, y2) = (568, 445) to Bob.Eve intercepts the transmission. Help Eve by solving the discrete logarithm problem 5b = 2071 (mod 2663)and using the value of b to decrypt the message. (You can use one of the algorithms in Section 7.2 in Stinson's 4th ed booksolve the given DLP.)

As per the policy we are allowed to solve only one question at a time. So, I am answering the first…

Answered: (5) Alice and Bob agree to use the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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