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(5) Alice and Bob agree to use the prime p = 2663 and the base a = 5 for communications using the ElGamal public-key cryptosystem (as described in Cryptosystem 7.1 in Stinson's 4th 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 Bob encrypts a message using Alice's public key and sends her the ciphertext (y₁, 32) = (568, 2223). Decrypt the message. Alice = 51589 = 2598 (mod 2663).

(5) Alice and Bob agree to use the prime p = 2663 and the base a = 5 for communications using the ElGamal public-key cryptosystem (as described in Cryptosystem 7.1 in Stinson's 4th 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 Bob encrypts a message using Alice's public key and sends her the ciphertext (y₁, 32) = (568, 2223). Decrypt the message. Alice = 51589 = 2598 (mod 2663).

Advanced Engineering Mathematics
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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Alice and Bob 2

(5) Alice and Bob agree to use the prime p = 2663 and the base a = 5 for communications using the ElGamal public-key cryptosystem (as described in Cryptosystem 7.1 in Stinson's 4th 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 Alice 51589 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 book solve the given DLP.)
Transcribed Image Text:(5) Alice and Bob agree to use the prime p = 2663 and the base a = 5 for communications using the ElGamal public-key cryptosystem (as described in Cryptosystem 7.1 in Stinson's 4th 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 Alice 51589 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 book solve the given DLP.)
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