(4) Elgamal public key cryptosystem (encryption): Start with the prime p = 29 and the primitive root g = 2. (a) Alice sends Bob the public key A = 12. Bob wants to send the message m₁ = 13 to Alice. Bob chooses the random element k = 3. Using the Elgamal public key cryptosystem, compute the pair of num- bers (C1, C₂) that Bob sends to Alice. Note: Do not work out how Alice computes the plaintext message m₁ from the ciphertext (C₁, C₂). (b) Bob encrypts another message m2 and sends the pair of numbers (12, 19) to Alice. Alice's secret key is a = 7. Using Elgamal public key decryption, Alice computes the plaintext message m₂ from the ciphertext (8,2). What is the number m2 that Alice obtains?

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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(4) Elgamal public key cryptosystem (encryption):
Start with the prime p = 29 and the primitive root g = 2.
(a) Alice sends Bob the public key A = 12.
Bob wants to send the message m₁ = 13 to Alice.
Bob chooses the random element k = 3.
Using the Elgamal public key cryptosystem, compute the pair of num-
bers (C1, C₂) that Bob sends to Alice.
Note: Do not work out how Alice computes the plaintext message m₁
from the ciphertext (C₁, C₂).
(b) Bob encrypts another message me and sends the pair of numbers
(12, 19) to Alice. Alice's secret key is a = 7.
Using Elgamal public key decryption, Alice computes the plaintext
message m₂ from the ciphertext (8,2). What is the number m2 that
Alice obtains?
Transcribed Image Text:(4) Elgamal public key cryptosystem (encryption): Start with the prime p = 29 and the primitive root g = 2. (a) Alice sends Bob the public key A = 12. Bob wants to send the message m₁ = 13 to Alice. Bob chooses the random element k = 3. Using the Elgamal public key cryptosystem, compute the pair of num- bers (C1, C₂) that Bob sends to Alice. Note: Do not work out how Alice computes the plaintext message m₁ from the ciphertext (C₁, C₂). (b) Bob encrypts another message me and sends the pair of numbers (12, 19) to Alice. Alice's secret key is a = 7. Using Elgamal public key decryption, Alice computes the plaintext message m₂ from the ciphertext (8,2). What is the number m2 that Alice obtains?
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