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Questions and Answers
What is the primary purpose of the ElGamal Algorithm?
What is the primary purpose of the ElGamal Algorithm?
In the ElGamal Algorithm, what is the role of the random integer 'k' during encryption?
In the ElGamal Algorithm, what is the role of the random integer 'k' during encryption?
Which value does Bob NOT publish as part of his public key in the ElGamal Algorithm?
Which value does Bob NOT publish as part of his public key in the ElGamal Algorithm?
What is the purpose of selecting a large prime 'p' in the ElGamal Algorithm?
What is the purpose of selecting a large prime 'p' in the ElGamal Algorithm?
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Which formula correctly represents the decryption process in the ElGamal Algorithm?
Which formula correctly represents the decryption process in the ElGamal Algorithm?
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What does 'e' represent in the Key Generation of the ElGamal Algorithm?
What does 'e' represent in the Key Generation of the ElGamal Algorithm?
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Why is 'k' chosen as a random integer within a specific range in the ElGamal Algorithm?
Why is 'k' chosen as a random integer within a specific range in the ElGamal Algorithm?
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Study Notes
ElGamal Algorithm
- Presented in 1984 by Taher ElGamal
- Based on the Discrete Logarithm problem
- Randomized encryption algorithm
Key Generation
- Bob generates public and private keys
- Selects a large prime number
p - Selects a random integer
dsuch that2 ≤ d ≤ p-1andgcd(d,p) = 1 - Selects a primitive root
g - Computes
e ≡ g^d mod p - Publishes
(p, g, e)as his public key - Keeps
das a private key
Encryption Procedure
- Alice encrypts data using Bob's public key
- Selects a random integer
ksuch that2 ≤ k ≤ p-2andgcd(k,p) = 1 - Computes
C1 = g^k mod p - Computes
C2 = (m * e^k) mod p - Sends the encrypted message
(C1, C2)to Bob
Decryption Procedure
- Bob decrypts the message
(C1, C2)to derivem - Computes
m = [C2 * (C1^d)^-1] mod pusing his private keyd
Example
- Alice chooses
p = 107,g = 2,d = 67 - Computes
e ≡ g^d mod p ≡ 2^67 mod 107 ≡ 94 - Publishes the public key as
(107, 2, 94)and private key as67
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Description
Learn the fundamentals of the ElGamal algorithm, a public-key cryptosystem based on the Discrete Logarithm problem, introduced by Taher Elgamal in 1984. Explore key aspects such as randomized encryption, key generation, and establishing secure channels for key sharing and message encryption.
