ElGamal Algorithm Basics

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Questions and Answers

What is the primary purpose of the ElGamal Algorithm?

  • Encrypting messages (correct)
  • Digital signature generation
  • Hashing data
  • Public key verification

In the ElGamal Algorithm, what is the role of the random integer 'k' during encryption?

  • Encrypting the data (correct)
  • Generating the private key
  • Decrypting the message
  • Calculating the public key

Which value does Bob NOT publish as part of his public key in the ElGamal Algorithm?

  • 'p'
  • 'g'
  • 'd' (correct)
  • 'e'

What is the purpose of selecting a large prime 'p' in the ElGamal Algorithm?

<p>Preventing brute force attacks (C)</p> Signup and view all the answers

Which formula correctly represents the decryption process in the ElGamal Algorithm?

<p>$m = [C2 * (C1^{d})^{-1}]$ mod p (B)</p> Signup and view all the answers

What does 'e' represent in the Key Generation of the ElGamal Algorithm?

<p>Public key (D)</p> Signup and view all the answers

Why is 'k' chosen as a random integer within a specific range in the ElGamal Algorithm?

<p>To prevent frequency analysis attacks (A)</p> Signup and view all the answers

Flashcards

ElGamal Algorithm's Purpose?

Encrypting messages.

Role of 'k' in Encryption?

The random integer 'k' is used to encrypt the data.

Value NOT in Public Key?

Bob does not publish 'd' as part of his public key.

Purpose of Large Prime 'p'?

A large prime 'p' prevents brute force attacks.

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Decryption Formula?

The decryption formula is: m = [C2 * (C1^{d})^{-1}] mod p

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What Does 'e' Represent?

'e' represents the public key.

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Why Random 'k'?

'k' is chosen randomly to prevent frequency analysis attacks.

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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 d such that 2 ≤ d ≤ p-1 and gcd(d,p) = 1
  • Selects a primitive root g
  • Computes e ≡ g^d mod p
  • Publishes (p, g, e) as his public key
  • Keeps d as a private key

Encryption Procedure

  • Alice encrypts data using Bob's public key
  • Selects a random integer k such that 2 ≤ k ≤ p-2 and gcd(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 derive m
  • Computes m = [C2 * (C1^d)^-1] mod p using his private key d

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 as 67

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