Friday, December 6, 2013

Notes - The ElGamal Public Key Cryptosystem

The following are notes from Introduction to Cyrptography with Coding Theory.
  • ElGamal Public Key Cryptosystem
    • Alice wants to send a message m to Bob
    • Bob chooses a large prime p and a primitive root α
    • Bob chooses a secret integer a and computes B ≡ α (mod p)
      • Make public (p, α, B) and is Bob's public key
    • Alice
      • downloads (p, α, B)
      • Chooses a secret random integer k and computes r ≡ α (mod p)
      • Computes t ≡ B k m (mod p)
      • sends the pair (r,t) to B
    • Bob decrypts by computing tr -a ≡ m (mod p)
  • Security
    • depends on a being kept secret which is reliant on the idea that discrete logs are difficult to compute

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