- 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
^{a }(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
^{k }(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

## Friday, December 6, 2013

### Notes - The ElGamal Public Key Cryptosystem

The following are notes from Introduction to Cyrptography with Coding Theory.

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