ElGamal

Published in 1985 by Taher Elgamal, who a decade later designed SSL at Netscape. The system rests on the same hard problem as Diffie-Hellman — the discrete logarithm in a finite group — but handles both encryption and signing.

Encryption is randomised: the same plaintext produces different ciphertext every time, because a fresh random value goes into each operation. That is both a strength and a trap. Reuse the random value and the private key can be computed — exactly what broke Sony's PS3 signing in 2010. Ciphertext comes out twice the size of the plaintext, and DSA, the US signature standard, is essentially ElGamal's signature half in tightened form.