ElGamal cryptosystem: Let p be a prime so that the discrete log problem in Zp is 'intractable' ;let 'a' be a primitive element modulo p and b=as (mod p )for some s. Keep s secret;make p,a,b public.

A message x is to e encrypted as an ordered pair

(ak (mod p ),xbk (mod p ))

where k is a (secret)random number chosen (for one use only) by the encoder.