The ElGamal cryptosystem uses an elementary arithmetic operation – multiplication of a numerical form of the message by a random number in some mod – to do the scrambling needed for encryption. Enough...The ElGamal cryptosystem uses an elementary arithmetic operation – multiplication of a numerical form of the message by a random number in some mod – to do the scrambling needed for encryption. Enough information is also passed along in the ciphertext so that the intended recipient, who knows the value of a certain discrete log, can cancel out this scrambling multiplication.