Two new public key techniques in the domain of Gaussian integers

This paper introduces two new public key techniques namely the "quadratic-exponentiation randomized, (QER)" and the "beta" cryptosystems and their extensions in the domain of Gaussian integers Z[i]. These two techniques employ the idea of the presence of a one-way trapdoor function. First the two cryptosystems are defined in the domain of real integers with explicit numerical examples. Then the required arithmetic of the domain of the Gaussian integers and the use of it in the extensions proposed for the two techniques are explained. Also numerical examples declaring these extensions are given. The proposed cryptosystems have many advantages over the famous and most popular public key cryptosystems the RSA and the generalized ElGamal. The proposed extensions in the domain of Gaussian integers add-up to these advantages; [Kyung-Mi Kim, February 2001].