New digital signature schemes in the real and Gaussian integers´ domains

The purpose of this paper is to provide digital signature schemes with appendix and message recovery in the real and Gaussian integers´ domains. The proposed schemes employ the idea of combining the integer factorization, and the generalized discrete logarithm problems. These proposed schemes are valid for the two new cryptosystems namely, the quadratic-exponentiation randomized (QER) and the Beta cryptosystems. An overview of the two cryptosystems and their extensions to the domain of Gaussian integers Z[i] are given. The validity of extending the digital signature schemes in Z[i] is illustrated. The proposed digital signature schemes are efficient. Extensions of the digital signature scheme with message recovery to Z[i] have many advantages. The digital signature schemes in the real and Z[i] domains are illustrated with extensive numerical examples.