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.