Rabin Public-Key Cryptosystem in the Domain of Gaussian Integers

In this paper, we extend Rabin public-key cryptosys-tern from its classical settings which is the domain of natural integers, ℤ
_N
, to a new setting which is the domain of Gaussian integers ℤ[i] modulo N. The modified methods are developed by extending arithmetics needed in the new setting, such as Legendre symbols, quadratic residues, and some well known theorems such as Wilson's theorem, and the Chinese Remainder Theorem. Proofs of the modified methods are presented. Algorithms and examples illustrating all of the modified methods are given. Finally, the advantages of the modified scheme are pointed out.