Some Properties of Algebraic Structures of RSA-like Systems

Abstract

The algebraic structure Z_n^* , with n being a product of safe primes, is widely used in RSA-like cryptosystems. We have investigated some properties of this kind of structure. Isomorphic structures are presented to represent elements of Z_n^* in a unique way. They also help to determine the form and the number of possible subgroups, to find, in a deterministic rather than probabilistic manner, the elements of any possible orders. The properties of quadratic and high degree residues are analyzed in detail, as well.