Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the complexity of the discrete logarithm problem to the system. The method enables encryption and (error-correcting) coding to be combined within one system. These gro...

The theory of groups, rings and modules is developed to a great depth. Group theory results include Zassenhaus’s theorem and the Jordan-Hoelder theorem. The ring theory development includes ideals, quotient rings and the Chinese remainder theorem. The module development includes the Nakayama lemma, exact sequences and Tensor products.

In this paper, we present an improved Rivest’s ring signature scheme. In our scheme, the size of the signature is only related to the ring members, and the signer needs no to publish amount of random numbers. On this basis, we propose a group-oriented ring signature. In this scheme, only the person who belongs to the designated group can verify the validity of the ring signature. The security o...

in his paper mentioned in the title, which appears in the same issue of this journal, mehdi radjabalipour derives the cyclic decomposition of an algebraic linear transformation. a more general structure theory for linear transformations appears in irving kaplansky's lovely 1954 book on infinite abelian groups. we present a translation of kaplansky's results for abelian groups into the...

Using the Luthar–Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Rudvalis sporadic simple group Ru. As a consequence, for this group we confirm Kimmerle’s conjecture on prime graphs.