For a finite abelian group G and a splitting field K of G, let d(G, K) denote the largest integer l ∈ N for which there is a sequence S = g1 · . . . · gl over G such that (X g1 − a1) · . . . · (Xl − al) 6= 0 ∈ K[G] for all a1, . . . , al ∈ K . If D(G) denotes the Davenport constant of G, then there is the straightforward inequality D(G)−1 ≤ d(G, K). Equality holds for a variety of groups, and a...

We present a fully symmetric constant round authenticated group key agreement protocol in dynamic scenario. Our proposed scheme achieves forward secrecy and is provably secure under DDH assumption in the security model of Bresson et al. providing, we feel, better security guarantee than previously published results. The protocol is efficient in terms of both communication and computation power.

H"{o}lder in 1893 characterized all groups of order $pqr$ where  $p>q>r$ are prime numbers. In this paper,  by using new presentations of these groups, we compute their full automorphism group.

Lipton and Zalcstein presented a constant time algorithm for testing if a group is abelian in 12. However, the reference only contains a short abstract without proof. In this paper, we give a self contained proof for an n 2 3 lower bound for the number of pairs (a, b) of elements with ab 6= ba in every non-commutative group of size n. It implies a constant time randomized algorithm that tests i...

The Cosmological Constant Problem emerges when Quantum Field Theory is applied to the gravitational theory, due to the enormous magnitude of the induced energy of the vacuum. The unique known solution of this problem involves an extremely precise fine-tuning of the vacuum counterpart. We review a few of the existing approaches to this problem based on the account of the quantum (loop) effects a...

Lattice-based group signature is an active research topic in recent years. Since the pioneering work by Gordon, Katz and Vaikuntanathan (Asiacrypt 2010), ten other schemes have been proposed, providing various improvements in terms of security, efficiency and functionality. However, in all known constructions, one has to fix the number N of group users in the setup stage, and as a consequence, ...

In this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. With this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. N(G) and S(G) are the set of all nilpotency classes and the set of all solvability classes for the group G with respect to different automorphi...