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Meletiou G.C.,ATEI of Epirus | Stamatiou Y.C.,University of Ioannina | Stamatiou Y.C.,University of Patras | Tsiakalos A.,University of Ioannina
Communications in Computer and Information Science | Year: 2011

In this paper we derive lower bounds for the degree of polynomials that approximate the square root of the discrete logarithm for Elliptic Curves with orders of various specific types. These bounds can serve as evidence for the difficulty in the computation of the square root of discrete logarithms for such elliptic curves, with properly chosen parameters that result in the curve having order of any of types studied in this paper. The techniques are potentially applicable to elliptic curves of order of any specific, allowable (by Hasse's bounds), order type that is of interest for the application in hand. © 2011 Springer-Verlag. Source


Garofalakis J.,University of Patras | Stergiou E.,ATEI of Epirus
Journal of Communications | Year: 2010

Multistage Interconnection Networks (MINs) are used to interconnect different processing modules in various parallel systems or on high bandwidth networks. In this paper an integrated performance methodology is presented. A new approximate performance model for self-routing MINs consisting of symmetrical switches which are subject to a backpressure blocking mechanism is analyzed. Based on this, the steady-state distribution of the queue utilization is estimated and then all important performance metrics are calculated. Moreover, a general evaluation factor which helps in choosing a better performance MIN in comparison with other similar MIN architecture specifications is defined. The model was exemplified for the case of symmetrical single- and double-buffered MINs. It provides accurate results and converges very quickly. The obtained results were validated by extensive simulations and were compared to existing related work in the literature. © 2010 ACADEMY PUBLISHER. Source


Garofalakis J.,University of Patras | Garofalakis J.,Research Academic Computer Technology Institute | Stergiou E.,ATEI of Epirus
International Journal of Parallel, Emergent and Distributed Systems | Year: 2011

In this paper, a discrete-time, single server with parallel multi-buffers, switching element (SE) is presented and analysed. This SE is used in the construction of multistage interconnection networks which have the ability to service the multi-priority traffic-supporting good quality of service. Through a queuing analysis and under various values of multi-traffic classifications, a performance evaluation is determined. This analytical model is based on the steady-state description of the system behaviour. An utilisation's formula is extracted by considering the steady state of the discrete-time multistage network. Consequently, we estimated the rest of the performance metrics. The results are validated using simulation. Apart from that our multi-priority architecture, validated in marginal cases, is compared to some existing single and two class priority models of multistage networks. This comparison is made by gathering metrics and comparing the total packet throughput. Also, the gain of the high-priority packets against the lower-priority packets under different configuration schemas is demonstrated. Eventually, this proposed analytical model is very accurate for various network sizes, with various values of offered multi-priority traffic on fabric's inputs and, therefore, can be used in performance prediction of multistage networks which supports quality of service. © 2011 Taylor & Francis. Source


Garofalakis J.,University of Patras | Garofalakis J.,Research Academic Computer Technology Institute | Stergiou E.,ATEI of Epirus
Future Generation Computer Systems | Year: 2013

The aim of this paper is to develop an analytical method for performance evaluation of double prioritized Multistage Interconnected Networks (MINs) with single or multilayers and backpressure operation which provide service differentiation and QoS guarantee to an end application running over next generation Internet or Grid systems. Specifically, a new architecture of switching elements is used for the construction of MINs. This switch element uses two parallel queues in order to serve dual priority traffic. Besides this, uniform traffic conditions are presupposed and the bulk of packet arrivals in each cycle to the network inputs follow a Bernoulli distribution. A new analytical model for evaluating single buffered MIN's with 2×2 special switching elements supporting internally two classes' priority traffic is presented. Equations for the steady state are derived. These equations are then used in finding the most important multistage network performance metrics, such as throughput, and packet latency. The results are also validated using simulation and compared with previous related work in marginal cases. This proposed analytical model is accurate for various network sizes and various values of offered traffic to the multistage network inputs. © 2012 Published by Elsevier B.V. All rights reserved. Source


Garofalakis J.,University of Patras | Garofalakis J.,Research Academic Computer Technology Institute | Stergiou E.,ATEI of Epirus
International Journal of Communication Systems | Year: 2011

Here a novel analytical method for performance prediction estimation of single- and multi-layer multistage interconnection networks (MINs) under multicast environments is presented. The 'Cell Replication While Routing' is used as a packet routing technique and the 'full multicast' mode as transmission policy is employed in all the MINs under study. This model is developed for single-layer MINs and is extended and applied to special types of multi-layer MINs, called semi-layer MINs, which support mixed traffic patterns such as unicast and multicast in uniform traffic conditions. The results confirm the significant performance saturation of single-layer MINs and the improvement of corresponding performance indicators by semi-layer MINs. The proposed analytical framework is anticipated to be a very useful tool in evaluating the performance of semi-layer MINs in designing more efficient QoS networks. © 2010 John Wiley & Sons, Ltd. Here a novel analytical method for performance prediction estimation of single- and multi-layer multistage interconnection networks [MINs] under multicast environments is presented. This model is developed for single-layer MINs and is extended and applied to special types of multi-layer MINs, called semi-layer MINs, which support mixed traffic patterns such as unicast and multicast in uniform traffic conditions. The results confirm the significant performance saturation of single-layer MINs and the improvement of corresponding performance indicators by semi-layer MINs. © 2010 John Wiley & Sons, Ltd. © 2010 John Wiley & Sons, Ltd. Source

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