Curves and Their Applications to Factoring Polynomials

We present new methods for computing square roots and factorization of polynomials over finite fields. We also describe a method for computing in the Jacobian of a singular hyperelliptic curve. There is a compact representation of an element in the Jacobian of a smooth hyperelliptic curve over any field. This compact representation leads an efficient method for computing in Jacobians which is called Cantor's Algorithm. In one part of the dissertation, we show that an extension of this compact representation and Cantor's Algorithm is possible for singular hyperelliptic curves. This extension lead to the use of singular hyperelliptic curves for factorization of polynomials and computing square roots in finite fields. Our study shows that computing the square root of a number mod p is equivalent to finding any of the particular group elements in the Jacobian of a certain singular hyperelliptic curve. This is also true in the case of polynomial factorizations. Therefore the efficiency of our algorithms depends on only the efficiency of the algorithms for computing in the Jacobian of a singular hyperelliptic curve. The algorithms for computing in Jacobians of hyperelliptic curves are very fast especially for small genus and this makes our algorithms especially computing square roots algorithms competitive with the other well-known algorithms. In this work we also investigate superelliptic curves for factorization of polynomials

Group Handover for Drone-Mounted Base Stations

The widespread use of new technologies such as the Internet of things (IoT) and machine type communication(MTC) forces an increase on the number of user equipments(UEs) and MTC devices that are connecting to mobile networks. Inherently, as the number of UEs inside a base station's (BS) coverage area surges, the quality of service (QoS) tends to decline. The use of drone-mounted BS (UxNB) is a solution in places where UEs are densely populated, such as stadiums. UxNB emerges as a promising technology that can be used for capacity injection purposes in the future due to its fast deployment. However, this emerging technology introduces a new security issue. Mutual authentication, creating a communication channel between terrestrial BS and UxNB, and fast handover operations may cause security issues in the use of UxNB for capacity injection. This new protocol also suggests performing UE handover from terrestrial to UxNB as a group. To the best of the authors' knowledge, there is no authentication solution between BSs according to LTE and 5G standards. The proposed scheme provides a solution for the authentication of UxNB by the terrestrial BS. Additionally, a credential sharing phase for each UE in handover is not required in the proposed method. The absence of a credential sharing step saves resources by reducing the number of communications between BSs. Moreover, many UE handover operations are completed in concise time within the proposed group handover method

Scalable Group Secret Key Generation over Wireless Channels

In this paper, we consider the problem of secret key generation for multiple parties. Multi-user networks usually require a trusted party to efficiently distribute keys to the legitimate users and this process is a weakness against eavesdroppers. With the help of the physical layer security techniques, users can securely decide on a secret key without a trusted party by exploiting the unique properties of the channel. In this context, we develop a physical layer group key generation scheme that is also based on the ideas of the analog function computation studies. We firstly consider the key generation as a function to be computed over the wireless channel and propose two novel methods depending on the users transmission capability (i.e. half-duplex and full-duplex transmissions). Secondly, we exploit the uniqueness of the prime integers in order to enable the simultaneous transmission of the users for key generation. As a result, our approach contributes to the scalability of the existing physical layer key generation algorithms since all users transmit simultaneously rather than using pairwise communications. We prove that our half-duplex network model reduces the required number of communications for group key generation down to a linear scale. Furthermore, the full-duplex network model reduces to a constant scale.Comment: 7 pages, 3 figure, transaction

Mentoring Relations in the Aircraft Industry: A Case Study In Turkey

The aim of this study is to evaluate the mentoring process in a private organisation which utilises a very high technology and innovation process. In this organisation, the top managers consider themselves as informal mentors who facilitate the transfer of the organisational culture and knowledge to the working personnel, especially to the engineers. From this perspective, the study investigated the relationship of perceived mentoring functions and gender of the mentees and gender of the dyad relationships in a sample of 85 white-collar employees. Furthermore, interpersonal trust was analysed as the determinant of perceived mentoring relationships. As hypothesised, interpersonal trust was found as a strong factor in mentoring relationships. However, gender of the mentees and gender of the dyad mentoring failed to make significant contributions to perceived mentoring relationships. The findings from this preliminary study suggest that the need for more in-depth research on multicultural issues in mentoring. Specifically organisations under the impact of modern technology and management need more future multicultural quantitative studies

Differential cross section measurements for the production of a W boson in association with jets in proton–proton collisions at √s = 7 TeV

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript −1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio

Juxtaposing BTE and ATE – on the role of the European insurance industry in funding civil litigation

One of the ways in which legal services are financed, and indeed shaped, is through private insurance arrangement. Two contrasting types of legal expenses insurance contracts (LEI) seem to dominate in Europe: before the event (BTE) and after the event (ATE) legal expenses insurance. Notwithstanding institutional differences between different legal systems, BTE and ATE insurance arrangements may be instrumental if government policy is geared towards strengthening a market-oriented system of financing access to justice for individuals and business. At the same time, emphasizing the role of a private industry as a keeper of the gates to justice raises issues of accountability and transparency, not readily reconcilable with demands of competition. Moreover, multiple actors (clients, lawyers, courts, insurers) are involved, causing behavioural dynamics which are not easily predicted or influenced. Against this background, this paper looks into BTE and ATE arrangements by analysing the particularities of BTE and ATE arrangements currently available in some European jurisdictions and by painting a picture of their respective markets and legal contexts. This allows for some reflection on the performance of BTE and ATE providers as both financiers and keepers. Two issues emerge from the analysis that are worthy of some further reflection. Firstly, there is the problematic long-term sustainability of some ATE products. Secondly, the challenges faced by policymakers that would like to nudge consumers into voluntarily taking out BTE LEI

Penilaian Kinerja Keuangan Koperasi di Kabupaten Pelalawan

This paper describe development and financial performance of cooperative in District Pelalawan among 2007 - 2008. Studies on primary and secondary cooperative in 12 sub-districts. Method in this stady use performance measuring of productivity, efficiency, growth, liquidity, and solvability of cooperative. Productivity of cooperative in Pelalawan was highly but efficiency still low. Profit and income were highly, even liquidity of cooperative very high, and solvability was good