On lattice profile of the elliptic curve linear congruential generators

Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG

Finite Fields: Theory and Applications

Finite fields are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of finite field techniques in cryptography, error correcting codes, and random number generation

Perfect codes in the Lee and Chebyshev metrics and iterating Rédei functions

Orientadores: Sueli Irene Rodrigues Costa, Daniel Nelson Panario RodriguezTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: O conteúdo desta tese insere-se dentro de duas áreas de pesquisa muito ativas: a teoria de códigos corretores de erros e sistemas dinâmicos sobre corpos finitos. Para abordar problemas em ambos os tópicos introduzimos um tipo de sequência finita que chamamos v-séries. No conjunto destas definimos uma métrica que induz uma estrutura de poset usada no estudo das possíveis estruturas de grupo abeliano representadas por códigos perfeitos na métrica de Chebyshev. Por outro lado, cada v-série é associada a uma árvore com raiz, a qual terá um papel importante em resultados relacionados à estrutura dinâmica de iterações de funções de Rédei. Na teoria de códigos corretores de erros, estudamos códigos perfeitos na métrica de Lee e na métrica de Chebyshev (correspondentes à métrica lp para p=1 e p=infinito respetivamente). Os principais resultados aqui estão relacionados com a descrição dos códigos q-ários n-dimensionais com raio de empacotamento e que sejam perfeitos nestas métricas, a obtenção de suas matrizes geradoras e a classificação destes, a menos de isometrias e a menos de isomorfismos. Varias construções de códigos perfeitos e famílias interessantes destes códigos com respeito à métrica de Chebyshev são apresentadas. Em sistemas dinâmicos sobre corpos finitos centramos nossa atenção em iterações de funções de Rédei, sendo o principal resultado um teorema estrutural para estas funções, o qual permite estender vários resultados sobre funções de Rédei. Este teorema pode também ser aplicado para outras classes de funções permitindo obter provas alternativas mais simples de alguns resultados conhecidos como o número de componentes conexas, o número de pontos periódicos e o valor esperado para o período e preperíodo da aplicação exponencial sobre corpos finitosAbstract: The content of this thesis is inserted in two very active research areas: the theory of error correcting codes and dynamical systems over finite fields. To approach problems in both topics we introduce a type of finite sequence called v-series. A metric is introduced in the set of such sequences inducing a poset structure used to determine all possible abelian group structures represented by perfect codes in the Chebyshev metric. Moreover, each v-serie is associated with a rooted tree, which has an important role in results related to the cycle structure of iterating Rédei functions. Regarding the theory of error correcting codes, we study perfect codes in the Lee metric and Chebyshev metric (corresponding to the lp metric for p=1 and p=infinity, respectively). The main results here are related to the description of n-dimensional q-ary codes with packing radius e which are perfect in these metrics, obtaining their generator matrices and their classification up to isometry and up to isomorphism. Several constructions of perfect codes in the Chebyshev metric are given and interesting families of such codes are presented. Regarding dynamical system over finite fields we focus on iterating Rédei functions, where our main result is a structural theorem, which allows us to extend several results on Rédei functions. The above theorem can also be applied to other maps, allowing simpler proofs of some known results related to the number of components, the number of periodic points and the expected value for the period and preperiod for iterating exponentiations over finite fieldsDoutoradoMatematica AplicadaDoutor em Matemática Aplicada2012/10600-2FAPESPCAPE

Semianalytical and Numerical Studies of Relativistic Heavy Ion Collisions

The quark-gluon plasma (QGP) has been produced by relativistic heavy ion collisions, and understanding its properties is a primary goal in the field of nuclear physics. This research first elucidates recent semianalytical developments that improve the estimates of the initial energy and net conserved-charge densities and enable the calculation of trajectories in the quantum chromodynamics (QCD) phase diagram for the matter produced by nuclear collisions. A semianalytical model of the initial densities is developed by including the finite nuclear thickness for parton production. The new maximum energy density is found to have an analytical upper bound and satisfy an approximate scaling relation. QCD phase diagram trajectories are extracted from the semianalytical densities using several nuclear equations of state, and the calculated QGP lifetimes are found to depend significantly on the values of the model’s parameters. The study next presents a comparison between two solutions of the relativistic Boltzmann equation (RBE): one, a numerical solution using parton trans- port; the other, a theoretical solution for a homogeneous gas of massless particles. Parton transport in Zhang’s parton cascade (ZPC) is found to reproduce the results of a recent ex- act analytical solution of the RBE with an unexpected effectiveness at high densities when using new generalized collision schemes. Finally, the work discusses some open questions related to parton transport in ZPC and suggests some possible directions to uncover their answers. These future research goals include discovering the cause of an unexpected problem arising in simulations with three-dimensional (3D) expansion, understanding the theoretical distribution of the total center-of-mass (CM) energy squared for two-parton collisions, and studying curved parton motion in the presence of strong electromagnetic fields. Overall, the results presented in this dissertation improve the theoretical and numerical descriptions of the QGP and should be useful for future studies

Safety‐oriented discrete event model for airport A‐SMGCS reliability assessment

A detailed analysis of State of the Art Technologies and Procedures into Airport Advanced-Surface Movement Guidance and Control Systems has been provided in this thesis, together with the review ofStatistical Monte Carlo Analysis, Reliability Assessment and Petri Nets theories. This practical and theoretical background has lead the author to the conclusion that there is a lack of linkage in between these fields. At the same of time the rapid increasing of Air Traffic all over the world, has brought in evidence the urgent need of practical instruments able to identify and quantify the risks connected with Aircraft operations on the ground, since the Airport has shown to be the actual ‘bottle neck’ of the entire Air Transport System. Therefore, the only winning approach to such a critical matter has to be multi-disciplinary, sewing together apparently different subjects, coming from the most disparate areas of interest and trying to fulfil the gap. The result of this thesis work has come to a start towards the end, when a Timed Coloured Petri Net (TCPN) model of a ‘sample’ Airport A-SMGCS has been developed, that is capable of taking into account different orders of questions arisen during these recent years and tries to give them some good answers. The A-SMGCS Airport model is, in the end, a parametric tool relying on Discrete Event System theory, able to perform a Reliability Analysis of the system itself, that: • uses a Monte Carlo Analysis applied to a Timed Coloured Petri Net, whose purpose is to evaluate the Safety Level of Surface Movements along an Airport • lets the user to analyse the impact of Procedures and Reliability Indexes of Systems such as Surface Movement Radars, Automatic Dependent Surveillance-Broadcast, Airport Lighting Systems, Microwave Sensors, and so on… onto the Safety Level of Airport Aircraft Transport System • not only is a valid instrument in the Design Phase, but it is useful also into the Certifying Activities an in monitoring the Safety Level of the above mentioned System with respect to changes to Technologies and different Procedures.This TCPN model has been verified against qualitative engineering expectations by using simulation experiments and occupancy time schedules generated a priori. Simulation times are good, and since the model has been written into Simulink/Stateflow programming language, it can be compiled to run real-time in C language (Real-time workshop and Stateflow Coder), thus relying on portable code, able to run virtually on any platform, giving even better performances in terms of execution time. One of the most interesting applications of this work is the estimate, for an Airport, of the kind of A-SMGCS level of implementation needed (Technical/Economical convenience evaluation). As a matter of fact, starting from the Traffic Volume and choosing the kind of Ground Equipment to be installed, one can make predictions about the Safety Level of the System: if the value is compliant with the TLS required by ICAO, the A-SMGCS level of Implementation is sufficiently adequate. Nevertheless, even if the Level of Safety has been satisfied, some delays due to reduced or simplified performances (even if Safety is compliant) of some of the equipment (e.g. with reference to False Alarm Rates) can lead to previously unexpected economical consequences, thus requiring more accurate systems to be installed, in order to meet also Airport economical constraints. Work in progress includes the analysis of the effect of weather conditions and re-sequencing of a given schedule. The effect of re-sequencing a given schedule is not yet enough realistic since the model does not apply inter arrival and departure separations. However, the model might show some effect on different sequences based on runway occupancy times. A further developed model containing wake turbulence separation conditions would be more sensitive for this case. Hence, further work will be directed towards: • The development of On-Line Re-Scheduling based on the available actual runway/taxiway configuration and weather conditions. • The Engineering Safety Assessment of some small Italian Airport A-SMGCSs (Model validation with real data). • The application of Stochastic Differential Equations systems in order to evaluate the collision risk on the ground inside the Place alone on the Petri Net, in the event of a Short Term Conflict Alert (STCA), by adopting Reich Collision Risk Model. • Optimal Air Traffic Control Algorithms Synthesis (Adaptive look-ahead Optimization), by Dynamically Timed Coloured Petri Nets, together with the implementation of Error-Recovery Strategies and Diagnosis Functions

Direct Jet Reconstruction in Proton-Proton and Copper-Copper Collisions at √sNN = 200 GeV

Collision of heavy nuclei at the Relativistic Heavy Ion Collider (RHIC) recreates the state of high temperature quark-gluon plasma that existed shortly after the Big Bang. Measurement using single particle spectra and two-particle correlation shows that this medium is largely opaque to the transit of a high energy quark or gluon. Reconstructing the kinematics of these quarks and gluons can provide additional constraints for the property of their interaction with the medium. While the direct reconstruction of quantum chromodynamics jets, the final state showers of quarks and gluons, has become an indispensable tool at hadron and electron accelerator experiments, the application of this technique to heavy ion collisions at the RHIC energy has been considered a hard problem. The relatively low yield of high transverse momentum jets would have to be detected within a large, fluctuating background that can give rise to a false jet signal. At the RHIC PHENIX experiment, jet reconstruction also has to cope with the limited aperture of the central arm spectrometers. To overcome both problems, which can distort the jet signal in the traditional reconstruction algorithms, this thesis develops an algorithm that reconstructs the jets as maxima of the Gaussian filtered event transverse momentum distribution. The Gaussian angular weighting causes the algorithm to become more sensitive to the jet core versus the jet periphery. It is then combined with a fake jet rejection discriminant to remove the background fluctuation from the jet signal. This algorithm is used to obtain the first jet measurement in heavy ion environment at PHENIX, using data from the 2004/2005 RHIC run. The result includes the proton-proton inclusive jet spectrum, the proton-proton fragmentation function, the copper-copper jet nuclear modification factor, the copper-copper jet central-to-peripheral modification factor, and the copper-copper dijet azimuthal correlation. The measured copper-copper jet nuclear modification factor shows that there is a significant initial state effect to the jet suppression. The observation of no broadening in the copper-copper dijet azimuthal correlation indicates that the traditional energy loss picture via multiple soft scattering may not be applicable to the quark-gluon plasma

Advances in Information Security and Privacy

With the recent pandemic emergency, many people are spending their days in smart working and have increased their use of digital resources for both work and entertainment. The result is that the amount of digital information handled online is dramatically increased, and we can observe a significant increase in the number of attacks, breaches, and hacks. This Special Issue aims to establish the state of the art in protecting information by mitigating information risks. This objective is reached by presenting both surveys on specific topics and original approaches and solutions to specific problems. In total, 16 papers have been published in this Special Issue