Erscheinungsdatum: 19.04.2016, Medium: Buch, Einband: Gebunden, Titel: Algebraic Structures of Symmetric Domains, Autor: Satake, Ichiro, Verlag: Princeton University Press, Sprache: Englisch, Schlagworte: MATHEMATICS // Algebra // Linear, Rubrik: Mathematik // Arithmetik, Algebra, Seiten: 340, Informationen: HC gerader Rücken kaschiert, Gewicht: 677 gr, Verkäufer: averdo
We study maximum principles for a class of linear, degenerate elliptic differential operators of the second order. The Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypotheses on the principal part and on the degeneracy set of the operator. We prove a Poincaré inequality, which then allows to define the functional setting where to study weak solutions for equations and inequalities involving this class of operators. A good example of such an operator is the Grushin operator, to which we devote particular attention. As an application of these tools in the degenerate elliptic setting, we prove a partial symmetry result for classical solutions of semilinear problems on bounded, symmetric and suitably convex domains and a nonexistence result for classical solutions of semilinear equations with subcritical growth defined on the whole space. We use here the method of moving planes, implemented just in the directions parallel to the degeneracy set of the Grushin operator.
In this book, research work in symmetric domain of cryptography is preferred over asymmetric cryptography domain at FPGA PLATFORM. To minimize the attacks like brute force attacks, linear and differential attacks over the system or the network, the approach adopted in this research work, verifies and conforms the increased level of security in comparison to previous approaches and also keeping in mind the resource consumption. The idea behind is to achieve "OPTIMIZATION" simultaneously increasing the security so that it can be used in different domains whether being at the network, ubiquitous computing, RFID Technology, Crypto-Cards, SIM cards etc. So this highlights the increased security in symmetric cryptography algorithms by proposed FPGA based MULTI-ENCRYPTION ALGORITHM whose results are compared to the previous approaches.
Miniaturization of medical appliances and wireless communication enable the pervasive health monitoring of users in their daily life thus improving users’ health and well-being, helping for quick reaction on emergencies, and yet, allowing for cost reduction in the healthcare sector. In the simplest healthcare setting, a fixed set of wireless medical sensors forms a patient area network (PAN) monitoring the user’s vital signs. Medical staff can access, gather, or process data directly, or transmit it to a remote healthcare service. Pervasive health monitoring in these diverse situations and locations is carried out by different organizations, such as fitness centers or retirement homes, by means of a medical sensor network (MSN) allowing authorized parties to access to the sensed health information.In this context, the exchange of users’ medical data leads to severe privacy and security concerns. Meeting these strict security needs of these ubiquitous medical applications is a big challenge, since privacy of medical data has to be guaranteed all the way from the resource-constrained sensor nodes to the backend services, the system has to fulfill latency needs, and lots of mobility is involved. In fact, ensuring the smooth but secure interaction of the different system parts is one of the most testing tasks.This thesis addresses the challenge of deploying secure medical sensor networks, and to this end we propose algorithms, protocols, and systems that pursue three main goals. The first being the described solutions enabling the efficient deployment of security systems – bearing in mind that the underlying interactions and the expected system operation is fundamental for the successful system deployment. Secondly, the individual mechanisms and the overall architecture should provide a comprehensive solution for key and entity management, access control, and privacy-aware identification. These are the key challenges in the analyzed scenarios due to the pervasive nature of the system wherein a multitude of parties interact with each other. Finally, security methods and cryptographic algorithms should be lightweight to allow for efficient system deployment and operation on resource-constrained devices.Overall, this work proposes a security architecture that is comprised of three security layers, namely MSN, PAN, and backend security layers. In our architecture, the MSN and PAN security layers reflect the trend towards a patient-centric approach wherein both user and health institutions share responsibility on the control of the health information. The MSN security layer is in charge of providing the basic link-security within each MSN. The PAN layer creates a security domain around the user’s PAN giving him control on the disclosure of his health information. The backend security layer ensures smooth interaction between the MSN and PAN layers.The proposed security architecture is articulated and supported by the results in four complementary research areas. The first one refers to lightweight key establishment and information verification algorithms used at the MSN layer. With this we investigate and specify how the wireless medical sensors can agree on pairwise keys and verify information in an efficient way based on polynomial schemes in the scope of an MSN. We propose several optimizations for key establishment algorithms and introduce the concept of lightweight digital certificates that allows for distributed information verification without the need of public-key cryptography.Second, we examine how the polynomial keying material can be distributed and arranged at the MSN security layer to achieve a higher resiliency level, to reduce system requirements, and to provide other security functionalities. We also show how the proposed hierarchical and multidimensional systems – tailored to fit the underlying organization of health institutions – allow for efficient deployment. A resourceful approach for key establishment is not usable if it cannot be deployed and managed, hence, we describe two key distribution and management systems for the polynomial keying material fitting the specific system deployment and operational requirements. The first system, which applies to infrastructureless systems, relies on a lightweight but resilient device, a smart card, playing the role of trust center. The second one makes use of backend services to control and manage more complex systems comprised of a multitude of networks.Third, we introduce several lightweight security mechanisms running at the PAN security layer. We describe the system interactions between both the MSN and PAN layers based on dedicated-hardware including the formation and management of the PAN security domain within the MSN security domain. The main goal of this piece of hardware, the patient security manager star – that consists of a healthcare card linked to each user and a patient security manager managed by the MSN – is to allow for PAN roaming between MSNs while guaranteeing end-to-end security. Additionally, this layer provides user privacy-aware identification for roaming users based on a hierarchy of identifiers and context-aware access control depending, e.g., on the user’s health state.The fourth addressed research topic is denominated cooperative security, an approach that aims at leveraging system security by enforcing cooperation among the nodes in an MSN, converting PANs in authentic distributed security domains that are able to manage their trust relationships, and allowing for fast and distributed revocation when nodes misbehave thus enhancing the system security.After successfully analyzing, prototyping, and testing the key components in both the MSN and the PAN layers, we have shown that our comprehensive security architecture and its components can play a fundamental role in the efficient and progressive rollout of secure pervasive healthcare systems. Further research lines emerge from this work. The first one refers to the additional refinements and extensions of the overall security architecture as well as a closer analysis of the interactions between PAN and MSN in specific use cases. The second one refers to the design of identity-based pairwise key generation engines based on non-linear keying material structures that can allow any pair of peers to generate a common symmetric-key given their identifiers but without suffering from the alpha-secure property inherent to the polynomial schemes. Such schemes might become more and more important for future pervasive systems comprising thousands or millions of devices. The third one involves further extensions for cooperative security protocols to convert large-scale distributed systems into living networks capable of autonomously controlling their own security system and removing infected nodes.