General Description
Proposed theme: Starting from the fundamental study of particular spaces over non-super-singular elliptic curves and associated elliptic equations, accomplished in the IDEI PCCE 08/2010 project, the mathematical model associated to an asymmetric encryption system will be achieved and an information security system will be created for data transfer between communication systems. This is composed of developing mathematical models including the demonstration of their validity, differential analysis systems and space simulation, highlighting the fundamental systems from equation theory with inhomogeneous, degenerate, singular partial derivatives, non-super-singular elliptic equations. Based on those we will develop algorithms and implement a prototype which has included the hierarchical authentication protocol, session-level encryption and the digital declaration for information that is transferred / stored. The experimental model has functionality for every entity wishing hierarchical authentication, session-level security with an authentication and classification level superior to the digital signature. The mathematical models used are developments based on our own mathematical studies starting from existing standards.
Research Subjects The project will have three stages of development starting from the basic research results from previous projects. First Stage The main objectives are: - Developing the mathematical study model of the equations systems with partial inhomogeneous, degenerate, singular derivates, non-super-singular particular elliptic equations - Analyze the models created based on the potential theory and their extension by branching processes equations and spatial limit simulation, over which the equations solutions have proprieties with cryptographic applications The second stage The main objectives are: - Study of the intractability level of the functions described in the first stage - Comparison with existing standards by defining and securing information superiority obtained with these - Interfacing the model described with the algorithmic model by optimizing the implementation in VMWare systems, writing algorithms needed to implement The third stage The main objectives are: - Study of the complexity of algorithms created - Study of feasibility of the proposed model for the definition of the optimal hardware systems in different applications, in order to describe the necessary for the implementation types desired - Creation of an experimental portal model implementing authentication features based on own mathematical models, shown to be superior to the current standard ones Generating government security level certifications, optimized to be more effective than those used in the government and military circles, digital declaration services, superior to those of digital signature by the intractability provided and the associated information volume.
Main research points consists in The project has a component of applied research, based on previous results obtained in national and international prestige projects, won in competition, with internationally recognized results, comprising of members who are devoted to research. The main results consist in creating a new model with applications in information theory and a new product offered to the storage/data communications systems. The Digital Declaration Model introduced by this project is unique in the country (one EU country has a similar model, the one in the project being the next generation of that model, but with a mathematical apparatus with superior intractabilitate properties of the certificate generating functions) and is applicable to models of communication / storage / signature of digital and digitized data that are necessary in public, commercial and government applications. The experimental model created by the project can be used for commercial, government and academia purpose, with direct applicability and is a necessity for the current market, being a requirement of the informational integration program in the EU.
Young Researchers
By his structure, the project focus on development of research capacities of young people and their training in areas of high importance of theoretical and applied mathematics. Fulfilling this goal is apparent in the articles described in section results, which were accepted in publications of international circulation.
All the project's objectives, according with the schedule, were fullfield, more than that, were overcounted. Beside these, were created new research lines. All of these can be shown from Rezults section