On Graph-Based Cryptography and Symbolic Computations

We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed graphs of large girth and their cryptographical applications. It contains new explicit algebraic constructions of in finite families of such graphs. We show that they can be used for the implementation of secure and very fast symmetric encryption algorithms. The symbolic computations technique allow us to create a public key mode for the encryption scheme based on algebraic graphs.

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Ontological Multilevel Modeling Language

This paper presents ontological multilevel modeling language O2ML, aimed at using with metadata driven information systems. The first part of this paper briefly surveys existing modeling languages and approaches, while the last part proposes a new language to combine their benefits.

Online Access to the Encyclopaedia Slavica Sanctorum

Encyclopaedia Slavica Sanctorum project aims at building a repertoire of medieval and early modern Bulgarian texts for saints in combination with ethnological data and some visual sources. A basic project task is to produce an accessible on-line digital repository of this valuable cultural heritage treasure. The paper presents the Encyclopaedia Slavica Sanctorum environment, its architecture, functional specification, application modeling process and software implementation. The paper also discusses the specifics of the ―Encyclopaedia Slavica Sanctorum‖ project and its knowledge domain. The paper also presents the integration between the Encyclopaedia Slavica Sanctorum and the Bulgarian Iconographical Digital Library, a digital library keeping rare specimens, private collections of Orthodox icons, wall- paintings and other iconographical objects, selected from difficult-to-access storages, distant churches, chapels, and monasteries, objects in a risk environment or unstable conditions.