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 Democracy - Our Next Step in Europe

After about a quarter of a century of enlightened development and ongoing preparatory technological, scientific and political activities we are arrived at the realization period of the idea. The two major technological vehicles of progress are the World Wide Web, the most democratic international forum of information exchange and the advent of public key cryptography as a combined philosophical and practical device of individual integrity and collective responsibility.

Matrix Power S-box Analysis

* Work supported by the Lithuanian State Science and Studies Foundation.