Encryption Graph Based Algorithms Private Key Public Key Stream Ciphers Family Of Graphs of High Girth Small World Graphs
Issue Date:
2007
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Journal of Computing, Vol. 1, No 2, (2007), 131p-156p
Abstract:
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.
