On Graph-Based Cryptography and Symbolic Computations

V. A., Ustimenko. "On Graph-Based Cryptography and Symbolic Computations." Serdica Journal of Computing 1.2 (2007): 131-156. <http://eudml.org/doc/11415>.

@article{V2007,
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.},
author = {V. A., Ustimenko},
journal = {Serdica Journal of Computing},
keywords = {Encryption; Graph Based Algorithms; Private Key; Public Key; Stream Ciphers; Family Of Graphs of High Girth; Small World Graphs; encryption; graph-based algorithms; private key; public key; stream ciphers; graphs of high girth; small-world graphs},
language = {eng},
number = {2},
pages = {131-156},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On Graph-Based Cryptography and Symbolic Computations},
url = {http://eudml.org/doc/11415},
volume = {1},
year = {2007},
}

TY - JOUR
AU - V. A., Ustimenko
TI - On Graph-Based Cryptography and Symbolic Computations
JO - Serdica Journal of Computing
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 1
IS - 2
SP - 131
EP - 156
AB - 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.
LA - eng
KW - Encryption; Graph Based Algorithms; Private Key; Public Key; Stream Ciphers; Family Of Graphs of High Girth; Small World Graphs; encryption; graph-based algorithms; private key; public key; stream ciphers; graphs of high girth; small-world graphs
UR - http://eudml.org/doc/11415
ER -