On new results on Extremal Graph Theory, Theory of Algebraic Graphs and their applications in Cryptography and Coding Theory.

Vasyl Ustimenko

Paper 2022/296

On new results on Extremal Graph Theory, Theory of Algebraic Graphs and their applications in Cryptography and Coding Theory.

Vasyl Ustimenko

Abstract

New explicit constructions of infinite families of finite small world graphs of large girth with well defined projective limits which is an infinite tree are described. The applications of these objects to constructions of LDPC codes and cryptographic algorithms are shortly observed. We define families of homogeneous algebraic graphs of large girth over commutative ring K. For each commutative integrity ring K with |K|>2 we introduce a family of bipartite homogeneous algebraic graphs of large girth over K formed by graphs with sets of points and lines isomorphic K^n, n>1 and cycle indicator ≥ 2n+2 such that their projective limit is well defined and isomorphic to an infinite forest.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Minor revision. will be published in Dopovidi of Nath. Acad. of Ukraine
Keywords: family of graphs of large girth small world graphs cryptographic algorithms LDPC codes.
Contact author(s): vasyl @ hektor umcs lublin pl
History: 2022-03-07: received
Short URL: https://ia.cr/2022/296
License: CC BY

BibTeX

@misc{cryptoeprint:2022/296,
      author = {Vasyl Ustimenko},
      title = {On new results on Extremal Graph Theory, Theory of Algebraic Graphs and their applications in Cryptography and Coding Theory.},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/296},
      year = {2022},
      url = {https://eprint.iacr.org/2022/296}
}