On fast computations of numerical parameters of homogeneous algebraic graphs of large girth and small diameter and encryption of large files.

Tymoteusz Chojecki; Vasyl Ustimenko

Paper 2022/908

On fast computations of numerical parameters of homogeneous algebraic graphs of large girth and small diameter and encryption of large files.

Tymoteusz Chojecki, University of Maria Curie-Sklodowska, Poland

Vasyl Ustimenko, University of Maria Curie-Sklodowska, Poland, University of London (Royal Holloway), UK, Institute of Telecommunications and Global Information Space, Kyiv, Ukraine

Abstract

The paper is dedicated to computer evaluation of parameters of members of family A(n, F_q) , n ≥ 2 of small world algebraic graphs of large girth with well defined projective limit. We present the applications of these computations to some optimisation problems for algebraic graphs over various field and Cryptography. We show the impact of high girth property of known family of graphs A(n, F_q) on properties of fast stream ciphers based on these graphs. Finally we modify these symmrtric encryption algorithms to make them resistant to linearization attacks.

Note: This research is partially supported by British Academy Fellowship for Researchers under Risk 2022.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint.
Keywords: graph based cryptography linearisation attacks stream ciphers implementation
Contact author(s): tymoteusz chojecki @ umcs pl
vasylustimenko @ yahoo pl
History: 2022-07-14: approved; 2022-07-12: received; See all versions
Short URL: https://ia.cr/2022/908
License: CC BY

BibTeX

@misc{cryptoeprint:2022/908,
      author = {Tymoteusz Chojecki and Vasyl Ustimenko},
      title = {On fast computations of numerical parameters of homogeneous algebraic graphs of large girth and small diameter and encryption of large files.},
      howpublished = {Cryptology ePrint Archive, Paper 2022/908},
      year = {2022},
      note = {\url{https://eprint.iacr.org/2022/908}},
      url = {https://eprint.iacr.org/2022/908}
}