Extremal algebraic graphs, quadratic multivariate  public keys and temporal  rules

Vasyl Ustimenko; Aneta Wróblewska

Paper 2023/738

Extremal algebraic graphs, quadratic multivariate public keys and temporal rules

Vasyl Ustimenko

, Royal Holloway University of London

Aneta Wróblewska

, University of Maria Curie-Sklodowska

Abstract

We introduce large groups of quadratic transformations of a vector space over the finite fields defined via symbolic computations with the usage of algebraic constructions of Extremal Graph Theory. They can serve as platforms for the protocols of Noncommutative Cryptography with security based on the complexity of word decomposition problem in noncommutative polynomial transformation group. The modifications of these symbolic computations in the case of large fields of characteristic two allow us to define quadratic bijective multivariate public keys such that the inverses of public maps has a large polynomial degree. Another family of public keys is defined over arbitrary commutative ring with unity. We suggest the usage of constructed protocols for the private delivery of quadratic encryption maps instead of the public usage of these transformations, i.e. the idea of temporal multivariate rules with their periodical change.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Multivariate Cryptography Extremal Graph Theory Quadratic Multivariate Rules Noncommutative Cryptography
Contact author(s): Vasyl Ustymenko @ rhul ac uk
aneta wroblewska @ mail umcs pl
History: 2023-05-25: approved; 2023-05-22: received; See all versions
Short URL: https://ia.cr/2023/738
License: CC BY

BibTeX

@misc{cryptoeprint:2023/738,
      author = {Vasyl Ustimenko and Aneta Wróblewska},
      title = {Extremal algebraic graphs, quadratic multivariate  public keys and temporal  rules},
      howpublished = {Cryptology ePrint Archive, Paper 2023/738},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/738}},
      url = {https://eprint.iacr.org/2023/738}
}