On the Jordan-Gauss graphs and new multivariate  public keys

Vasyl Ustimenko; Tymoteusz Chojecki; Aneta Wróblewska

Paper 2024/1793

On the Jordan-Gauss graphs and new multivariate public keys

Vasyl Ustimenko

, Royal Holloway University of London

Tymoteusz Chojecki

, Maria Curie-Skłodowska University

Aneta Wróblewska

, Maria Curie-Skłodowska University

Abstract

We suggest two families of multivariate public keys defined over arbitrary finite commutative ring $K$ with unity. The first one has quadratic multivariate public rule, this family is an obfuscation of previously defined cryptosystem defined in terms of well known algebraic graphs $D (n, K)$ with the partition sets isomorphic to $K^{n}$ . Another family of cryptosystems uses the combination of Eulerian transformation of sending each variable to a monomial term with the quadratic encryption map of the first cryptosystem. The resulting map has unbounded degree and the density like the cubic multivariate map. The space of plaintexts of the second cryptosystem is the variety and the space of ciphertexts is the affine space .

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: cryptography over commutative rings graph based quadratic public keys multivariate keys of unbounded degree
Contact author(s): Vasyl Ustymenko @ rhul ac uk
chojecki tymoteusz @ gmail com
wroblewska-aneta @ wp pl
History: 2024-11-04: approved; 2024-11-02: received; See all versions
Short URL: https://ia.cr/2024/1793
License: CC BY

BibTeX

@misc{cryptoeprint:2024/1793,
      author = {Vasyl Ustimenko and Tymoteusz Chojecki and Aneta Wróblewska},
      title = {On the Jordan-Gauss graphs and new multivariate  public keys},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1793},
      year = {2024},
      url = {https://eprint.iacr.org/2024/1793}
}