On new multivariate cryptosystems based on hidden Eulerian equations over finite fields

Vasyl Ustimenko

Paper 2017/093

On new multivariate cryptosystems based on hidden Eulerian equations over finite fields

Vasyl Ustimenko

Abstract

We propose new multivariate cryptosystems over $n$ -dimensional vector space over a finite field $F_{q}$ based on idea of hidden discrete logarithm problem for ${F^{*}}_{q}$ . These cryptosystems are based on hidden eulerian equations $x^{α} = a$ , $(α, q - 1) = 1$ . The method is based on the idea of Eulerian transformations, which allow us to use asymmetric algorithms based on families of nonlinear multiplicatively injective maps of prescribed polynomial density and flexible degree.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Multivariate Cryptography Finite Filds Eulerian equations Eulerian transformations Linguistic Graphs Multivariate Maps of Low Density}
Contact author(s): vasyl @ hektor umcs lublin pl
History: 2017-02-10: received
Short URL: https://ia.cr/2017/093
License: CC BY

BibTeX

@misc{cryptoeprint:2017/093,
      author = {Vasyl Ustimenko},
      title = {On new multivariate cryptosystems based on hidden Eulerian equations over finite fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/093},
      year = {2017},
      url = {https://eprint.iacr.org/2017/093}
}