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 $x^{\alpha}=a$, $(\alpha, q-1)=1$. 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 CryptographyFinite FildsEulerian equationsEulerian transformationsLinguistic GraphsMultivariate 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2017/093}},
      url = {https://eprint.iacr.org/2017/093}
}
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