## Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / Multivariate Cryptography, Finite Filds, Eulerian equations, Eulerian transformations, Linguistic Graphs, Multivariate Maps of Low Density}

Date: received 7 Feb 2017

Contact author: vasyl at hektor umcs lublin pl

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2017/093

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