CRYPTIM: Graphs as tools for symmetric encryption. A combinatorial method of encryption is presented. The general idea is to treat vertices of a graph as messages and walks of a certain length as encryption tools. We study the quality of such an encryption in the case of graphs of high girth by comparing the probability to guess the message (vertex) at random with the probability to break the key, i.e. to guess the encoding walk. In fact the quality is good for graphs which are close to the Erdős bound, defined by the even cycle theorem. We construct special linguistic graphs of affine type whose vertices (messages) and walks (encoding tools) could be both naturally identified with vectors over GF(q), and neighbors of the vertex defined by a system of linear equations. For them the computation of walks has a strong similarity with the classical scheme of linear coding. The algorithm has been implemented and tested.

References in zbMATH (referenced in 28 articles , 1 standard article )

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  1. Polak, Monika; Ustimenko, Vasyl: On stream cipher based on a family of graphs (\widetildeD(n, q)) of increasing girth (2014)
  2. Ustimenko, Vasyl: On multivariate cryptosystems based on computable maps with invertible decomposition (2014)
  3. Wróblewska, Aneta; Ustimenko, Vasyl: On new examples of families of multivariate stable maps and their cryptographical applications (2014)
  4. Ustimenko, Vasyl; Wroblewska, Aneta: On the key exchange and multivariate encryption with nonlinear polynomial maps of stable degree (2013)
  5. Klisowski, Michał; Ustimenko, Vasyl: On the comparison of cryptographical properties of two different families of graphs with large cycle indicator (2012)
  6. Romańczuk, Urszula; Ustimenko, Vasyl: On the family of cubical multivariate cryptosystems based on the algebraic graph over finite commutative rings of characteristic 2 (2012)
  7. Romańczuk, Urszula; Ustimenko, Vasyl: On families of graphs of large cycle indicator, matrices of large order and key exchange protocols with nonlinear polynomial maps of small degree (2012)
  8. Ustimenko, Vasyl; Wroblewska, Aneta: Dynamical systems as the main instrument for the constructions of new quadratic families and their usage in cryptography (2012)
  9. Romańczuk, Urszula; Ustimenko, Vasyl: On the key exchange with new cubical maps based on graphs (2011)
  10. Touzene, Abderezak; Ustimenko, Vasyl; AlRaissi, Marwa; Boudelioua, Imene: Performance of algebraic graphs based stream-ciphers using large finite fields (2011)
  11. Ustimenko, Vasyl; Wróblewska, Aneta: On the key expansion of (D(n, K))-based cryptographical algorithm (2011)
  12. Romańczuk, Urszula; Ustimenko, Vasyl: On the key exchange with matrices of large order and graph based nonlinear maps (2010)
  13. Ustimenko, Vasyl Alex: Schubert cells in Lie geometries and key exchange via symbolic computations (2010)
  14. Wroblewska, Aneta; Ustimenko, Vasyl: On the key exchange with nonlinear polynomial maps of degree 4 (2010)
  15. Shaska, T.; Ustimenko, V.: On the homogeneous algebraic graphs of large girth and their applications (2009)
  16. Ustimenko, V. A.: Algebraic groups and small world graphs of high girth (2009)
  17. Shaska, Tanush; Ustimenko, V.: On some applications of graphs to cryptography and turbocoding (2008)
  18. Wroblewska, Aneta: On some properties of graph based public keys (2008)
  19. Futorny, Vyacheslav; Ustimenko, Vasyl: On small world semiplanes with generalised Schubert cells (2007)
  20. Ustimenko, V. A.: On graph-based cryptography and symbolic computations (2007)

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