On new key exchange multivariate protocols based on pseudorandom walks on incidence structures
DOI:
https://doi.org/10.15407/dopovidi2015.01.041Keywords:
common walk, cryptography, graph, keyAbstract
A new key exchange protocol formulated in terms of multivariate cryptography and based on the elaboration of a common walk in the linguistic graph by correspondents is proposed. This algorithm is described in details in the case of a known family of graphs of large girth given by nonlinear equations over a finite field.Downloads
References
Biggs N. L. Algebraic graph theory, Cambridge: Cambridge Univ. Press, 1993.
Moore E. H. Amer. J. Math., 1886, 18: 264–303. https://doi.org/10.2307/2369797
Ustimenko V. J. Alg. Discr. Math., 2005, 1: 133–150.
Ustimenko V. Reports of the National Academy of Sciences of Ukraine, 2014, 3: 55–150. https://doi.org/10.15407/dopovidi2014.03.055
Lazebnik F., Ustimenko V. A., Woldar A. J. Bull. Amer. Math. Soc. (New Series), 1995, 32, 1: 73–79. https://doi.org/10.1090/S0273-0979-1995-00569-0
Lazebnik F., Ustimenko V. A., Woldar A. J. Discr. Math., 1996, 157: 271–283. https://doi.org/10.1016/S0012-365X(96)83019-6
Diffie M., Hellman M. E. IEEE Trans. Inform. Theory, 1976, IT, 22: 644–654.
Hoory S., Linial N., Wigderson A. Bull. Amer. Math. Soc. (New Series), 2006, 43, 4: 439–561. https://doi.org/10.1090/S0273-0979-06-01126-8
Ustimenko V. In: Voronoj's Impact on Modern Science, Kiev: Institute of Mathematics, 1998, Vol. 2: 125–152.
Ustimenko V. Lecture Notes in Computer Science, Proceedings of AAECC-14 Symposium on Applied Algebra, Algebraic Algorithms and Error Correction Codes, Berlin: Springer, 2001, 278–286. https://doi.org/10.1007/3-540-45624-4_29
Kotorowicz J., Ustimenko V. Condens. Matt. Phys., 2008, 11, 2: 347–360. https://doi.org/10.5488/CMP.11.2.347
Ustimenko V. Acta Appl. Math., 2002, 74: 117–153. https://doi.org/10.1023/A:1020686216463
Ustimenko V. J. Alg. Discr. Math., 2003, 3: 102–109.
Lovasz L. Bolyai Soc. Math. Studies, 1993, 2: 1–46.
Romanczuk U., Ustimenko V. In: Artificial Intelligence, Evolutionary Computing and Metaheuristics, Berlin: Springer, 2013: 257–285.
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