Cryptanalysis of the CFVZ cryptosystem

Joan-Josep Climent; Elisa Gorla; Joachim Rosenthal

doi:10.3934/amc.2007.1.1

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2007, Volume 1, Issue 1: 1-11. Doi: 10.3934/amc.2007.1.1

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Cryptanalysis of the CFVZ cryptosystem

1.
Institut Universitari d'Investigació Informàtica, Departament de Ciència de la Computació i Intel$\cdot$ligència Artificial, Universitat d'Alacant, Ap. correus 99, E-03080 Alacant
2.
Department of Mathematics, University of Zürich, Winterthurerstr 190, CH-8057 Zürich
3.
Institut für Mathematik, Universität Zürich, Zürich, CH-8057

Received: January 31, 2006

Revised: September 30, 2006

Published: January 2007

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Abstract

The paper analyzes CFVZ, a new public key cryptosystem whose security is based on a matrix version of the discrete logarithm problem over an elliptic curve. It is shown that the complexity of solving the underlying problem for the proposed system is dominated by the complexity of solving a fixed number of discrete logarithm problems in the group of an elliptic curve. Using an adapted Pollard rho algorithm it is shown that this problem is essentially as hard as solving one discrete logarithm problem in the group of an elliptic curve. Hence, the CFVZ cryptosystem has no advantages over traditional elliptic curve cryptography and should not be used in practice.

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Mathematics Subject Classification: Primary: 94A60, 11T71; Secondary: 14H52.

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