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February  2007, 1(1): 1-11. doi: 10.3934/amc.2007.1.1

Cryptanalysis of the CFVZ cryptosystem

Joan-Josep Climent 1, , Elisa Gorla 2, and  Joachim Rosenthal 3,

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, Spain
2. 

Department of Mathematics, University of Zürich, Winterthurerstr 190, CH-8057 Zürich, Switzerland
3. 

Institut für Mathematik, Universität Zürich, Zürich, CH-8057, Switzerland

Received  February 2006 Revised  October 2006 Published  January 2007

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.
Keywords: generalized birthday problem., elliptic curve cryptography, Diffie-Hellman protocol, Public key cryptography.
Mathematics Subject Classification: Primary: 94A60, 11T71; Secondary: 14H5.
Citation: Joan-Josep Climent, Elisa Gorla, Joachim Rosenthal. Cryptanalysis of the CFVZ cryptosystem. Advances in Mathematics of Communications, 2007, 1 (1) : 1-11. doi: 10.3934/amc.2007.1.1
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