Advances in Mathematics of Communications (AMC)

Cryptanalysis of the CFVZ cryptosystem

Pages: 1 - 11, Volume 1, Issue 1, February 2007      doi:10.3934/amc.2007.1.1

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Joan-Josep Climent - 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 (email)
Elisa Gorla - Department of Mathematics, University of Zürich, Winterthurerstr 190, CH-8057 Zürich, Switzerland (email)
Joachim Rosenthal - Institut für Mathematik, Universität Zürich, Zürich, CH-8057, Switzerland (email)

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.

Keywords:  Public key cryptography, Diffie-Hellman protocol, elliptic curve cryptography, generalized birthday problem.
Mathematics Subject Classification:  Primary: 94A60, 11T71; Secondary: 14H52.

Received: February 2006;      Revised: October 2006;      Available Online: January 2007.