International Journal of Computer Network and Information Security(IJCNIS)

ISSN: 2074-9090 (Print), ISSN: 2074-9104 (Online)

Published By: MECS Press

IJCNIS Vol.1, No.1, Oct. 2009

Using P systems to Solve the Discrete Logarithm Problem used in Diffie-Hellman Key Exchange Protocol

Full Text (PDF, 196KB), PP.24-31

Views:88   Downloads:4


Xiaojing Ma,Zhitang Li,Hao Tu

Index Terms

P systems, Discrete Logarithm Problem, Diffie-Hellman key exchange protocol


The discrete logarithm problem has been used as the basis of several cryptosystems, especially the Diffie- Hellman key exchange protocol. P systems are a cluster of distributed parallel computing devices in a biochemical type. This paper presents a P system with active membranes and strong priority to solve the discrete logarithm problem used in Diffie-Hellman key exchange protocol. To the best of our knowledge, it’s the first time to solve the problem using P systems.

Cite This Paper

Xiaojing Ma,Zhitang Li,Hao Tu,"Using P systems to Solve the Discrete Logarithm Problem used in Diffie-Hellman Key Exchange Protocol", IJCNIS, vol.1, no.1, pp.24-31, 2009.


[1]G. Paun, “Computing with Membranes,” Journal of Computer and System Sciences, vol. 61, 2000, pp. 108-143.

[2]“Home - The P Systems Webpage”;

[3]W. Diffie and M.E. Hellman, “Multiuser cryptographic techniques,” IEEE Transactions on Information Theory, 1976.

[4]P.W. Shor, “Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer” SIAM J.Sci.Statist.Comput. 26 (1997) 1484

[5]G. Ciobanu, G.P. aun, and M.J. Pérez-Jiménez, eds., Applications of Membrane Computing, Springer-Verlag,2005.

[6]A. Obtulowicz, “On P systems with Active Membranes Solving Integer Factorizing Problem in a Polynomial Time,” C. Calude et al., ed., Springer-Verlag, 2001, p. 267―286.

[7]G. Paun, “P systems with active membranes: attacking NPcomplete problems,” Journal of Automata, Languages and Combinatorics, vol. 6, 2001, pp. 75-90.

[8]G. Paun, Membrane Computing: An Introduction, Springer, 2002.

[9]Whit Diffie and Martin Hellman. New Directions in Cryptography. IEEE Transactions on Information Theory, IT-2 (6):644-654, November 1976.

[10]A. Evans, Jr., W. Kantrowitz, and E. Weiss, A improved algorithm for computing algorithm in GF(p) and its cryptographic significance. IEEE Transactions on Information Theory, vol. 24, 2003, pp. 106-110.