Journal of Biomedicine and Biotechnology
Volume 2008 (2008), Article ID 518093, 10 pages
doi:10.1155/2008/518093
Research Article

Fast Parallel Molecular Algorithms for DNA-Based Computation: Solving the Elliptic Curve Discrete Logarithm Problem over GF(2n)

1Embedded System and Networking Laboratory, College of Computer and Communication, Hunan University, Changsha 410082, China
2Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Received 16 July 2007; Accepted 25 January 2008

Academic Editor: Daniel Howard

Copyright © 2008 Kenli Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. M. Adleman, “Molecular computation of solutions to combinatorial problems,” Science, vol. 266, no. 5187, pp. 1021–1024, 1994. View at Publisher · View at Google Scholar
  2. E. Csuhaj-Varjú, L. Kari, and G. Paun, “Test tube distributed systems based on splicing,” Computers and Artificial Intelligence, vol. 15, no. 2-3, pp. 211–232, 1996.
  3. N. Koblitz, “Elliptic curve cryptosystems,” Mathematics of Computation, vol. 48, no. 177, pp. 203–209, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  4. N. Koblizt, Introduction to Elliptic Curves and Modular Forms, Springer, New York, NY, USA, 1984.
  5. S. Lang, Elliptic Curves: Diophantine Analysis, Springer, New York, NY, USA, 1978.
  6. V. S. Miller, “Use of elliptic curves in cryptography,” in Proceedings of the 5th Annual International Cryptology Conference (CRYPTO '85), Santa Barbara, Calif, USA, August 1985.
  7. A. M. Odlyzko, “Discrete logarithms in finite fields and their cryptographic significance,” in Proceedings of the 2nd Workshop on Advances in Cryptology: Theory and Application of Cryptographic Techniques (EUROCRYPT '84), pp. 224–314, Springer, Paris, France, April 1985.
  8. R. P. Feynman, “There's plenty of room at the bottom,” in Minaturization, D. H. Gilbert, Ed., pp. 282–296, Reinhold, New York, NY, USA, 1961.
  9. R. J. Lipton, “DNA solution of hard computational problems,” Science, vol. 268, no. 5210, pp. 542–545, 1995. View at Publisher · View at Google Scholar
  10. R. R. Sinden, DNA Structure and Function, Academic Press, New York, NY, USA, 1994.
  11. G. Paun, G. Rozenberg, and A. Salomaa, DNA Computing: New Computing Paradigms, Springer, New York, NY, USA, 1998.
  12. W.-L. Chang, M. S.-H. Ho, and M. Guo, “Molecular solutions for the subset-sum problem on DNA-based supercomputing,” Biosystems, vol. 73, no. 2, pp. 117–130, 2004. View at Publisher · View at Google Scholar · View at PubMed
  13. M. Guo, M. S.-H. Ho, and W.-L. Chang, “Fast parallel molecular solution to the dominating-set problem on massively parallel bio-computing,” Parallel Computing, vol. 30, no. 9-10, pp. 1109–1125, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. S.-H. Ho, “Fast parallel molecular solutions for DNA-based supercomputing: the subset-product problem,” Biosystems, vol. 80, no. 3, pp. 233–250, 2005. View at Publisher · View at Google Scholar
  15. D. Boneh, C. Dunworth, and R. J. Lipton, “Breaking DES using a molecular computer,” Princeton University, Princeton, NJ, USA, 1995.
  16. W.-L. Chang, M. Guo, and M. S.-H. Ho, “Fast parallel molecular algorithms for DNA-based computation: factoring integers,” IEEE Transactions on Nanobioscience, vol. 4, no. 2, pp. 149–163, 2005. View at Publisher · View at Google Scholar
  17. J. Watson, M. Gilman, J. Witkowski, and M. Zoller, Recombinant DNA, Freeman, San Francisco, Calif, USA, 2nd edition, 1992.
  18. F. Eckstein, Oligonucleotides and Anologues, Oxford University Press, Oxford, UK, 1991.
  19. J. Watson, N. Hoplins, J. Roberts, J. Steitz, and A. Weiner, Molecular Biology of the Gene, Benjamin/Cummings, Menlo Park, Calif, USA, 1987.
  20. G. M. Blackburn and M. J. Gait, Nucleic Acids in Chemistry and Biology, IRL Press, Washington, DC, USA, 1990.
  21. M. Wiener and R. Zuccherato, “Faster attacks on elliptic curve cryptosystems,” in Selected Areas in Cryptography, vol. 1556 of Lecture Notes in Computer Science, pp. 190–200, Springer, New York, NY, USA, 1999. View at Publisher · View at Google Scholar