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Mathematical Problems in Engineering
Volume 2014, Article ID 630421, 11 pages
http://dx.doi.org/10.1155/2014/630421
Research Article

A Digital Signature Scheme Based on MST3 Cryptosystems

Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 5 December 2013; Revised 13 March 2014; Accepted 14 March 2014; Published 20 May 2014

Academic Editor: Wang Xing-yuan

Copyright © 2014 Haibo Hong 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. C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossingin,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, pp. 175–179, Bangalore, India, 1984.
  2. C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Physical Review Letters, vol. 68, no. 21, pp. 3121–3124, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell's theorem,” Physical Review Letters, vol. 68, no. 5, pp. 557–559, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Reviews of Modern Physics, vol. 74, no. 1, pp. 146–195, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. R. Matthews, “On the derivation of a “chaotic” encryption algorithm,” Cryptologia, vol. 13, no. 1, pp. 29–42, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. S. Baptista, “Cryptography with chaos,” Physics Letters A, vol. 240, no. 1-2, pp. 50–54, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. G. Alvarez, G. Pastor, F. Montoya, and M. Romera, “Chaotic cryptosystems,” in Proceedings of the IEEE International Carnahan Conference on Security Technology, pp. 332–338, 1999.
  8. X.-Y. Wang and Q. Yu, “Block encryption algorithm based on dynamic sequences of multiple chaotic systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 574–581, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. X. Wang and J. Zhao, “An improved key agreement protocol based on chaos,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 4052–4057, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Y. Niu and X. Wang, “An anonymous key agreement protocol based on chaotic maps,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 1986–1992, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. L. Hongjun, W. Xingyuan, and K. Abdurahman, “Image encryption using DNA complementary rule and chaotic maps,” Applied Soft Computing, vol. 12, no. 5, pp. 1457–1466, 2012. View at Publisher · View at Google Scholar
  12. X. Wang and D. Luan, “A novel image encryption algorithm using chaos and reversible cellular automata,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 11, pp. 3075–3085, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  13. W. Xingyuan and L. Dapeng, “A secure key agreement protocol based on chaotic maps,” Chinese Physics B, vol. 22, no. 11, Article ID 110503, 2013. View at Google Scholar
  14. Y.-Q. Zhang and X.-Y. Wang, “Spatiotemporal chaos in mixed linear—nonlinear coupled logistic map lattice,” Physica A: Statistical Mechanics and Its Applications, vol. 402, pp. 104–118, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  15. 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 · View at Scopus
  16. D. Boneh, C. Dunworth, R. J. Lipton, and J. Sgall, “On the computational power of DNA,” Discrete Applied Mathematics, vol. 71, no. 1–3, pp. 79–94, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. G. Cui, L. Qin, Y. Wang, and X. Zhang, “An encryption scheme using DNA technology,” in Proceedings of the 3rd International Conference on Bio-Inspired Computing: Theories and Applications (BICTA '08), pp. 37–41, October 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. W. Lempken, T. van Trung, S. S. Magliveras, and W. Wei, “A public key cryptosystem based on non-abelian finite groups,” Journal of Cryptology, vol. 22, no. 1, pp. 62–74, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. N. R. Wagner and M. R. Magyarik, “A public-key cryptosystem based on the word problem,” in Advances in Cryptology, vol. 196 of Lecture Notes in Computer Science, pp. 19–36, Springer, Berlin, Germany, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. K. H. Ko, S. J. Lee, J. H. Cheon, J. W. Han, J. Kang, and C. Park, “New public-key cryptosystem using braid groups,” in Advances in cryptology—CRYPTO 2000, vol. 1880 of Lecture Notes in Computer Science, pp. 166–183, Springer, Berlin, Germany, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. B. Eick and D. Kahrobaei, “Polycyclic groups: a new platform for cryptology?” http://arxiv.org/abs/math/0411077.
  22. V. Shpilrain and A. Ushakov, “Thompsons group and public key cryptography,” in Applied Cryptography and Network Security, vol. 3531 of Lecture Notes in Computer Science, pp. 151–164, 2005. View at Publisher · View at Google Scholar
  23. D. Kahrobaei, C. Koupparis, and V. Shpilrain, “Public key exchange using matrices over group rings,” Groups, Complexity, and Cryptology, vol. 5, no. 1, pp. 97–115, 2013. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. S. S. Magliveras, “A cryptosystem from logarithmic signatures of finite groups,” in Proceedings of the 29th Midwest Symposium on Circuits and Systems, pp. 972–975, Elsevier Publishing, Amsterdam, The Netherlands, 1986.
  25. S. S. Magliveras and N. D. Memon, “Algebraic properties of cryptosystem PGM,” Journal of Cryptology, vol. 5, no. 3, pp. 167–183, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. A. Caranti and F. Dalla Volta, “The round functions of cryptosystem PGM generate the symmetric group,” Designs, Codes and Cryptography, vol. 38, no. 1, pp. 147–155, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. S. S. Magliveras, D. R. Stinson, and T. van Trung, “New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups,” Journal of Cryptology, vol. 15, no. 4, pp. 285–297, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. M. I. González Vasco and R. Steinwandt, “Obstacles in two public key cryptosystems based on group factorizations,” Tatra Mountains Mathematical Publications, vol. 25, pp. 23–37, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. J.-M. Bohli, R. Steinwandt, M. I. González Vasco, and C. Martínez, “Weak keys in MST1,” Designs, Codes and Cryptography, vol. 37, no. 3, pp. 509–524, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  30. M. I. González Vasco, C. Martínez, and R. Steinwandt, “Towards a uniform description of several group based cryptographic primitives,” Designs, Codes and Cryptography, vol. 33, no. 3, pp. 215–226, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. S. S. Magliveras, P. Svaba, T. van Trung, and P. Zajac, “On the security of a realization of cryptosystem MST3,” Tatra Mountains Mathematical Publications, vol. 41, pp. 65–78, 2008. View at Google Scholar · View at MathSciNet
  32. S. R. Blackburn, C. Cid, and C. Mullan, “Cryptanalysis of the MST3 public key cryptosystem,” Journal of Mathematical Cryptology, vol. 3, no. 4, pp. 321–338, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  33. M. I. G. Vasco, A. L. P. del Pozo, and P. T. Duarte, “A note on the security of MST3,” Designs, Codes and Cryptography, vol. 55, no. 2-3, pp. 189–200, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  34. P. Svaba and T. van Trung, “Public key cryptosystem MST3 cryptanalysis and realization,” Journal of Mathematical Cryptology, vol. 4, no. 3, pp. 271–315, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  35. W. Lempken and T. van Trung, “On minimal logarithmic signatures of finite groups,” Experimental Mathematics, vol. 14, no. 3, pp. 257–269, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. P. Marquardt, P. Svaba, and T. van Trung, “Pseudorandom number generators based on random covers for finite groups,” Designs, Codes and Cryptography, vol. 64, no. 1-2, pp. 209–220, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet