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The Scientific World Journal
Volume 2014, Article ID 650537, 9 pages
http://dx.doi.org/10.1155/2014/650537
Research Article

On the Improvement of Wiener Attack on RSA with Small Private Exponent

1Department of Mathematics, Soochow University, Taipei, Taiwan
2School of Computer Science and Technology, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China
3Shenzhen Key Laboratory of Internet Information Collaboration, Shenzhen, China
4CyLab, Carnegie Mellon University, Pittsburgh, PA 15213, USA
5Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan

Received 7 February 2014; Accepted 27 February 2014; Published 27 March 2014

Academic Editors: T. Cao and F. Yu

Copyright © 2014 Mu-En Wu 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. R. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Communications of the ACM, vol. 21, no. 2, pp. 120–126, 1978. View at Publisher · View at Google Scholar · View at Scopus
  2. C. Patsakis, “Number theoretic SETUPs for RSA like factoring based algorithms,” Journal of Information Hiding and Multimedia Signal Processing, vol. 3, no. 2, pp. 191–204, 2012. View at Google Scholar
  3. Q. Kong, P. Li, and Y. Ma, “On the feasibility and security of image secret sharing scheme to identify cheaters,” Journal of Information Hiding and Multimedia Signal Processing, vol. 4, no. 4, pp. 2073–4212, 2013. View at Google Scholar
  4. N. Peng, G. Luo, K. Qin, and A. Chen, “Query-biased preview over outsourced and encrypted data,” The Scientific World Journal, vol. 2013, Article ID 860621, 13 pages, 2013. View at Publisher · View at Google Scholar
  5. H. Lenstra Jr., “Factoring integers with elliptic curves,” Annals of Mathematics, vol. 126, no. 3, pp. 649–673, 1987. View at Publisher · View at Google Scholar
  6. J. Pollard, “Theorems on factorization and primality testing,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 76, no. 3, pp. 521–528, 1974. View at Publisher · View at Google Scholar
  7. D. Boneh and H. Shacham, “Fast variants of RSA,” CryptoBytes, vol. 5, no. 1, pp. 1–9, 2002. View at Google Scholar
  8. S. Galbraith, C. Heneghan, and J. McKee, “Tunable balancing of RSA,” in Information Security and Privacy, vol. 3574 of Lecture Notes in Computer Science, pp. 280–292, Springer, Berlin, Germany, 2005. View at Publisher · View at Google Scholar
  9. M. Hinek, “Another look at small RSA exponents,” in Topics in Cryptology-CT-RSA 2006, vol. 3860 of Lecture Notes in Computer Science, pp. 82–98, Springer, Berlin, Germany, 2006. View at Publisher · View at Google Scholar
  10. H. Sun, W. Yang, and C. Laih, “On the design of RSA with short secret exponent,” in Advances in Cryptology-ASIACRYPT '99, vol. 1716 of Lecture Notes in Computer Science, pp. 150–164, Springer, Berlin, Germany, 1999. View at Publisher · View at Google Scholar
  11. H. Sun and C. Yang, “RSA with balanced short exponents and its application to entity authentication,” in Public Key Cryptography-PKC 2005, vol. 3386 of Lecture Notes in Computer Science, pp. 199–215, Springer, Berlin, Germany, 2005. View at Publisher · View at Google Scholar
  12. S. Vanstone and R. Zuccherato, “Short RSA keys and their generation,” Journal of Cryptology, vol. 8, no. 2, pp. 101–114, 1995. View at Publisher · View at Google Scholar · View at Scopus
  13. D. Boneh, R. Rivest, A. Shamir et al., “Twenty years of attacks on the RSA cryptosystem,” Notices of the American Mathematical Society, vol. 46, no. 2, pp. 203–213, 1999. View at Google Scholar
  14. A. Dujella, “Continued fractions and RSA with small secret exponent,” Tatra Mountains Mathematical Publications, vol. 29, pp. 101–112, 2004. View at Google Scholar
  15. E. Jochemsz and B. de Weger, “A partial key exposure attack on RSA using a 2-dimensional lattice,” in Information Security, vol. 4176 of Lecture Notes in Computer Science, pp. 203–216, Springer, Berlin, Germany, 2006. View at Publisher · View at Google Scholar
  16. M. J. Wiener, “Cryptanalysis of short RSA secret exponents,” IEEE Transactions on Information Theory, vol. 36, no. 3, pp. 553–558, 1990. View at Publisher · View at Google Scholar · View at Scopus
  17. B. de Weger, “Cryptanalysis of RSA with small prime difference,” Applicable Algebra in Engineering, Communications and Computing, vol. 13, no. 1, pp. 17–28, 2002. View at Publisher · View at Google Scholar · View at Scopus
  18. J. Blömer and A. May, “A generalized Wiener attack on RSA,” in Public Key Cryptography-PKC 2004, vol. 2947 of Lecture Notes in Computer Science, pp. 1–13, Springer, Berlin, Germany, 2004. View at Publisher · View at Google Scholar
  19. D. Boneh and G. Durfee, “Cryptanalysis of RSA with private key d less than N0.292,” in Advances in Cryptology-EUROCRYPT '99, vol. 1592 of Lecture Notes in Computer Science, pp. 1–11, Springer, Berlin, Germany, 1999. View at Google Scholar
  20. E. Verheul and H. van Tilborg, “Cryptanalysis of “less short” RSA secret exponents,” Applicable Algebra in Engineering, Communications and Computing, vol. 8, no. 5, pp. 425–435, 1997. View at Publisher · View at Google Scholar · View at Scopus
  21. D. Coppersmith, M. Franklin, J. Patarin, and M. Reiter, “Low-exponent RSA with related messages,” in Advances in Cryptology-EUROCRYPT '96, vol. 1070 of Lecture Notes in Computer Science, pp. 1–9, Springer, Berlin, Germany, 1996. View at Publisher · View at Google Scholar
  22. D. Boneh and G. Durfee, “Cryptanalysis of RSA with private key d less than d less than N0.292,” IEEE Transactions on Information Theory, vol. 46, no. 4, pp. 1339–1349, 2000. View at Publisher · View at Google Scholar · View at Scopus
  23. H. M. Sun, M. E. Wu, and Y. H. Chen, “Estimating the prime-factors of an rsa modulus and an extension of the wiener attack,” in Applied Cryptography and Network Security, vol. 4521 of Lecture Notes in Computer Science, pp. 116–128, Springer, Berlin, Germany, 2007. View at Publisher · View at Google Scholar
  24. C. M. Chen, Y. H. Lin, Y. H. Chen, and H. M. Sun, “SASHIMI: secure aggregation via successively hierarchical inspecting of message integrity on WSN,” Journal of Information Hiding and Multimedia Signal Processing, vol. 4, no. 1, pp. 57–72, 2013. View at Publisher · View at Google Scholar
  25. C. M. Chen, Y. H. Lin, Y. C. Lin, and H. M. Sun, “RCDA: recoverable concealed data aggregation for data integrity in wireless sensor networks,” IEEE Transactions on Parallel and Distributed Systems, vol. 23, no. 4, pp. 727–734, 2012. View at Publisher · View at Google Scholar · View at Scopus
  26. H.-M. Sun, C.-M. Chen, and Y.-C. Hsiao, “An efficient countermeasure to the selective forwarding attack in wireless sensor networks,” in Proceedings of the IEEE Region 10 Conference (TENCON '07), pp. 1–4, IEEE, Taipei, Taiwan, November 2007. View at Publisher · View at Google Scholar · View at Scopus
  27. K. Wei-Chi, C. Chien-Ming, and L. Hui-Lung, “Cryptanalysis of a variant of Peyravian-Zunic's password authentication scheme,” IEICE Transactions on Communications, vol. 86, no. 5, pp. 1682–1684, 2003. View at Google Scholar · View at Scopus
  28. D. Coppersmith, “Finding a small root of a bivariate integer equation; factoring with high bits known,” in Advances in Cryptology-EUROCRYPT '96, vol. 1070 of Lecture Notes in Computer Science, pp. 178–189, Springer, Berlin, Germany, 1996. View at Publisher · View at Google Scholar
  29. D. Coppersmith, “Finding a small root of a univariate modular equation,” in Advances in Cryptology-EUROCRYPT '96, vol. 1070 of Lecture Notes in Computer Science, pp. 155–165, Springer, Berlin, Germany, 1996. View at Publisher · View at Google Scholar
  30. H. Sun, M. Wu, W. Ting, and M. Hinek, “Dual RSA and its security analysis,” IEEE Transactions on Information Theory, vol. 53, no. 8, pp. 2922–2933, 2007. View at Publisher · View at Google Scholar · View at Scopus
  31. D. Bleichenbacher and A. May, “New attacks on RSA with small secret CRT-exponents,” in Public Key Cryptography-PKC 2006, vol. 3958 of Lecture Notes in Computer Science, pp. 1–13, Springer, Berlin, Germany, 2006. View at Publisher · View at Google Scholar
  32. D. Boneh, G. Durfee, and Y. Frankel, “An attack on RSA given a small fraction of the private key bits,” in Advances in Cryptology-ASIACRYPT '98, vol. 1514 of Lecture Notes in Computer Science, pp. 25–34, Springer, Berlin, Germany, 1998. View at Publisher · View at Google Scholar