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The Scientific World Journal
Volume 2014, Article ID 650537, 9 pages
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.


RSA system is based on the hardness of the integer factorization problem (IFP). Given an RSA modulus , it is difficult to determine the prime factors and efficiently. One of the most famous short exponent attacks on RSA is the Wiener attack. In 1997, Verheul and van Tilborg use an exhaustive search to extend the boundary of the Wiener attack. Their result shows that the cost of exhaustive search is bits when extending the Weiner's boundary r bits. In this paper, we first reduce the cost of exhaustive search from bits to bits. Then, we propose a method named EPF. With EPF, the cost of exhaustive search is further reduced to bits when we extend Weiner's boundary bits. It means that our result is 214 times faster than Verheul and van Tilborg's result. Besides, the security boundary is extended 7 bits.