title: On the improvement of Wiener attack on RSA with small private exponent.
abstract: RSA system is based on the hardness of the integer factorization problem (IFP). Given an RSA modulus N = pq, it is difficult to determine the prime factors p and q 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 2r + 8 bits when extending the Weiner's boundary r bits. In this paper, we first reduce the cost of exhaustive search from 2r + 8 bits to 2r + 2 bits. Then, we propose a method named EPF. With EPF, the cost of exhaustive search is further reduced to 2r - 6 bits when we extend Weiner's boundary r bits. It means that our result is 2(14) times faster than Verheul and van Tilborg's result. Besides, the security boundary is extended 7 bits.
authors: Department of Mathematics, Soochow University, Taipei, Taiwan.
authors: Mu-En
authors: 0000-0002-4839-3849
authors: ME
authors: Wu
authors: School of Computer Science and Technology, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China ; Shenzhen Key Laboratory of Internet Information Collaboration, Shenzhen, China.
authors: Chien-Ming
authors: CM
authors: Chen
authors: CyLab, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
authors: Yue-Hsun
authors: YH
authors: Lin
authors: Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan.
authors: Hung-Min
authors: 0000-0003-0870-9973
authors: HM
authors: Sun
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical