On the Improvement of Wiener Attack on RSA with Small Private Exponent
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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/650537 |
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| author | Mu-En Wu Chien-Ming Chen Yue-Hsun Lin Hung-Min Sun |
| author_facet | Mu-En Wu Chien-Ming Chen Yue-Hsun Lin Hung-Min Sun |
| author_sort | Mu-En Wu |
| collection | DOAJ |
| description | 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 214 times faster than Verheul and van Tilborg's result. Besides, the security boundary is extended 7 bits. |
| format | Article |
| id | doaj-art-7fbb57f97f3f4ed1875234875e9acb21 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-7fbb57f97f3f4ed1875234875e9acb212025-08-20T03:35:20ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/650537650537On the Improvement of Wiener Attack on RSA with Small Private ExponentMu-En Wu0Chien-Ming Chen1Yue-Hsun Lin2Hung-Min Sun3Department of Mathematics, Soochow University, Taipei, TaiwanSchool of Computer Science and Technology, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, ChinaCyLab, Carnegie Mellon University, Pittsburgh, PA 15213, USADepartment of Computer Science, National Tsing Hua University, Hsinchu, TaiwanRSA 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 214 times faster than Verheul and van Tilborg's result. Besides, the security boundary is extended 7 bits.http://dx.doi.org/10.1155/2014/650537 |
| spellingShingle | Mu-En Wu Chien-Ming Chen Yue-Hsun Lin Hung-Min Sun On the Improvement of Wiener Attack on RSA with Small Private Exponent The Scientific World Journal |
| title | On the Improvement of Wiener Attack on RSA with Small Private Exponent |
| title_full | On the Improvement of Wiener Attack on RSA with Small Private Exponent |
| title_fullStr | On the Improvement of Wiener Attack on RSA with Small Private Exponent |
| title_full_unstemmed | On the Improvement of Wiener Attack on RSA with Small Private Exponent |
| title_short | On the Improvement of Wiener Attack on RSA with Small Private Exponent |
| title_sort | on the improvement of wiener attack on rsa with small private exponent |
| url | http://dx.doi.org/10.1155/2014/650537 |
| work_keys_str_mv | AT muenwu ontheimprovementofwienerattackonrsawithsmallprivateexponent AT chienmingchen ontheimprovementofwienerattackonrsawithsmallprivateexponent AT yuehsunlin ontheimprovementofwienerattackonrsawithsmallprivateexponent AT hungminsun ontheimprovementofwienerattackonrsawithsmallprivateexponent |