New weak findings upon RSA modulo of type N = p2 q
This paper proposes new attacks on RSA with the modulus N = p2 q. The first attack is based on the equation eX −NY = p2 u+q2 v +Z such that u is an integer multiple of 2 and v is an integer multiple of 3. If |p2 u − q2 v| < N1/2, |Z| ■(|p^2 - q^2 | @3(p^2 + q^2)) < N1/3 and X < ▁((...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Research India Publications
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/53380/1/New%20weak%20findings%20upon%20RSA%20.pdf |
| _version_ | 1796975876676517888 |
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| author | Kamel Ariffin, Muhammad Rezal Nek Abd Rahman, Normahirah |
| author_facet | Kamel Ariffin, Muhammad Rezal Nek Abd Rahman, Normahirah |
| author_sort | Kamel Ariffin, Muhammad Rezal |
| collection | UPM |
| description | This paper proposes new attacks on RSA with the modulus N = p2 q. The first attack is based on the equation eX −NY = p2 u+q2 v +Z such that u is an integer multiple of 2 and v is an integer multiple of 3. If
|p2 u − q2 v| < N1/2,
|Z| ■(|p^2 - q^2 | @3(p^2 + q^2)) < N1/3
and
X < ▁((■(N@3(p^2 u + q^2 v))) ̅ )
then N can be factored in polynomial time using continued fractions. For the second and third attacks, this paper proposes new vulnerabilities in k RSA Moduli Ni = p_i^2 qi for k ≥ 2 and i = 1,...,k. The attacks work when k RSA public keys (Ni, ei) are related through
eix − Niyi = p_i^2 u + q_i^2 v + zi
or
eixi − Niy = p_i^2 u + q_i^2 v + zi
where the parameters x, xi, y, yi and zi are suitably small. |
| first_indexed | 2024-03-06T09:17:42Z |
| format | Article |
| id | upm.eprints-53380 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:17:42Z |
| publishDate | 2016 |
| publisher | Research India Publications |
| record_format | dspace |
| spelling | upm.eprints-533802022-03-18T07:18:31Z http://psasir.upm.edu.my/id/eprint/53380/ New weak findings upon RSA modulo of type N = p2 q Kamel Ariffin, Muhammad Rezal Nek Abd Rahman, Normahirah This paper proposes new attacks on RSA with the modulus N = p2 q. The first attack is based on the equation eX −NY = p2 u+q2 v +Z such that u is an integer multiple of 2 and v is an integer multiple of 3. If |p2 u − q2 v| < N1/2, |Z| ■(|p^2 - q^2 | @3(p^2 + q^2)) < N1/3 and X < ▁((■(N@3(p^2 u + q^2 v))) ̅ ) then N can be factored in polynomial time using continued fractions. For the second and third attacks, this paper proposes new vulnerabilities in k RSA Moduli Ni = p_i^2 qi for k ≥ 2 and i = 1,...,k. The attacks work when k RSA public keys (Ni, ei) are related through eix − Niyi = p_i^2 u + q_i^2 v + zi or eixi − Niy = p_i^2 u + q_i^2 v + zi where the parameters x, xi, y, yi and zi are suitably small. Research India Publications 2016 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/53380/1/New%20weak%20findings%20upon%20RSA%20.pdf Kamel Ariffin, Muhammad Rezal and Nek Abd Rahman, Normahirah (2016) New weak findings upon RSA modulo of type N = p2 q. Global Journal of Pure and Applied Mathematics, 12 (4). pp. 3159-3185. ISSN 0973-1768; ESSN: 0973-9750 http://www.ripublication.com/Volume/gjpamv12n4.htm |
| spellingShingle | Kamel Ariffin, Muhammad Rezal Nek Abd Rahman, Normahirah New weak findings upon RSA modulo of type N = p2 q |
| title | New weak findings upon RSA modulo of type N = p2 q |
| title_full | New weak findings upon RSA modulo of type N = p2 q |
| title_fullStr | New weak findings upon RSA modulo of type N = p2 q |
| title_full_unstemmed | New weak findings upon RSA modulo of type N = p2 q |
| title_short | New weak findings upon RSA modulo of type N = p2 q |
| title_sort | new weak findings upon rsa modulo of type n p2 q |
| url | http://psasir.upm.edu.my/id/eprint/53380/1/New%20weak%20findings%20upon%20RSA%20.pdf |
| work_keys_str_mv | AT kamelariffinmuhammadrezal newweakfindingsuponrsamodulooftypenp2q AT nekabdrahmannormahirah newweakfindingsuponrsamodulooftypenp2q |