New vulnerability of RSA modulus type N = p2q
This paper proposes new attacks on modulus of type N = p2q. Given k moduli of the form Ni = p2iqi for k ≥ 2 and i = 1, …, k, the attack works when k public keys (Ni, ei) are such that there exist k relations of the shape eix – Niyi = zi – (ap2i + bq2i)yi or of the shape eixi – Niy = zi – (ap2i + bq2...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/58178/ http://psasir.upm.edu.my/id/eprint/58178/1/75-88.pdf |
| _version_ | 1848853574129287168 |
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| author | Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal |
| author_facet | Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal |
| author_sort | Nek Abd Rahman, Normahirah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper proposes new attacks on modulus of type N = p2q. Given k moduli of the form Ni = p2iqi for k ≥ 2 and i = 1, …, k, the attack works when k public keys (Ni, ei) are such that there exist k relations of the shape eix – Niyi = zi – (ap2i + bq2i)yi or of the shape eixi – Niy = zi – (ap2i + bq2i)y where the parameters x, xi, y, yi and zi are suitably small in terms of the prime factors of the moduli. The proposed attacks utilizing the LLL algorithm enables one to factor the k moduli Ni simultaneously. |
| first_indexed | 2025-11-15T10:56:08Z |
| format | Article |
| id | upm-58178 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:56:08Z |
| publishDate | 2017 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-581782018-01-04T03:07:30Z http://psasir.upm.edu.my/id/eprint/58178/ New vulnerability of RSA modulus type N = p2q Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal This paper proposes new attacks on modulus of type N = p2q. Given k moduli of the form Ni = p2iqi for k ≥ 2 and i = 1, …, k, the attack works when k public keys (Ni, ei) are such that there exist k relations of the shape eix – Niyi = zi – (ap2i + bq2i)yi or of the shape eixi – Niy = zi – (ap2i + bq2i)y where the parameters x, xi, y, yi and zi are suitably small in terms of the prime factors of the moduli. The proposed attacks utilizing the LLL algorithm enables one to factor the k moduli Ni simultaneously. Institute for Mathematical Research, Universiti Putra Malaysia 2017 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/58178/1/75-88.pdf Nek Abd Rahman, Normahirah and Kamel Ariffin, Muhammad Rezal (2017) New vulnerability of RSA modulus type N = p2q. Malaysian Journal of Mathematical Sciences, 11 (spec. Aug.). pp. 75-88. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal/fullpaper/vol11saugust/75-88.pdf |
| spellingShingle | Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal New vulnerability of RSA modulus type N = p2q |
| title | New vulnerability of RSA modulus type N = p2q |
| title_full | New vulnerability of RSA modulus type N = p2q |
| title_fullStr | New vulnerability of RSA modulus type N = p2q |
| title_full_unstemmed | New vulnerability of RSA modulus type N = p2q |
| title_short | New vulnerability of RSA modulus type N = p2q |
| title_sort | new vulnerability of rsa modulus type n = p2q |
| url | http://psasir.upm.edu.my/id/eprint/58178/ http://psasir.upm.edu.my/id/eprint/58178/ http://psasir.upm.edu.my/id/eprint/58178/1/75-88.pdf |