New vulnerability on system of Ni = p²iqi using good approximation of Φ(N)
This paper proposes new vulnerability in m moduli of the form Ni = p2iqi for m ≥ 2 and i = 1, ...,m. The attack works when m public keys (Ni, ei) there exist m relations of the form eid − kΦ (Ni) = 1 or eidi − kiΦ (Ni) = 1 with the parameters d, di, k and ki are suitably small. By using the term N −...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
Institute for Mathematical Research, Universiti Putra Malaysia
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/66552/ http://psasir.upm.edu.my/id/eprint/66552/1/Cryptology2018-7.pdf |
| _version_ | 1848855601718755328 |
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| author | Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal Asbullah, Muhammad Asyraf Yunos, Faridah |
| author_facet | Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal Asbullah, Muhammad Asyraf Yunos, Faridah |
| author_sort | Nek Abd Rahman, Normahirah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper proposes new vulnerability in m moduli of the form Ni = p2iqi for m ≥ 2 and i = 1, ...,m. The attack works when m public keys (Ni, ei) there exist m relations of the form eid − kΦ (Ni) = 1 or eidi − kiΦ (Ni) = 1 with the parameters d, di, k and ki are suitably small. By using the term N − 2N2/3 − N1/3 as a good approximation of Φ(N) applying the LLL algorithm enables one to factor m moduli of the form Ni = p2iqi simultaneously. |
| first_indexed | 2025-11-15T11:28:22Z |
| format | Conference or Workshop Item |
| id | upm-66552 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:28:22Z |
| publishDate | 2018 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-665522019-03-04T00:04:52Z http://psasir.upm.edu.my/id/eprint/66552/ New vulnerability on system of Ni = p²iqi using good approximation of Φ(N) Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal Asbullah, Muhammad Asyraf Yunos, Faridah This paper proposes new vulnerability in m moduli of the form Ni = p2iqi for m ≥ 2 and i = 1, ...,m. The attack works when m public keys (Ni, ei) there exist m relations of the form eid − kΦ (Ni) = 1 or eidi − kiΦ (Ni) = 1 with the parameters d, di, k and ki are suitably small. By using the term N − 2N2/3 − N1/3 as a good approximation of Φ(N) applying the LLL algorithm enables one to factor m moduli of the form Ni = p2iqi simultaneously. Institute for Mathematical Research, Universiti Putra Malaysia 2018 Conference or Workshop Item PeerReviewed text en http://psasir.upm.edu.my/id/eprint/66552/1/Cryptology2018-7.pdf Nek Abd Rahman, Normahirah and Kamel Ariffin, Muhammad Rezal and Asbullah, Muhammad Asyraf and Yunos, Faridah (2018) New vulnerability on system of Ni = p²iqi using good approximation of Φ(N). In: 6th International Cryptology and Information Security Conference 2018 (CRYPTOLOGY2018), 9-11 July 2018, Port Dickson, Negeri Sembilan, Malaysia. (pp. 139-150). |
| spellingShingle | Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal Asbullah, Muhammad Asyraf Yunos, Faridah New vulnerability on system of Ni = p²iqi using good approximation of Φ(N) |
| title | New vulnerability on system of Ni = p²iqi using good approximation of Φ(N) |
| title_full | New vulnerability on system of Ni = p²iqi using good approximation of Φ(N) |
| title_fullStr | New vulnerability on system of Ni = p²iqi using good approximation of Φ(N) |
| title_full_unstemmed | New vulnerability on system of Ni = p²iqi using good approximation of Φ(N) |
| title_short | New vulnerability on system of Ni = p²iqi using good approximation of Φ(N) |
| title_sort | new vulnerability on system of ni = p²iqi using good approximation of φ(n) |
| url | http://psasir.upm.edu.my/id/eprint/66552/ http://psasir.upm.edu.my/id/eprint/66552/1/Cryptology2018-7.pdf |