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 −...
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Institute for Mathematical Research, Universiti Putra Malaysia
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/66552/1/Cryptology2018-7.pdf http://psasir.upm.edu.my/id/eprint/66552/ |
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my.upm.eprints.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). |
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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. |
| format |
Conference or Workshop Item |
| author |
Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal Asbullah, Muhammad Asyraf Yunos, Faridah |
| 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) |
| author_facet |
Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal Asbullah, Muhammad Asyraf Yunos, Faridah |
| author_sort |
Nek Abd Rahman, Normahirah |
| title |
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_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_sort |
new vulnerability on system of ni = p²iqi using good approximation of φ(n) |
| publisher |
Institute for Mathematical Research, Universiti Putra Malaysia |
| publishDate |
2018 |
| url |
http://psasir.upm.edu.my/id/eprint/66552/1/Cryptology2018-7.pdf http://psasir.upm.edu.my/id/eprint/66552/ |
| _version_ |
1643838640631054336 |
| score |
13.211869 |