New vulnerabilities of RSA modulus type N = p²q
This paper proposes new attacks on RSA modulus of type N = p²q. Given k RSA moduli Nі = p²iqi for k ≥ 2 and i = 1, ..., k, the attack works when k RSA 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...
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Institute for Mathematical Research, Universiti Putra Malaysia
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/66511/1/Cryptology2016-4.pdf http://psasir.upm.edu.my/id/eprint/66511/ |
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my.upm.eprints.665112019-03-03T23:55:21Z http://psasir.upm.edu.my/id/eprint/66511/ New vulnerabilities of RSA modulus type N = p²q Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal This paper proposes new attacks on RSA modulus of type N = p²q. Given k RSA moduli Nі = p²iqi for k ≥ 2 and i = 1, ..., k, the attack works when k RSA 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 RSA moduli Ni simultaneously. Institute for Mathematical Research, Universiti Putra Malaysia 2016 Conference or Workshop Item PeerReviewed text en http://psasir.upm.edu.my/id/eprint/66511/1/Cryptology2016-4.pdf Nek Abd Rahman, Normahirah and Kamel Ariffin, Muhammad Rezal (2016) New vulnerabilities of RSA modulus type N = p²q. In: 5th International Cryptology and Information Security Conference 2016 (CRYPTOLOGY2016), 31 May-2 June 2016, Kota Kinabalu, Sabah, Malaysia. (pp. 72-82). |
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This paper proposes new attacks on RSA modulus of type N = p²q. Given k RSA moduli Nі = p²iqi for k ≥ 2 and i = 1, ..., k, the attack works when k RSA 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 RSA moduli Ni simultaneously. |
| format |
Conference or Workshop Item |
| author |
Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal |
| spellingShingle |
Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal New vulnerabilities of RSA modulus type N = p²q |
| author_facet |
Nek Abd Rahman, Normahirah Kamel Ariffin, Muhammad Rezal |
| author_sort |
Nek Abd Rahman, Normahirah |
| title |
New vulnerabilities of RSA modulus type N = p²q |
| title_short |
New vulnerabilities of RSA modulus type N = p²q |
| title_full |
New vulnerabilities of RSA modulus type N = p²q |
| title_fullStr |
New vulnerabilities of RSA modulus type N = p²q |
| title_full_unstemmed |
New vulnerabilities of RSA modulus type N = p²q |
| title_sort |
new vulnerabilities of rsa modulus type n = p²q |
| publisher |
Institute for Mathematical Research, Universiti Putra Malaysia |
| publishDate |
2016 |
| url |
http://psasir.upm.edu.my/id/eprint/66511/1/Cryptology2016-4.pdf http://psasir.upm.edu.my/id/eprint/66511/ |
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