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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Main Authors: Nek Abd Rahman, Normahirah, Kamel Ariffin, Muhammad Rezal
Format: Conference or Workshop Item
Language:English
Published: Institute for Mathematical Research, Universiti Putra Malaysia 2016
Online Access:http://psasir.upm.edu.my/id/eprint/66511/1/Cryptology2016-4.pdf
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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
collection UPM
description 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.
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spelling 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).
spellingShingle Nek Abd Rahman, Normahirah
Kamel Ariffin, Muhammad Rezal
New vulnerabilities of RSA modulus type N = p²q
title 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_short New vulnerabilities of RSA modulus type N = p²q
title_sort new vulnerabilities of rsa modulus type n p²q
url http://psasir.upm.edu.my/id/eprint/66511/1/Cryptology2016-4.pdf
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