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New vulnerability on system of Ni = p²iqi using good approximation of Φ(N)


Citation

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).

Abstract

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.


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Additional Metadata

Item Type: Conference or Workshop Item (Paper)
Divisions: Faculty of Science
Institute for Mathematical Research
Publisher: Institute for Mathematical Research, Universiti Putra Malaysia
Keywords: Factorization; LLL algorithm; Simultaneous diophantine approximations
Depositing User: Nabilah Mustapa
Date Deposited: 04 Mar 2019 00:04
Last Modified: 04 Mar 2019 00:04
URI: http://psasir.upm.edu.my/id/eprint/66552
Statistic Details: View Download Statistic

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