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A new simultaneous diophantine attack upon RSA moduli N = pq


Abubakar, Saidu Isah and Kamel Ariffin, Muhammad Rezal and Asbullah, Muhammad Asyraf (2018) A new simultaneous diophantine attack upon RSA moduli N = pq. In: 6th International Cryptology and Information Security Conference 2018 (CRYPTOLOGY2018), 9-11 July 2018, Port Dickson, Negeri Sembilan, Malaysia. (pp. 119-138).

Abstract / Synopsis

This paper reports four new cryptanalytic attacks which show that the t instances of RSA moduli N = pq can be simultaneously factored in polynomial time using simultaneous diophantine approximations and lattice basis reduction techniques. In our technique we utilize the relation given by N−[(a j/i+b j/I / (2ab) j/2i + a 1/j+b 1/j / (2ab) 1/2j) √N] + 1 as a good approximations of Φ (N) for unknown positive integers d, di, ki, k, and zi. We construct four system of equations of the form esd − ksΦ(Ns) = 1, esds − kΦ (Ns) = 1, esd − kΦ (Ns) = zs and esds − kΦ (Ns) = zs where s = 1, 2, ..., t. In our attacks, we improve the short decryption exponent bounds of some reported attacks.

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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: RSA moduli; Simultaneous; Diophantine; Approximations; Lattice; Basis; Reduction; LLL algorithm
Depositing User: Nabilah Mustapa
Date Deposited: 04 Mar 2019 08:04
Last Modified: 04 Mar 2019 08:04
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