Citation
Abubakar, Saidu Isah and Kamel Ariffin, Muhammad Rezal and Asbullah, Muhammad Asyraf
(2019)
Successful cryptanalytic attacks upon RSA moduli N = pq.
Malaysian Journal of Mathematical Sciences, 13 (spec. Aug.).
pp. 141-189.
ISSN 1823-8343; ESSN: 2289-750X
Abstract
This paper reports four new cryptanalytic attacks which show that t instances of RSA moduli Ns = psqs for s = 1, . . . , t where t ≥ 2 can be simultaneously factored in polynomial time using simultaneous Diophantine approximations and lattice basis reduction techniques. 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 using N – [(a i+1/i + b i+1/i / 2(ab) i+1/2i + a 1/j + b 1/j / 2(ab) 1/2j) √N] + 1 as a good approximations of φ(Ns) for unknown positive integers d, ds, ks, k, and zs . In our attacks, we found an improved short decryption exponent bound of some reported attacks.
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Official URL or Download Paper: http://einspem.upm.edu.my/journal/fullpaper/vol13s...
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science Institute for Mathematical Research Centre of Foundation Studies for Agricultural Science |
| Publisher: | Institute for Mathematical Research, Universiti Putra Malaysia |
| Notes: | Special Issue: The 6th International Cryptology and Information Security Conference (CRYPTOLOGY2018) |
| Keywords: | RSA moduli; Simultaneous; Diophantine; Approximations; Lattice; Basis; Reduction; LLL algorithm |
| Depositing User: | Nabilah Mustapa |
| Date Deposited: | 04 Feb 2020 04:09 |
| Last Modified: | 04 Feb 2020 04:09 |
| URI: | http://psasir.upm.edu.my/id/eprint/76378 |
| Statistic Details: | View Download Statistic |
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