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New weak findings upon RSA modulo of type N = p2 q


Kamel Ariffin, Muhammad Rezal and Nek Abd Rahman, Normahirah (2016) New weak findings upon RSA modulo of type N = p2 q. Global Journal of Pure and Applied Mathematics, 12 (4). pp. 3159-3185. ISSN 0973-1768; ESSN: 0973-9750


This paper proposes new attacks on RSA with the modulus N = p2 q. The first attack is based on the equation eX −NY = p2 u+q2 v +Z such that u is an integer multiple of 2 and v is an integer multiple of 3. If |p2 u − q2 v| < N1/2, |Z| ■(|p^2 - q^2 | @3(p^2 + q^2)) < N1/3 and X < ▁((■(N@3(p^2 u + q^2 v))) ̅ ) then N can be factored in polynomial time using continued fractions. For the second and third attacks, this paper proposes new vulnerabilities in k RSA Moduli Ni = p_i^2 qi for k ≥ 2 and i = 1,...,k. The attacks work when k RSA public keys (Ni, ei) are related through eix − Niyi = p_i^2 u + q_i^2 v + zi or eixi − Niy = p_i^2 u + q_i^2 v + zi where the parameters x, xi, y, yi and zi are suitably small.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
Publisher: Research India Publications
Keywords: RSA; Factorization; Continued fraction; LLL algorithm; Simultaneous diophantine approximations
Depositing User: Ms. Ainur Aqidah Hamzah
Date Deposited: 18 Mar 2022 07:18
Last Modified: 18 Mar 2022 07:18
URI: http://psasir.upm.edu.my/id/eprint/53380
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