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New attacks on RSA with modulus N = p2q using continued fractions

Asbullah, Muhammad Asyraf and Kamel Ariffin, Muhammad Rezal (2015) New attacks on RSA with modulus N = p2q using continued fractions. In: 3rd International Conference on Science & Engineering in Mathematics, Chemistry and Physics 2015 (ScieTech 2015), 31 Jan.-1 Feb. 2015, Bali, Indonesia. pp. 1-9.

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Abstract

In this paper, we propose two new attacks on RSA with modulus N = p2q using continued fractions. Our first attack is based on the RSA key equation ed - φ(N)k = 1 where φ(N) = p(p - 1)(q - 1). Assuming that and , we show that can be recovered among the convergents of the continued fraction expansion of . Our second attack is based on the equation eX - (N - (ap2 + bq2)) Y = Z where a,b are positive integers satisfying gcd(a,b) = 1, |ap2 - bq2| < N1/2 and ap2 + bq2 = N2/3+α with 0 < α < 1/3. Given the conditions , we show that one can factor N = p2q in polynomial time.

Item Type:Conference or Workshop Item (Paper)
Keyword:N = p2q; RSA; Continued fraction
Faculty or Institute:Faculty of Science
Institute for Mathematical Research
Publisher:IOP Publishing
DOI Number:10.1088/1742-6596/622/1/012019
Altmetrics:http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1088/1742-6596/622/1/012019
ID Code:43055
Deposited By: Nabilah Mustapa
Deposited On:17 May 2016 17:19
Last Modified:17 May 2016 17:19

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