New weak findings upon RSA modulo of type N = p2 q
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 < ▁((...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Research India Publications
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/53380/1/New%20weak%20findings%20upon%20RSA%20.pdf http://psasir.upm.edu.my/id/eprint/53380/ http://www.ripublication.com/Volume/gjpamv12n4.htm |
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| Institution: | Universiti Putra Malaysia |
| Language: | English |
| Summary: | 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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