<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we consider the RSA variant based on the key equation <italic>ed ≡ 1</italic> (mod <italic>φ</italic>(<italic>N</italic>)) where <italic>N = p<sup>r</sup>q, r ≥ 2</italic>. We show that if the secret exponent <italic>d</italic> is close to any multiple of the prime factor <italic>p</italic> or its powers, then it is possible to factor <italic>N</italic> in polynomial time in log <italic>N</italic>.</p></abstract>

In this paper, we consider the RSA variant based on the key equation ed ≡ 1 (mod φ(N)) where N = prq, r ≥ 2. We show that if the secret exponent d is close to any multiple of the prime factor p or its powers, then it is possible to factor N in polynomial time in log N.

Factoring multi power RSA moduli with a class of secret exponents

Laboratory of Mathematics, Cryptography and Mechanics, Fstm, University Hassan II of Casablanca, Morocco

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Factoring multi power RSA moduli with a class of secret exponents"}

In this paper, we consider the RSA variant based on the key equation ed ≡ 1 (mod φ(N)) where N = prq, r ≥ 2. We show that if the secret exponent d is close to...

Factoring multi power RSA moduli with a class of secret exponents

Published Online: Jan 22, 2016

Page range: 143 - 150

Received: Aug 08, 2015

Accepted: Oct 26, 2015

DOI: https://doi.org/10.1515/ausi-2015-0016

© 2015 Omar Akchiche et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.