Abstract
We consider an RSA variant with Modulus \(N=p^rq\). This variant is known as Prime Power RSA. In PKC 2004, May proved when decryption exponent \(d<N^{ \frac{r}{(r+1)^2}}\) or \(d< N^{\left( \frac{r-1}{r+1}\right) ^2}\), one can factor \(N\) in polynomial time. In this paper, we improve this bound when \(r \le 5\). We provide detailed experimental results to justify our claim.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.
This is a thoroughly revised and extended version of the paper “Small Secret Exponent Attack on RSA Variant with Modulus \(N=p^2q\)” that has been presented in WCC 2013, April 15–19, 2013, Bergen, Norway. In this paper, we consider the general case \(N=p^rq\) for \(r \ge 2\).
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Sarkar, S. Small secret exponent attack on RSA variant with modulus \(N=p^rq\) . Des. Codes Cryptogr. 73, 383–392 (2014). https://doi.org/10.1007/s10623-014-9928-6
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DOI: https://doi.org/10.1007/s10623-014-9928-6