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We give a new algorithm to attack RSA with small private exponent, when some partial information of $p + q$ is given. The algorithm is a very simple modification of original Wiener’s attack with continued fractions, and allows us to factor $n$ whenever $d<n^{(1+\delta)/2}$ if we know a $δ$-fraction of the most significant bits of $n$. The algorithm is unconditional, which is not the case in previous improvements that use Coppersmith method. As a simple example, our algorithm can be applied to break any cryptosystem with modulus $n$ of $512$ bits and $d < n^{0.3}$, given an improvement in the original. attack of Wiener.
Note: Some typos removed.
BibTeX
@misc{cryptoeprint:2026/1295,
author = {Jorge Jimenez Urroz},
title = {A new attack to {RSA} with small private exponent and partial information.},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1295},
year = {2026},
url = {https://eprint.iacr.org/2026/1295}
}
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