Paper 2025/875 Original: eprint.iacr.org/2025/875 ↗
Improved Cryptanalysis of an RSA Variant Based on Cubic Pell Curve
Abstract
In 2024, based on the cubic Pell curve, Nitaj and Seck proposed a variant of the RSA cryptosystem where the modulus is in the form $N=p^rq^s$, and the public key $e$ and private key $d$ satisfy the equation $ed\equiv 1\pmod{(p-1)^2(q-1)^2}$. They showed that $N$ can be factored when $d$ is less than a certain bound that depends on $r$ and $s$ in the situation $rs\geq 2$, which is not extendable to $r=s=1$. In this paper, we propose a cryptanalysis of this scheme in the situation $r=s=1$, and give an explicit bound for $d$ that makes the scheme insecure. The method is based on Coppersmith's method and lattice reduction.
Metadata
- Available format(s)
PDF- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- History
- 2025-05-16: last updated
- 2025-05-16: published
- Short URL
- https://ia.cr/2025/875
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2025/875,
author = {Mohammed Rahmani and Abderrahmane Nitaj},
title = {Improved Cryptanalysis of an RSA Variant Based on Cubic Pell Curve},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/875},
year = {2025},
url = {https://eprint.iacr.org/2025/875}
}