Paper 2026/1137 Original: eprint.iacr.org/2026/1137 ↗
A Review of Lattice Attacks Applied to Two Types of RSA Variants
Abstract
In recent years, various RSA variants based on diverse algebraic structures have been proposed with the aim of enhancing its security. In this paper, we focus on type-A and type-B variants, which generalize RSA-type constructions over the ring of Gaussian integers modulo $N = pq$ and constructions based on the cubic Pell equation, respectively. First, we present a lattice-based method for finding, in polynomial time, solutions to the equation $xH(y)+cz\equiv 0 \bmod \beta$, where $H(y)$ is a monic polynomial, thereby generalizing previously established bounds. We then apply this method to factor the modulus in both type-A and type-B cryptosystems under multiple attack scenarios, such as partial key information attacks. Therefore, we provide certain bounds for the secret exponent under which these cryptosystems can be compromised.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2026-06-02: last updated
- 2026-06-02: published
- Short URL
- https://ia.cr/2026/1137
- License
- https://creativecommons.org/licenses/by-nc-sa/4.0/
BibTeX
@misc{cryptoeprint:2026/1137,
author = {Ramona Corbeanu and George Teseleanu},
title = {A Review of Lattice Attacks Applied to Two Types of RSA Variants},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1137},
year = {2026},
url = {https://eprint.iacr.org/2026/1137}
}